Surface tension wikipedia

Surface tension wikipedia DEFAULT

Surface tension biomimetics

Surface tension is one of the areas of interest in biomimetics research. Surface tension forces will only begin to dominate gravitational forces below length scales on the order of the fluid's capillary length, which for water is about 2 millimeters. Because of this scaling, biomimetic devices that utilize surface tension will generally be very small, however there are many ways in which such devices could be used.

Applications[edit]

Coatings[edit]

Unitary roughness structure versus hierarchical structure

A lotus leaf is well known for its ability to repel water and self-clean. Yuan [1] and his colleagues fabricated a negative mold of alotus leaf from polydimethylsiloxane (PDMS) to capture the tiny hierarchical structures integral for the leaf's ability to repel water, known as the lotus effect. The lotus leaf's surface was then replicated by allowing a copper sheet to flow into the negative mold with the assistance of ferric chloride and pressure. The result was a lotus leaf-like surface inherent on the copper sheet. Static water contact angle measurements of the biomimetic surface were taken to be 132° after etching the copper and 153° after a stearic acid surface treatment to mimic the lotus leaf's waxy coating. A surface that mimics the lotus leaf could have numerous applications by providing water repellent outdoor gear.

Salvinia auriculata-lake-yercaud-salem-India

Various species of floating fern are able to sustain a liquid-solid barrier of air between the fern and the surrounding water when they are submerged. Like the lotus leaf, floating fern species have tiny hierarchical structures that prevent water from wetting the plant surface. Mayser and Barthlott[2] demonstrated this ability by submerging different species of the floating fern salvinia in water inside a pressure vessel to study how the air barrier between the leaf and surrounding water react to changes in pressure that would be similar to those experienced by the hull of a ship. Much other research is ongoing using these hierarchical structures in coatings on ship hulls to reduce viscous drag effects.

Biomedical[edit]

A lung is composed of many small sacks called alveoli that allow oxygen and carbon dioxide to diffuse in and out of the blood respectively as the blood is passed through small capillaries that surround these alveoli. Surface tension is exploited by alveoli by means of a surfactant that is produced by one of the cells and released to lower the surface tension of the fluid coating the inside of the alveoli to prevent these sacks from collapsing. Huh [3] and his fellow researchers created a lung mimic that replicated the function of native alveolar cells. An extracellular matrix of gel, human alveolar epithelial cells, and human pulmonary microvascular endothelial cells were cultured on a polydimethylsiloxane membrane that was bound in a flexible vacuum diaphragm. Pressurization cycles of the vacuum diaphragm, which simulated breathing, showed similar form and function to an actual lung. The type II cells were also shown to emit the same surfactant that lowered the surface tension of the fluid coating the lung mimic. This research will hopefully some day lead to the creation of lungs that could be grown for patients that need to have a transplant or repair performed.

Locomotion[edit]

Microvelia exploit surface tension by creating a surface tension gradient that propels them forward by releasing a surfactant behind them through a tongue-like protrusion. Biomimetic engineering was used in a creative and fun way to make and edible cocktail boat that mimicked the ability of microvelia to propel themselves on the surface of water by means of a phenomenon called the marangoni effect. Burton [4] and her colleagues used 3D printing to make small plastic boats that released different types of alcohol behind the boat to lower the surface tension and create a surface tension gradient that propelled each boat. This type of propulsion could one day be used to make sea vessels more efficient.

Actuators[edit]

Polypody (a fern) - the underside - geograph.org.uk - 974672
Image from page 395 of "The structure and development of mosses and ferns (Archegoniatae)" (1918) (14598564448)

Fern sporangia consist of hygroscopic ribs that protrude from a spine on the part of the plant that encapsulate spores in a sack (diagram). A capillary bridge is formed when water condenses on to the surface of these spines. When this water evaporates, surface tension forces between each rib cause the spine to retract and rip open the sack, spilling the spores. Borno [5] and her fellow researchers fabricated a biomimetic device from polydimethylsiloxane using standard photolithography techniques. The devices used the same hygroscopic ribs and spine that resemble fern sporangia. The researchers varied the dimensions and spacing of the features of the device and were able to fine-tune and predict movements of the device as a whole in hopes of using a similar device as a microactuator that can perform functions using free energy from a humid atmosphere.

Leaf Beetle (Gastrophysa viridula) - male

A leaf beetle has an incredible ability to adhere to dry surfaces by using numerous capillary bridges between the tiny hair-like setae on its feet. Vogel and Steen [6] noted this and designed and constructed a switchable wet adhesion mechanism that mimics this ability. They used standard photolithography techniques to fabricate a switchable adhesion gripper that used a pump driven by electro-osmosis to create many capillary bridges that would hold on to just about any surface. The leaf beetle can also reverse this effect by trapping air bubbles between its setae to walk on wet surfaces or under water. This effect was demonstrated by Hosoda and Gorb [7] when they constructed a biomimetic surface that could adhere objects to surfaces under water. Using this technology could help to create autonomous robots that would be able to explore treacherous terrain that is otherwise too dangerous to explore.

Water strider, from Kerala

Various life forms found in nature exploit surface tension in different ways. Hu [8] and his colleagues looked at a few examples to create devices that mimic the abilities of their natural counterparts to walk on water, jump off the liquid interface, and climb menisci. Two such devices were a rendition of the water strider. Both devices mimicked the form and function of a water strider by incorporating a rowing motion of one pair of legs to propel the device, however one was powered with elastic energy and the other was powered by electrical energy. This research compared the various biomimetic devices to their natural counterparts by showing the difference between many physical and dimensionless parameters. This research could one day lead to small, energy efficient water walking robots that could be used to clean up spills in waterways.

Environment[edit]

The Stenocara beetle, a native of the Namib Desert has a unique structure on its body that allows it to capture water from a humid atmosphere. In the Namib Desert, rain is not a very common occurrence, but on some mornings a dense fog will roll over the desert. The stenocara beetle uses tiny raised hydrophilic spots on its hydrophobic body to collect water droplets from the fog. Once these droplets are large enough, they can detach from these spots and roll down the beetle's back and into its mouth. Garrod et al.[9] has demonstrated a biomimetic surface that was created using standard photolithography and plasma etching to create hydrophilic spots on a hydrophobic substrate for water collection. The optimal sizing and spacing of these spots that allowed the most water to be collected was similar to the spacing of the spots on the body of the stenocara beetle. Currently, this surface technology is being studied to implement as a coating on the inside of a water bottle the will allow the water bottle to self fill if left open in a humid environment, and could help to provide aid where water is scarce.

References[edit]

  1. ^Yuan, Zhiqing (15 November 2013). "A novel fabrication of a superhydrophobic surface with highly similar hierarchical structure of the lotus leaf on a copper sheet". Applied Surface Science. 285: 205–210. Bibcode:2013ApSS..285..205Y. doi:10.1016/j.apsusc.2013.08.037.
  2. ^Mayser, Matthias (12 June 2014). "Layers of Air in the Water beneath the Floating Fern Salvinia are Exposed to Fluctuations in Pressure". Integrative and Comparative Biology. 56 (5): 1000–7000. doi:10.1093/icb/icu072. PMID 24925548.
  3. ^Huh, Dongeun (25 June 2010). "Reconstituting Organ-Level Lung Functions on a Chip". Science. 328 (5986): 1662–1668. Bibcode:2010Sci...328.1662H. doi:10.1126/science.1188302. PMC 8335790. PMID 20576885.
  4. ^Burton, Lisa (22 May 2014). "The Cocktail Boat". Integrative and Comparative Biology. 54 (6): 969–973. doi:10.1093/icb/icu052. PMID 24853727.
  5. ^Borno, Ruba (21 September 2006). "Transpiration actuation: the design, fabrication and characterization of biomimetic microactuators driven by the surface tension of water". Journal of Micromechanics and Microengineering. 16 (11): 2375–2383. Bibcode:2006JMiMi..16.2375B. doi:10.1088/0960-1317/16/11/018. hdl:2027.42/49048.
  6. ^Vogel, Michael (22 December 2009). "Capillarity-based switchable adhesion". Proceedings of the National Academy of Sciences. 107 (8): 3377–3381. doi:10.1073/pnas.0914720107. PMC 2840443. PMID 20133725.
  7. ^Hosoda, N. "How a leaf beetle walks underwater". Science Daily.
  8. ^Hu, David (1 June 2007). "Water-walking devices". Experiments in Fluids. 43 (5): 769–778. Bibcode:2007ExFl...43..769H. doi:10.1007/s00348-007-0339-6. S2CID 12754027.
  9. ^Garrod, R. (4 October 2006). "Mimicking a Stenocara Beetle's Back for Microcondensation Using Plasmachemical Patterned Superhydrophobic-Superhydrophilic Surfaces". Langmuir. 23 (2): 689–693. doi:10.1021/la0610856. PMID 17209621.
Sours: https://en.wikipedia.org/wiki/Surface_tension_biomimetics

Surface tension

Surface tension is an effect where the surface of a liquid is strong. The surface can hold up a weight, and the surface of a water droplet holds the droplet together, in a ball shape. Some small things can float on a surface because of surface tension, even though they normally could not float. Some insects (e.g. water striders) can run on the surface of water because of this. This property is caused by the molecules in the liquid being attracted to each other (cohesion), and is responsible for many of the behaviors of liquids.

Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.

In materials science, surface tension is used for either surface stress or surface free energy.

Causes[change | change source]

Diagram of the forces on molecules in liquid
Surface tension prevents the paper clip from submerging.

The cohesive forces among the liquid molecules cause surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure and forces liquid surfaces to contract to the minimal area.

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Another way to view it is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules). So, the boundary molecules have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.[1]

As a result of surface area minimization, a surface will assume the smoothest shape it can.[note 1] Any curvature in the surface shape results in greater area and a higher energy. So, the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

Effects in everyday life[change | change source]

Water[change | change source]

Studying water shows several effects of surface tension:

A. Rain water forms beads on the surface of a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

B. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.[2]

C. Objects denser than water still float when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension.[1] For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area.[3]

D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its physics are the same.

E. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol. It is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

  • A. Water beading on a leaf

  • B. Water dripping from a tap

  • D.Lava lamp with interaction between dissimilar liquids; water and liquid wax

Surfactants[change | change source]

Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

  • Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.
  • Emulsions are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Basic physics[change | change source]

Two definitions[change | change source]

Diagram shows, in cross-section, a needle floating on the surface of water. Its weight, Fw, depresses the surface, and is balanced by the surface tension forces on either side, Fs, which are each parallel to the water's surface at the points where it contacts the needle. Notice that the horizontal components of the two Fsarrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up[1]to balance Fw.

Surface tension, represented by the symbol γ is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2{\displaystyle \scriptstyle \gamma }L (the factor of 2 is because the soap film has two sides, hence two surfaces).[4] Surface tension is therefore measured in forces per unit length. Its SI unit is newton per meter but the cgs unit of dyne per cm is also used.[5] One dyn/cm corresponds to 0.001 N/m.

An equivalent definition, one that is useful in thermodynamics, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, {\displaystyle \scriptstyle \gamma }δA, is needed.[4] This work is stored as potential energy. Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume.

The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.[4]

Surface curvature and pressure[change | change source]

Surface tension forces acting on a tiny (differential) patch of surface. δθxand δθyindicate the amount of bend over the dimensions of the patch. Balancing the tension forces with pressure leads to the Young–Laplace equation

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation:[6]

{\displaystyle \Delta p\ =\ \gamma \left({\frac {1}{R_{x}}}+{\frac {1}{R_{y}}}\right)}

where:

  • Δp is the pressure difference.
  • {\displaystyle \scriptstyle \gamma } is surface tension.
  • Rx and Ry are radii of curvature in each of the axes that are parallel to the surface.

The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalization).

Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension. (Another example is the shape of the impressions that a water strider's feet make on the surface of a pond).

The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

Δp for water drops of different radii at STP
Droplet radius 1 mm 0.1 mm 1 μm10 nm
Δp (atm)0.00140.01441.436143.6

Liquid surface[change | change source]

It is hard to find the shape of the minimal surface bounded by some arbitrary shaped frame using just mathematics. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.[4][7]

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles[change | change source]

Main article: Contact angle

The surface of any liquid is an interface between that liquid and some other medium.[note 2] The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater than) its surface tension with the walls of a container. Where the two surfaces meet, the geometry will balance all forces.[4][6]

Forces at contact point shown for contact angle greater than 90° (left) and less than 90° (right)

Where the two surfaces meet, they form a contact angle, {\displaystyle \scriptstyle \theta }, which is the angle the tangent to the surface makes with the solid surface. The diagram to the right shows two examples. Tension forces are shown for the liquid-air interface, the liquid-solid interface, and the solid-air interface. The example on the left is where the difference between the liquid-solid and solid-air surface tension, {\displaystyle \scriptstyle \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }}, is less than the liquid-air surface tension, {\displaystyle \scriptstyle \gamma _{\mathrm {la} }}, but is still positive, that is

{\displaystyle \gamma _{\mathrm {la} }\ >\ \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }\ >\ 0}

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of {\displaystyle \scriptstyle f_{\mathrm {la} }} is canceled by the adhesive force, {\displaystyle \scriptstyle f_{\mathrm {A} }}.[4]

{\displaystyle f_{\mathrm {A} }\ =\ f_{\mathrm {la} }\sin \theta }

The more important balance of forces, though, is in the vertical direction. The vertical component of {\displaystyle \scriptstyle f_{\mathrm {la} }} must exactly cancel the force, {\displaystyle \scriptstyle f_{\mathrm {ls} }}.[4]

{\displaystyle f_{\mathrm {ls} }-f_{\mathrm {sa} }\ =\ -f_{\mathrm {la} }\cos \theta }

Since the forces are in direct proportion to their respective surface tensions, we also have:[6]

{\displaystyle \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }\ =\ -\gamma _{\mathrm {la} }\cos \theta }

where

This means that although the difference between the liquid-solid and solid-air surface tension, {\displaystyle \scriptstyle \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }}, is difficult to measure directly, it can be inferred from the liquid-air surface tension, {\displaystyle \scriptstyle \gamma _{\mathrm {la} }}, and the equilibrium contact angle, {\displaystyle \scriptstyle \theta }, which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid-solid/solid-air surface tension difference must be negative:

{\displaystyle \gamma _{\mathrm {la} }\ >\ 0\ >\ \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }}

Special contact angles[change | change source]

Observe that in the special case of a water-silver interface where the contact angle is equal to 90°, the liquid-solid/solid-air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this.[6] Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.

{\displaystyle \gamma _{\mathrm {la} }\ =\ \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }\ >\ 0\qquad \theta \ =\ 180^{\circ }}

Methods of measurement[change | change source]

Surface tension can be measured using the pendant drop method on a goniometer.

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed.

  • Du Noüy Ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.[8]
  • Du Noüy-Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds. First commercial multichannel tensiometers [CMCeeker] were recently built based on this principle.
  • Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.[9]
  • Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
  • Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For details, see Drop.[9]
  • Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.
  • Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.[10]
  • Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed below.[11]
  • Stalagmometric method: A method of weighting and reading a drop of liquid.
  • Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).[12]
  • Vibrational frequency of levitated drops: The surface tension of superfluid 4He has been measured by studying the natural frequency of vibrational oscillations of drops held in the air by magnetics. This value is estimated to be 0.375 dyn/cm at T = 0° K.[13]

Effects[change | change source]

Liquid in a vertical tube[change | change source]

Main article: Capillary action

Diagram of a mercury barometer

An old style mercurybarometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

Illustration of capillary rise and fall. Red=contact angle less than 90°; blue=contact angle greater than 90°

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height the column is lifted to is given by:[4]

{\displaystyle h\ =\ {\frac {2\gamma _{\mathrm {la} }\cos \theta }{\rho gr}}}

where

Puddles on a surface[change | change source]

Profile curve of the edge of a puddle where the contact angle is 180°. The curve is given by the formula:[6]{\displaystyle \scriptstyle x-x_{0}\ =\ {\frac {1}{2}}H\cosh ^{-1}\left({\frac {H}{h}}\right)-H{\sqrt {1-{\frac {h^{2}}{H^{2}}}}}}where {\displaystyle \scriptstyle H\ =\ 2{\sqrt {\frac {\gamma }{g\rho }}}}
Small puddles of water on a smooth clean surface have perceptible thickness.

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimeter thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only if the liquid does not adhere to the flat surface material. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:[6]

{\displaystyle h\ =\ 2{\sqrt {\frac {\gamma }{g\rho }}}}

where

Illustration of how lower contact angle leads to reduction of puddle depth

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:[6]

{\displaystyle h\ =\ {\sqrt {\frac {2\gamma _{\mathrm {la} }\left(1-\cos \theta \right)}{g\rho }}}.}

For mercury on glass, γHg = 487 dyn/cm, ρHg = 13.5 g/cm3 and θ = 140°, which gives hHg = 0.36 cm. For water on paraffin at 25 °C, γ = 72 dyn/cm, ρ = 1.0 g/cm3, and θ = 107° which gives hH2O = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops[change | change source]

Intermediate stage of a jet breaking into drops. Radii of curvature in the axial direction are shown. Equation for the radius of the stream is {\displaystyle \scriptstyle R\left(z\right)=R_{0}+A_{k}\cos \left(kz\right)}, where {\displaystyle \scriptstyle R_{0}}is the radius of the unperturbed stream, {\displaystyle \scriptstyle A_{k}}is the amplitude of the perturbation, {\displaystyle \scriptstyle z}is distance along the axis of the stream, and {\displaystyle \scriptstyle k}is the wave number

Main article: Plateau–Rayleigh instability

In day-to-day life we all observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability,[6] which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Data table[change | change source]

Gallery of effects[change | change source]

  • Breakup of a moving sheet of water bouncing off of a spoon.

  • Photo of flowing water adhering to a hand. Surface tension creates the sheet of water between the flow and the hand.

  • Surface tension prevents a coin from sinking: the coin is indisputably denser than water, so it must be displacing a volume greater than its own for buoyancy to balance mass.

  • A daisy. The entirety of the flower lies below the level of the (undisturbed) free surface. The water rises smoothly around its edge. Surface tension prevents water filling the air between the petals and possibly submerging the flower.

  • A metal paper clip floats on water. Several can usually be carefully added without overflow of water.

  • An aluminium coin floats on the surface of the water at 10 °C. Any extra weight would drop the coin to the bottom.

Notes[change | change source]

  1. ↑The mathematical proof that "smooth" shapes minimize surface area relies on use of the Euler–Lagrange equation.
  2. ↑In a mercury barometer, the upper liquid surface is an interface between the liquid and a vacuum containing some molecules of evaporated liquid.

References[change | change source]

  1. 1.01.11.2White, Harvey E. (1948). Modern College Physics. van Nostrand. ISBN .
  2. John W. M. Bush (May 2004). "MIT Lecture Notes on Surface Tension, lecture 5"(PDF). Massachusetts Institute of Technology. Retrieved April 1, 2007.
  3. John W.M. Bush (May 2004). "MIT Lecture Notes on Surface Tension, lecture 3"(PDF). Massachusetts Institute of Technology. Retrieved April 1, 2007.
  4. 4.04.14.24.34.44.54.64.74.84.9Sears, Francis Weston; Zemanski, Mark W. University Physics 2nd ed. Addison Wesley 1955
  5. John W.M. Bush (April 2004). "MIT Lecture Notes on Surface Tension, lecture 1"(PDF). Massachusetts Institute of Technology. Retrieved April 1, 2007.
  6. 6.06.16.26.36.46.56.66.7Pierre-Gilles de Gennes; Françoise Brochard-Wyart; David Quéré (2002). Capillary and Wetting Phenomena—Drops, Bubbles, Pearls, Waves. Alex Reisinger. Springer. ISBN .
  7. Aaronson, Scott. "SIGACT News".
  8. "Surface Tension by the Ring Method (Du Nouy Method)"(PDF). PHYWE. Retrieved 2007-09-08.
  9. 9.09.1"Surface and Interfacial Tension". Langmuir-Blodgett Instruments. Archived from the original on 2007-10-12. Retrieved 2007-09-08.
  10. "Surfacants at interfaces"(PDF). lauda.de. Archived from the original(PDF) on 2007-09-27. Retrieved 2007-09-08.
  11. Calvert, James B. "Surface Tension (physics lecture notes)". University of Denver. Retrieved 2007-09-08.
  12. "Sessile Drop Method". Dataphysics. Archived from the original on August 8, 2007. Retrieved 2007-09-08.
  13. Vicente, C.; Yao, W.; Maris, H.; Seidel, G. (2002). "Surface tension of liquid 4He as measured using the vibration modes of a levitated drop". Physical Review B. 66 (21). Bibcode:2002PhRvB..66u4504V. doi:10.1103/PhysRevB.66.214504.
  14. Lange's Handbook of Chemistry (1967) 10th ed. pp 1661–1665 ISBN 0070161909 (11th ed.)

Other websites[change | change source]

  • On surface tension and interesting real-world cases
  • MIT Lecture Notes on Surface Tension
  • Surface Tensions of Various Liquids
  • Calculation of temperature-dependent surface tensions for some common components
  • Surface Tension Calculator For Aqueous Solutions Containing the Ions H+, NH4+, Na+, K+, Mg2+, Ca2+, SO42–, NO3, Cl, CO32–, Br and OH.
  • The Bubble Wall[permanent dead link] (Audio slideshow from the National High Magnetic Field Laboratory explaining cohesion, surface tension and hydrogen bonds)
Sours: https://simple.wikipedia.org/wiki/Surface_tension
  1. Viking wedding gown
  2. Angular 11 upgrade
  3. 686 snow gear
  4. Planets embroidery designs

Surface tension

In physics, surface tension is a force present within the surface layer of a liquid that causes the layer to behave as an elastic sheet. It is the force that supports insects that walk on water, for example.

Surface tension is caused by the attraction between the molecules of the liquid. In the bulk of the liquid each molecule is pulled equally in all directions by neighbouring molecules, resulting in a net force of zero. At the surface of the liquid, the molecules are pulled inwards by other molecules deeper inside the liquid, but there are no liquid molecules on the outside to balance these forces, so the surface molecules are subject to a net inward force. There may be a small outward attraction caused by air molecules, but air is much less dense than the liquid, so this force is negligible.

Surface tension is measured in newton per metre (Nm-1), is represented by the symbol γ and is defined as the force along a line of unit length perpendicular to the surface.

Dimensional analysis shows that the units of surface tension (Nm-1) are equivalent to joules per square metre (Jm-2). This means that surface tension can also be considered as surface energy. If a surface with surface tension γ is expanded by a unit area, then the increase in the surface's stored energy is also equal to γ.

wikipedia.org dumped 2003-03-17 with terodump

Sours: http://69.63.68.22/archive/doc/wikipedia/wikipedia-terodump-0.1/tero-dump/wikipedia/su/Surface_tension.html
Surface tension Wikipedia

Surface tension

Tendency of a liquid surface to shrink to reduce surface area

For the short story by James Blish, see Surface Tension (short story).

Surface tension experimental demonstration with soap

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged.

At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion).[citation needed][further explanation needed]

There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract.[1][2] Second is a tangential force parallel to the surface of the liquid.[2] This tangential force (per unit length) is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the membrane while surface tension is an inherent property of the liquidair or liquidvapour interface.[3]

Because of the relatively high attraction of water molecules to each other through a web of hydrogen bonds, water has a higher surface tension (72.8 millinewtons (mN) per meter at 20 °C) than most other liquids. Surface tension is an important factor in the phenomenon of capillarity.

Surface tension has the dimension of force per unit length, or of energy per unit area.[3] The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids.

In materials science, surface tension is used for either surface stress or surface energy.

Causes[edit]

Diagram of the cohesive forces on molecules of a liquid

Due to the cohesive forces a molecule is pulled equally in every direction by neighbouring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have the same molecules on all sides of them and therefore are pulled inward. This creates some internal pressure and forces liquid surfaces to contract to the minimum area.[1]

There is also a tension parallel to the surface at the liquid-air interface which will resist an external force, due to the cohesive nature of water molecules.[1][2]

The forces of attraction acting between the molecules of same type are called cohesive forces while those acting between the molecules of different types are called adhesive forces. The balance between the cohesion of the liquid and its adhesion to the material of the container determines the degree of wetting, the contact angle and the shape of meniscus. When cohesion dominates (specifically, adhesion energy is less than half of cohesion energy) the wetting is low and the meniscus is convex at a vertical wall (as for mercury in a glass container). On the other hand, when adhesion dominates (adhesion energy more than half of cohesion energy) the wetting is high and the similar meniscus is concave (as in water in a glass).

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the imbalance in cohesive forces of the surface layer. In the absence of other forces, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Water droplet lying on a damask. Surface tension is high enough to prevent floating below the textile

Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone. The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized number of boundary molecules results in a minimal surface area.[4] As a result of surface area minimization, a surface will assume the smoothest shape it can (mathematical proof that "smooth" shapes minimize surface area relies on use of the Euler–Lagrange equation). Since any curvature in the surface shape results in greater area, a higher energy will also result.

Effects of surface tension[edit]

Water[edit]

Several effects of surface tension can be seen with ordinary water:

  1. Beading of rain water on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.
  2. Formation of drops occurs when a mass of liquid is stretched. The animation (below) shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer keep the drop linked to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.[5]
  3. Flotation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension.[4] For example, water striders use surface tension to walk on the surface of a pond in the following way. The nonwettability of the water strider's leg means there is no attraction between molecules of the leg and molecules of the water, so when the leg pushes down on the water, the surface tension of the water only tries to recover its flatness from its deformation due to the leg. This behavior of the water pushes the water strider upward so it can stand on the surface of the water as long as its mass is small enough that the water can support it. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area[6] and tendency of minimization of surface curvature (so area) of the water pushes the insect's feet upward.
  4. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its chemistry is the same.
  5. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.
  • A. Water beading on a leaf

  • B. Water dripping from a tap

  • C.Water striders stay at the top of liquid because of surface tension

  • D.Lava lamp with interaction between dissimilar liquids: water and liquid wax

Surfactants[edit]

Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

  • Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Note that surfactants actually reduce the surface tension of water by a factor of three or more.
  • Emulsions are a type of colloid in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Physics[edit]

Physical units[edit]

Surface tension, represented by the symbol γ (alternatively σ or T), is measured in force per unit length. Its SI unit is newton per meter but the cgs unit of dyne per centimeter is also used. For example,[7]

{\displaystyle \gamma =1~\mathrm {\frac {dyn}{cm}} =1~\mathrm {\frac {erg}{cm^{2}}} =1~\mathrm {\frac {10^{-7}\,m\cdot N}{10^{-4}\,m^{2}}} =0.001~\mathrm {\frac {N}{m}} =0.001~\mathrm {\frac {J}{m^{2}}} .}

Surface area growth[edit]

This diagram illustrates the force necessary to increase the surface area. This force is proportional to the surface tension.

Surface tension can be defined in terms of force or energy.

In terms of force[edit]

Surface tension γ of a liquid is the force per unit length. In the illustration on the right, the rectangular frame, composed of three unmovable sides (black) that form a "U" shape, and a fourth movable side (blue) that can slide to the right. Surface tension will pull the blue bar to the left; the force F required to hold the movable side is proportional to the length L of the immobile side. Thus the ratio F/L depends only on the intrinsic properties of the liquid (composition, temperature, etc.), not on its geometry. For example, if the frame had a more complicated shape, the ratio F/L, with L the length of the movable side and F the force required to stop it from sliding, is found to be the same for all shapes. We therefore define the surface tension as

{\displaystyle \gamma ={\frac {1}{2}}{\frac {F}{L}}.}

The reason for the 1/2 is that the film has two sides (two surfaces), each of which contributes equally to the force; so the force contributed by a single side is γL = F/2.

In terms of energy[edit]

Surface tension γ of a liquid is the ratio of the change in the energy of the liquid to the change in the surface area of the liquid (that led to the change in energy). This can be easily related to the previous definition in terms of force:[8] if F is the force required to stop the side from starting to slide, then this is also the force that would keep the side in the state of sliding at a constant speed (by Newton's Second Law). But if the side is moving to the right (in the direction the force is applied), then the surface area of the stretched liquid is increasing while the applied force is doing work on the liquid. This means that increasing the surface area increases the energy of the film. The work done by the force F in moving the side by distance Δx is W = FΔx; at the same time the total area of the film increases by ΔA = 2LΔx (the factor of 2 is here because the liquid has two sides, two surfaces). Thus, multiplying both the numerator and the denominator of γ = 1/2F/L by Δx, we get

\gamma=\frac{F}{2L}=\frac{F \Delta x}{2 L \Delta x}=\frac{W}{\Delta A} .

This work W is, by the usual arguments, interpreted as being stored as potential energy. Consequently, surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume. The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.[9]

Surface curvature and pressure[edit]

Surface tension forces acting on a tiny (differential) patch of surface. δθxand δθyindicate the amount of bend over the dimensions of the patch. Balancing the tension forces with pressure leads to the Young–Laplace equation

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation:[10]

{\displaystyle \Delta p=\gamma \left({\frac {1}{R_{x}}}+{\frac {1}{R_{y}}}\right)}

where:

The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalisation). Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a water strider's feet make on the surface of a pond). The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

Droplet radius 1 mm 0.1 mm 1 μm10 nm
Δp (atm) 0.0014 0.0144 1.436 143.6

Floating objects[edit]

Cross-section of a needle floating on the surface of water. Fwis the weight and Fsare surface tension resultant forces.

When an object is placed on a liquid, its weight Fw depresses the surface, and if surface tension and downward force becomes equal than is balanced by the surface tension forces on either side Fs, which are each parallel to the water's surface at the points where it contacts the object. Notice that small movement in the body may cause the object to sink. As the angle of contact decreases, surface tension decreases. The horizontal components of the two Fs arrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up[4] to balance Fw. The object's surface must not be wettable for this to happen, and its weight must be low enough for the surface tension to support it. If m denotes the mass of the needle and g acceleration due to gravity, we have

{\displaystyle F_{\mathrm {w} }=2F_{\mathrm {s} }\sin \theta \quad \Leftrightarrow \quad mg=2\gamma L\sin \theta }

Liquid surface[edit]

To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.[9][12]

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young–Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles[edit]

Main article: Contact angle

The surface of any liquid is an interface between that liquid and some other medium.[note 1] The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater) than its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.[9][10]

Forces at contact point shown for contact angle greater than 90° (left) and less than 90° (right)

Where the two surfaces meet, they form a contact angle, θ, which is the angle the tangent to the surface makes with the solid surface. Note that the angle is measured through the liquid, as shown in the diagrams above. The diagram to the right shows two examples. Tension forces are shown for the liquid–air interface, the liquid–solid interface, and the solid–air interface. The example on the left is where the difference between the liquid–solid and solid–air surface tension, γlsγsa, is less than the liquid–air surface tension, γla, but is nevertheless positive, that is

{\displaystyle \gamma _{\mathrm {la} }>\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }>0}

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of fla is canceled by the adhesive force, fA.[9]

{\displaystyle f_{\mathrm {A} }=f_{\mathrm {la} }\sin \theta }

The more telling balance of forces, though, is in the vertical direction. The vertical component of fla must exactly cancel the difference of the forces along the solid surface, flsfsa.[9]

{\displaystyle f_{\mathrm {ls} }-f_{\mathrm {sa} }=-f_{\mathrm {la} }\cos \theta }

Since the forces are in direct proportion to their respective surface tensions, we also have:[10]

{\displaystyle \gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }=-\gamma _{\mathrm {la} }\cos \theta }

where

  • γls is the liquid–solid surface tension,
  • γla is the liquid–air surface tension,
  • γsa is the solid–air surface tension,
  • θ is the contact angle, where a concave meniscus has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.[9]

This means that although the difference between the liquid–solid and solid–air surface tension, γlsγsa, is difficult to measure directly, it can be inferred from the liquid–air surface tension, γla, and the equilibrium contact angle, θ, which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid–solid/solid–air surface tension difference must be negative:

{\displaystyle \gamma _{\mathrm {la} }>0>\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }}

Special contact angles[edit]

Observe that in the special case of a water–silver interface where the contact angle is equal to 90°, the liquid–solid/solid–air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this.[10] Contact angle of 180° occurs when the liquid–solid surface tension is exactly equal to the liquid–air surface tension.

{\displaystyle \gamma _{\mathrm {la} }=\gamma _{\mathrm {ls} }-\gamma _{\mathrm {sa} }>0\qquad \theta =180^{\circ }}

Methods of measurement[edit]

Force tensiometer.
Force tensiometer is using Du Noüy ring method and Wilhelmy plate method.

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed. An instrument that measures surface tension is called tensiometer.

  • Du Noüy ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.[13]
  • Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.[14]
  • Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
  • Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For pendant drops the maximum diameter and the ratio between this parameter and the diameter at the distance of the maximum diameter from the drop apex has been used to evaluate the size and shape parameters in order to determine surface tension.[14]
  • Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.
  • Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.[15]
  • Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed below.[16]
    Surface tension can be measured using the pendant drop method on a goniometer.
  • Stalagmometric method: A method of weighting and reading a drop of liquid.
  • Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).[17]
  • Du Noüy–Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds.
  • Vibrational frequency of levitated drops: The natural frequency of vibrational oscillations of magnetically levitated drops has been used to measure the surface tension of superfluid 4He. This value is estimated to be 0.375 dyn/cm at T = 0 K.[18]
  • Resonant oscillations of spherical and hemispherical liquid drop: The technique is based on measuring the resonant frequency of spherical and hemispherical pendant droplets driven in oscillations by a modulated electric field. The surface tension and viscosity can be evaluated from the obtained resonant curves.[19][20][21]
  • Drop-bounce method: This method is based on aerodynamic levitation with a split-able nozzle design. After dropping a stably levitated droplet onto a platform, the sample deforms and bounces back, oscillating in mid-air as it tries to minimize its surface area. Through this oscillation behavior, the liquid's surface tension and viscosity can be measured. [22]
  • By smartphone: Some smartphones can be used to measure the surface tension of a transparent liquid. The method is based on measuring the wavelength of capillary waves of known frequency. The smartphone is placed on top of a cup with the liquid. Then smartphone's vibro-motor excites (through the cup) capillary ripples on the surface of the liquid, which are captured by smartphone's camera.[23]

Effects[edit]

Liquid in a vertical tube[edit]

Main article: Capillary action

An old style mercurybarometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire cross-section of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere to glass at all. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube was made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

Illustration of capillary rise and fall. Red=contact angle less than 90°; blue=contact angle greater than 90°

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height to which the column is lifted is given by Jurin's law:[9]

{\displaystyle h={\frac {2\gamma _{\mathrm {la} }\cos \theta }{\rho gr}}}

where

  • h is the height the liquid is lifted,
  • γla is the liquid–air surface tension,
  • ρ is the density of the liquid,
  • r is the radius of the capillary,
  • g is the acceleration due to gravity,
  • θ is the angle of contact described above. If θ is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.

Puddles on a surface[edit]

Profile curve of the edge of a puddle where the contact angle is 180°. The curve is given by the formula:[10]
{\displaystyle x-x_{0}={\frac {1}{2}}H\cosh ^{-1}\left({\frac {H}{h}}\right)-H{\sqrt {1-{\frac {h^{2}}{H^{2}}}}}}
where {\displaystyle H=2{\sqrt {\frac {\gamma }{g\rho }}}}
Small puddles of water on a smooth clean surface have perceptible thickness.

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimetre thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result of the compromise is a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only on a surface made of a substance to which water does not adhere. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:[10]

{\displaystyle h=2{\sqrt {\frac {\gamma }{g\rho }}}}

where

  • h is the depth of the puddle in centimeters or meters.
  • γ is the surface tension of the liquid in dynes per centimeter or newtons per meter.
  • g is the acceleration due to gravity and is equal to 980 cm/s2 or 9.8 m/s2
  • ρ is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter
Illustration of how lower contact angle leads to reduction of puddle depth

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:[10]

{\displaystyle h={\sqrt {\frac {2\gamma _{\mathrm {la} }\left(1-\cos \theta \right)}{g\rho }}}.}

For mercury on glass, γHg = 487 dyn/cm, ρHg = 13.5 g/cm3 and θ = 140°, which gives hHg = 0.36 cm. For water on paraffin at 25 °C, γ = 72 dyn/cm, ρ = 1.0 g/cm3, and θ = 107° which gives hH2O = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops[edit]

Breakup of an elongated stream of water into droplets due to surface tension.

Main article: Plateau–Rayleigh instability

In day-to-day life all of us observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability,[10] which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Thermodynamics[edit]

Thermodynamic theories of surface tension[edit]

J.W. Gibbs developed the thermodynamic theory of capillarity based on the idea of surfaces of discontinuity.[24] Gibbs considered the case of a sharp mathematical surface being placed somewhere within the microscopically fuzzy physical interface that exists between two homogeneous substances. Realizing that the exact choice of the surface's location was somewhat arbitrary, he left it flexible. Since the interface exists in thermal and chemical equilibrium with the substances around it (having temperature T and chemical potentials μi), Gibbs considered the case where the surface may have excess energy, excess entropy, and excess particles, finding the natural free energy function in this case to be {\displaystyle U-TS-\mu _{1}N_{1}-\mu _{2}N_{2}\cdots }, a quantity later named as the grand potential and given the symbol \Omega .

Gibbs' placement of a precise mathematical surface in a fuzzy physical interface.

Considering a given subvolume V containing a surface of discontinuity, the volume is divided by the mathematical surface into two parts A and B, with volumes {\displaystyle V_{\rm {A}}} and {\displaystyle V_{\rm {B}}}, with {\displaystyle V=V_{\rm {A}}+V_{\rm {B}}} exactly. Now, if the two parts A and B were homogeneous fluids (with pressures {\displaystyle p_{\rm {A}}}, {\displaystyle p_{\rm {B}}}) and remained perfectly homogeneous right up to the mathematical boundary, without any surface effects, the total grand potential of this volume would be simply {\displaystyle -p_{\rm {A}}V_{\rm {A}}-p_{\rm {B}}V_{\rm {B}}}. The surface effects of interest are a modification to this, and they can be all collected into a surface free energy term {\displaystyle \Omega _{\rm {S}}} so the total grand potential of the volume becomes:

{\displaystyle \Omega =-p_{\rm {A}}V_{\rm {A}}-p_{\rm {B}}V_{\rm {B}}+\Omega _{\rm {S}}.}

For sufficiently macroscopic and gently curved surfaces, the surface free energy must simply be proportional to the surface area:[24][25]

{\displaystyle \Omega _{\rm {S}}=\gamma A,}

for surface tension \gamma and surface area A.

As stated above, this implies the mechanical work needed to increase a surface area A is dW = γ dA, assuming the volumes on each side do not change. Thermodynamics requires that for systems held at constant chemical potential and temperature, all spontaneous changes of state are accompanied by a decrease in this free energy \Omega , that is, an increase in total entropy taking into account the possible movement of energy and particles from the surface into the surrounding fluids. From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous, provided it is not coupled to any other energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.

Gibbs and other scientists have wrestled with the arbitrariness in the exact microscopic placement of the surface.[26] For microscopic surfaces with very tight curvatures, it is not correct to assume the surface tension is independent of size, and topics like the Tolman length come into play. For a macroscopic sized surface (and planar surfaces), the surface placement does not have a significant effect on γ however it does have a very strong effect on the values of the surface entropy, surface excess mass densities, and surface internal energy,[24]: 237  which are the partial derivatives of the surface tension function {\displaystyle \gamma (T,\mu _{1},\mu _{2},\cdots )}.

Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension):[24]: 315  the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction between forming and stretching because the fluids and the surface completely replenish their nature when the surface is stretched. For a solid, stretching the surface, even elastically, results in a fundamentally changed surface. Further, the surface stress on a solid is a directional quantity (a stress tensor) while surface energy is scalar.

Fifteen years after Gibbs, J.D. van der Waals developed the theory of capillarity effects based on the hypothesis of a continuous variation of density.[27] He added to the energy density the term {\displaystyle c(\nabla \rho )^{2},} where c is the capillarity coefficient and ρ is the density. For the multiphase equilibria, the results of the van der Waals approach practically coincide with the Gibbs formulae, but for modelling of the dynamics of phase transitions the van der Waals approach is much more convenient.[28][29] The van der Waals capillarity energy is now widely used in the phase field models of multiphase flows. Such terms are also discovered in the dynamics of non-equilibrium gases.[30]

Thermodynamics of bubbles[edit]

The pressure inside an ideal spherical bubble can be derived from thermodynamic free energy considerations.[25] The above free energy can be written as:

{\displaystyle \Omega =-\Delta PV_{\rm {A}}-p_{\rm {B}}V+\gamma A}

where {\displaystyle \Delta P=p_{\rm {A}}-p_{\rm {B}}} is the pressure difference between the inside (A) and outside (B) of the bubble, and {\displaystyle V_{\rm {A}}} is the bubble volume. In equilibrium, = 0, and so,

{\displaystyle \Delta P\,dV_{\rm {A}}=\gamma \,dA}.

For a spherical bubble, the volume and surface area are given simply by

{\displaystyle V_{\rm {A}}={\tfrac {4}{3}}\pi R^{3}\quad \rightarrow \quad dV_{\rm {A}}=4\pi R^{2}\,dR,}

and

{\displaystyle A=4\pi R^{2}\quad \rightarrow \quad dA=8\pi R\,dR.}

Substituting these relations into the previous expression, we find

{\displaystyle \Delta P={\frac {2}{R}}\gamma ,}

which is equivalent to the Young–Laplace equation when Rx = Ry.

Influence of temperature[edit]

Temperature dependence of the surface tension between the liquid and vapor phases of pure water
Temperature dependency of the surface tension of benzene

Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the critical temperature. For further details see Eötvös rule. There are only empirical equations to relate surface tension and temperature:

{\displaystyle \gamma V^{\frac {2}{3}}=k(T_{\mathrm {C} }-T).}

Here V is the molar volume of a substance, TC is the critical temperature and k is a constant valid for almost all substances.[13] A typical value is k = 2.1×10−7 J K−1 mol−2⁄3.[13][32] For water one can further use V = 18 ml/mol and TC = 647 K (374 °C).[33]

A variant on Eötvös is described by Ramay and Shields:[34]

{\displaystyle \gamma V^{\frac {2}{3}}=k\left(T_{\mathrm {C} }-T-6\right)}

where the temperature offset of 6 K provides the formula with a better fit to reality at lower temperatures.

{\displaystyle \gamma =\gamma ^{\circ }\left(1-{\frac {T}{T_{\mathrm {C} }}}\right)^{n}}

γ° is a constant for each liquid and n is an empirical factor, whose value is 11/9 for organic liquids. This equation was also proposed by van der Waals, who further proposed that γ° could be given by the expression

{\displaystyle K_{2}T_{\mathrm {C} }^{\frac {1}{3}}P_{\mathrm {C} }^{\frac {2}{3}},}

where K2 is a universal constant for all liquids, and PC is the critical pressure of the liquid (although later experiments found K2 to vary to some degree from one liquid to another).[31]

Both Guggenheim–Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.

Influence of solute concentration[edit]

Solutes can have different effects on surface tension depending on the nature of the surface and the solute:

  • Little or no effect, for example sugar at water|air, most organic compounds at oil/air
  • Increase surface tension, most inorganic salts at water|air
  • Non-monotonic change, most inorganic acids at water|air
  • Decrease surface tension progressively, as with most amphiphiles, e.g., alcohols at water|air
  • Decrease surface tension until certain critical concentration, and no effect afterwards: surfactants that form micelles

What complicates the effect is that a solute can exist in a different concentration at the surface of a solvent than in its bulk. This difference varies from one solute–solvent combination to another.

Gibbs isotherm states that:

{\displaystyle \Gamma =-{\frac {1}{RT}}\left({\frac {\partial \gamma }{\partial \ln C}}\right)_{T,P}}
  • Γ is known as surface concentration, it represents excess of solute per unit area of the surface over what would be present if the bulk concentration prevailed all the way to the surface. It has units of mol/m2
  • C is the concentration of the substance in the bulk solution.
  • R is the gas constant and T the temperature

Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applied to ideal (very dilute) solutions with two components.

Influence of particle size on vapor pressure[edit]

See also: Gibbs–Thomson effect

The Clausius–Clapeyron relation leads to another equation also attributed to Kelvin, as the Kelvin equation. It explains why, because of surface tension, the vapor pressure for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the equilibrium concentration of its vapor in its surroundings is greater. This arises because the pressure inside the droplet is greater than outside.[34]

{\displaystyle P_{\mathrm {v} }^{\mathrm {fog} }=P_{\mathrm {v} }^{\circ }e^{\frac {V2\gamma }{RTr_{\mathrm {k} }}}}
Moleculeson the surface of a tiny droplet (left) have, on average, fewer neighbors than those on a flat surface (right). Hence they are bound more weakly to the droplet than are flat-surface molecules.
  • Pv° is the standard vapor pressure for that liquid at that temperature and pressure.
  • V is the molar volume.
  • R is the gas constant
  • rk is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation of vapors. In the absence of nucleation sites, tiny droplets must form before they can evolve into larger droplets. This requires a vapor pressure many times the vapor pressure at the phase transition point.[34]

This equation is also used in catalyst chemistry to assess mesoporosity for solids.[35]

The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).

The table shows some calculated values of this effect for water at different drop sizes:

P/P0 for water drops of different radii at STP[31]
Droplet radius (nm) 1000 100 10 1
P/P01.0011.0111.1142.95

The effect becomes clear for very small drop sizes, as a drop of 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a quantum mechanics analysis.

Surface tension of water and of seawater[edit]

The two most abundant liquids on the Earth are fresh water and seawater. This section gives correlations of reference data for the surface tension of both.

Surface tension of water[edit]

The surface tension of pure liquid water in contact with its vapor has been given by IAPWS[36] as

{\displaystyle \gamma _{\text{w}}=235.8\left(1-{\frac {T}{T_{\text{C}}}}\right)^{1.256}\left[1-0.625\left(1-{\frac {T}{T_{\text{C}}}}\right)\right]~{\text{mN/m}},}

where both T and the critical temperature TC = 647.096 K are expressed in kelvins. The region of validity the entire vapor–liquid saturation curve, from the triple point (0.01 °C) to the critical point. It also provides reasonable results when extrapolated to metastable (supercooled) conditions, down to at least −25 °C. This formulation was originally adopted by IAPWS in 1976 and was adjusted in 1994 to conform to the International Temperature Scale of 1990.

The uncertainty of this formulation is given over the full range of temperature by IAPWS.[36] For temperatures below 100 °C, the uncertainty is ±0.5%.

Surface tension of seawater[edit]

Nayar et al.[37] published reference data for the surface tension of seawater over the salinity range of 20 ≤ S ≤ 131 g/kg and a temperature range of 1 ≤ t ≤ 92 °C at atmospheric pressure. The range of temperature and salinity encompasses both the oceanographic range and the range of conditions encountered in thermal desalination

Sours: https://en.wikipedia.org/wiki/Surface_tension

Wikipedia surface tension

Surface tension - Wikipedia, the free encyclopedia - iSites

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Surfacetension

From Wikipedia, thefreeencyclopedia

In physics, surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. This

effect allows insects (such as the water strider) to walk on water. It allows small metal objects such as needles, razor blades, or foil

fragments to float on the surface of water, and causes capillary action.

The physical and chemical behavior of liquids cannot be understood without taking surface tension into account. It governs the

shape that small masses of liquid can assume and the degree of contact a liquid can make wi th another substance.

Continuum mechanics

Key topics

Conservation of mass

Conservation of momentum

Navier-Stokes equations

Classical mechanics

Stress · Strain · Tensor

Solid mechanics

Solids · Elasticity

Plasticity · Hooke's law

Rheology · Viscoelasticity

Fluid mechanics

Fluids · Fluid statics

Fluid dynamics · Viscosity ·

Newtonian fluids

Non-Newtonian fluids

Surfacetension

Scientists

Newton · Stokes · others

When a liquid makes a contact with another liquid (oil with water, for example), the same e ffect is observed, but in this case is called interface tension.

Contents

1 The cause

2 Effects in everyday life

3 Basic physics

3.1 Definition

3.2 Water striders

3.3 Surface curvature and pressure

3.4 Liquid surface as a computer

3.5 Contact angles

4 Methods of measurement

5 Effects

5.1 Liquid in a vertical tube

5.2 Puddles on a surface

5.3 The break up of streams into drops

6 Thermodynamics

6.1 Thermodynamic definition

6.2 Influence of temperature

6.3 Influence of solute concentration

6.4 Influence of particle size on vapour pressure

7 Gallery of effects

8 See also

9 References

10 External links

The cause

Help Your us continued improve donations Wikipedia keep by supporting Wikipedia it running! financially.

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Surfacetension is caused by the attraction between the molecules of the liquid by various intermolecular forces. In the bulk of

the liquid each molecule is pulled equally in all directions by neighboring liquid molecule s, resulting in a net force of zero. At the surface of the liquid, the

molecules are pulled inwards by other molecules deeper inside the liquid but they are not a ttracted as intensely by the molecules in the neighbouring medium (be

it vacuum, air or another liquid). Therefore all of the molecules at the surface are subjec t to an inward force of molecular attraction which can be balanced only

by the resistance of the liquid to compression. Thus the liquid squeezes itself together un til it has the locally lowest surface area possible.

Another way to think about it is that a molecule in contact with a neighbor is in a lower s tate of energy than if it weren't in contact with a neighbor. The interior

molecules all have as many neighbors as they can possibly have. But the boundary molecules have fewer neighbors than interior molecules and are therefore in a

higher state of energy. For the liquid to minimize its energy state, it must minimize its number of boundary molecules and therefore minimize its surface

area. [1][2]

As a result of this minimizing of surface area, the surface will assume the smoothest flattest shape it can (rigorous proof that "smooth" shapes minimize surface

area relies on use of the Euler-Lagrange Equation). Since any curvature in the surface shape results in higher area, a higher energy will al so result.

Consequently, the surface will push back on the disturbing object in much the same way a ba ll pushed uphill will push back to minimize its gravitational energy.

Effects in everyday life

Some examples of the effects of surface tension seen with ordinary water:

Beading of rain water on the surface of a waxed automobile. Water adheres weakly to

wax and strongly to itself, so water clusters in drops. Surfacetension gives them their

near-spherical shape, because a sphere has the smallest possible surface area to volume

ratio

Formation of drops occurs when a mass of liquid is stretched. The animation shows

water adhering to the faucet gaining mass until it is stretched to a point where the

surface tension can no longer bind it to the faucet. It then separates and surface tension

forms the drop into a sphere. If a stream of water were running from the faucet, the

stream would break up into drops during its fall. This is because of gravity stretching

the stream, and surface tensionthen pinching it into spheres. [3]

Floatation of objects denser than water occurs when the object is nonwettable and

its weight is small enough to be born by the forces arising from surface tension. [2]

Surfacetension has a big influence on other common phenomena, especially when certain subs tances, surfactants, are used to decrease it:

Soap Bubbles

have very large surface areas for very small masses. Bubbles cannot be formed from pure water because water has very high surface tension, but the use of

surfactants can reduce the surface tension more than tenfold, making it very easy to increase its surface area.

Emulsions

are a type of solution where surface tension is also very important. Oil will not spontaneo usly mix with water, but the presence of a surfactant provides a

decrease in surface tension that allows the formation of small droplets of oil in the bulk of water (or vice versa).

Basic physics

Definition

Water beading on a leaf

Diagram of the forces on a

molecule of liquid.

Water drop animation

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Surfacetension is represented by the symbol σ, γ or T and is defined as the force along a line of unit

length where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut

thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2γL (the factor of 2 is because the soap film has two sides hence

two surfaces). [4] Surfacetension is therefore measured in newtons per meter (N·m -1 ), although the cgs unit of dynes per cm is normally used. [5]

An equivalent definition of surface tension, in order to treat its thermodynamics, is work done per unit area. As such, in order to increase the surface area of a

mass of liquid an amount, δA, a quantity of work, γδA, is needed. [4]

Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape. This is because a sphere

has the minimum surface area for a given volume. Therefore surface tension can be also measured in joules per square metre (J·m -2 ), or, in the cgs system, ergs

per cm 2 .

The equivalence of measurement of energy per unit area to force per unit length can be prov en by dimensional analysis. [4]

Water striders

The photograph shows water striders standing on the surface of a pond. It is clearly visible that their feet cause

indentations in the water's surface. And it is intuitively evident that the surface with in dentations has more surface area than a flat surface. If surface tension

tends to minimize surface area, how is it that the water striders are increasing the surface area?

Recall that what nature really tries to minimize is potential energy. By increasing the sur face area of the water, the water striders have increased the potential

energy of that surface. But note also that the water striders' center of mass is lower than it would be if they were standing on a flat surface. So their potential

energy is decreased. Indeed when you combine the two effects, the net potential energy is m inimized. If the water striders depressed the surface any more, the

increased surface energy would more than cancel the decreased energy of lowering the insect s' center of mass. If they depressed the surface any less, their higher

center of mass would more than cancel the reduction in surface energy. [6]

The photo of the water striders also illustrates the notion of surface tension being like h aving an elastic film over the surface of the liquid. In the surface

depressions at their feet it is easy to see that the reaction of that imagined elastic film is exactly countering the weight of the insects.

Surface curvature and pressure

Diagram shows, in crossection, a needle floating on the

surface of water. Its weight, , depresses the surface, and is

balanced by the surface tension forces on either side, ,

which are each parallel to the water's surface at the points

where it contacts the needle. Notice that the horizontal

components of the two arrows point in opposite directions,

so they cancel each other, but the vertical components point

in the same direction and therefore add up. [2]

Water striders using water surface tension

when mating.

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If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side,

the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be

curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the

patch. When all the forces are balanced, the resulting equation is known as the Young-Laplace equation: [1]

where:

ΔP is the pressure difference.

γ is surface tension.

Rx and Ry are radii of curvature in each of the axes that are parallel to the surface.

Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbl es, and all other shapes determined by surface tension (such as the

shape of the impressions that a water strider's feet make on the surface of a pond).

The table below shows how the internal pressure of a water droplet increases with decreasin g radius. For not very small drops the effect is subtle, but the

pressure difference becomes enormous when the drop sizes approach the molecular size.

ΔP for water drops of different radii at STP

Droplet radius 1 mm 0.1 mm 1 μm 10 nm

ΔP (atm) 0.0014 0.0144 1.436 143.6

Liquid surface as a computer

To find the shape of the minimal surface

bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in

soap-solution, an approximately minimal surface (exact in the absence of gravity) will appe ar in the resulting soap-film within seconds. Without a single

[4] [7]

calculation, the soap-film arrives at a solution to a complex minimization equation on its own.

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an

open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles

Since no liquid can exist in a perfect vacuum, the surface of any liquid is an interface be tween that liquid and some other medium. The top surface of a pond, for

example, is an interface between the pond water and the air. Surfacetension, then, is not a property of the liquid alone, but a property of the liquid's interface

with another medium. If a liquid is in a container, then besides the liquid/air interface a t its top surface, there is also an interface between the liquid and the walls

of the container. The surface tension between the liquid and air is usually different (grea ter than) its surface tension with the walls of a container. And where the

two surfaces meet, their geometry must be such that all forces balance. [1][4]

Where the two surfaces meet, they form a contact angle, . The diagram to the right shows two examples. The

example on the left is where the liquid/solid surface tension, , is less than the liquid/air surface tension, , but

Surfacetension forces acting on a tiny (differential) patch of

surface. δθx and δθy indicate the amount of bend over the

dimensions of the patch. Balancing thetension forces with pressure

leads to the Young-Laplace equation

Minimal surface

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is nevertheless positive, that is

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point. The horizontal component of is canceled by the adhesive

force, . [4]

The more telling balance of forces, though, is in the vertical direction. The vertical comp onent of must exactly cancel the force, . [4]

Since the forces are in direct proportion to their respective surface tensions, we also hav e [1]

where

is the liquid-solid surface tension,

is the liquid-air surface tension,

is the contact angle, where a concave meniscus has contact angle less than 90° and a convex

meniscus has contact angle of greater than 90°. [4]

This means that although the liquid/solid surface tension, , is difficult to measure directly, it can be

inferred from the easily measured contact angle, , if the liquid/air surface tension, , is known.

Liquid Solid Contact angle

water

ethanol

soda-lime glass

diethyl ether

lead glass

carbon tetrachloride

fused quartz

glycerol

acetic acid


water

paraffin wax

silver

107°

90°

soda-lime glass 29°

methyl iodide lead glass 30°

fused quartz 33°

mercury soda-lime glass 140°

Some liquid/solid contact angles [4]

This same relationship exists in the diagram on the right. But in this case we see that bec ause the contact angle is less than 90°, the liquid/solid surface tension

must be negative:

Observe that in the special case of a water/silver interface where the contact angle is equ al to 90°, the liquid/solid surface tension is exactly zero. Another special

case is where the contact angle is exactly 180°. Water with specially prepared Teflon® approaches this. [1] Contact angle of 180° occurs when the liquid/solid

surface tension is exactly equal to the liquid/air surface tension.

Methods of measurement

Forces at contact point shown for contact

angle greater than 90° (left) and less than

90° (right)

Du Noüy Ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little

influence on this measuring technique. Maximum pull exerted on the ring by the surface is m easured. [8]

Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is

attached to a balance, and the force due to wetting is measured. [9]

Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop wi thin a heavy phase is measured while both

are rotated.

Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated tempe ratures and pressures. Geometry of a drop

is analyzed optically. For details, see Drop. [9]

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Effects

Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension

at short surface ages. Maximum pressure of each bubble is measured.

Drop volume method: A method for determining interfacial tension as a function of interface age.

Liquid of one density is pumped into a second liquid of a different density and time betwee n drops

produced is measured. [10]

Capillary rise method: The end of a capillary is immersed into the solution. The height at which the

solution reaches inside the capillary is related to the surface tension by the previously d iscussed

equation. [11]

Stalagmometric method: A method of weighting and reading a drop of liquid.

Sessile drop method: A method for determining surface tension and density by placing a drop on a

substrate and measuring the contact angle (see Sessile drop technique). [12]

Liquid in a vertical tube

An old style mercury barometer

Surfacetension can be measured using the pendant

drop method on a goniometer.

Diagram of a Mercury

Barometer

consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum in the unfilled volume (see diagram to the right). Notice

that the mercury level at the center of the tube is higher than at the edges, making the up per surface of the mercury dome-shaped. The center of mass of the

entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top

gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is

known as a convex meniscus.

The reason we consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, is because mercury does

not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass,

the tube were made out of copper, the situation would be very different. Mercury aggressive ly adheres to copper. So in a copper tube, the level of mercury at the

center of the tube will be lower rather than higher than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls

of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to

maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That

decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

Illustration of capillary rise.

Red=contact angle less than

90°; blue=contact angle

greater than 90°

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as

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capillary action. The height the column is lifted to is given by: [4]

where

is the height the liquid is lifted,

is the liquid-air surface tension,

is the density of the liquid,

is the radius of the capillary,

is the acceleration due to gravity,

is the angle of contact described above. Note that if

is greater than 90°, as with mercury in a glass container, the liquid will be depressed rat her than lifted.

Puddles on a surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible

thickness (do not try this except under a fume hood. Mercury vapor is a toxic hazard). The puddle

will spread out only to the point where it is a little under half a centimeter thick, and n o thinner.

Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as

possible. But the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, but only on a surface made o f a substance that the water does not adhere to. Wax is such a

substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of g lass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by: [1]

where

is the depth of the puddle in centimeters or meters.

is the surface tension of the liquid in dynes per centimeter or newtons per meter.

is the acceleration due to gravity and is equal to 980 cm/s 2 or 9.8 m/s 2

is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter

Profile curve of the edge of a puddle where the contact angle is

180°. The curve is given by the formula [1] :

where

Small puddles of water on a

smooth clean surface have

perceptible thickness.

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In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180°

with any liquid. When the contact angle is less than 180°, the thickness is given by: [1]

For mercury on glass, , , and , which gives . For water on paraffin at 25 °C, ,

, and which gives .

The formula also predicts that when the contact angle is 0°, the liquid will spread out int o a micro-thin layer over the surface. Such a surface is said to be fully

wettable by the liquid.

The break up of streams into drops

Illustration of how lower contact

angle leads to reduction of puddle

depth

Intermediate stage of a jet breaking into

drops. Radii of curvature in the axial

direction are shown. Equation for the

radius of the stream is

, where is the

radius of the unperturbed stream, is

the amplitude of the perturbation, is

distance along the axis of the stream, and

is the wave number

In day to day life we all observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from

the faucet. This is due to a phenomenon called the Plateau-Rayleigh instability, [1] which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If

the perturbations are resolved into sinusoidal

components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than

others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per

centimeter) and the radius of the original cylindrical stream. The diagram to the right sho ws an exaggeration of a single component.

By assuming that all possible components exist initially in roughly equal (but minuscule) a mplitudes, the size of the final drops can be predicted by determining

by wave number which component grows the fastest. As time progresses, it is the component whose growth rate is maximum that will come to dominate and

will eventually be the one that pinches the stream into drops. [3]

Although a thorough understanding of how this happens requires a mathematical development ( see references [1][3] ), the diagram can provide a conceptual

understanding. Observe the two bands shown girdling the stream – one at a peak and the othe r at a trough of the wave. At the trough, the radius of the stream is

smaller, hence according to the Young-Laplace equation

(discussed above) the pressure due to surface tension is increased. Likewise at the peak th e radius of the stream is greater and, by the same reasoning, pressure

due to surface tension is reduced. If this were the only effect, we would expect that the h igher pressure in the trough would squeeze liquid into the lower

pressure region in the peak. In this way we see how the wave grows in amplitude over time.

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But the Young-Laplace equation

is influenced by two separate radius components. In this case one is the radius, already di scussed, of the stream itself. The other is the radius of curvature of the

wave itself. The fitted arcs in the diagram show these at a peak and at a trough. Observe t hat the radius of curvature at the trough is, in fact, negative, meaning

that, according to Young-Laplace, it actually decreases

the pressure in the trough. Likewise the radius of curvature at the peak is positive and in creases the pressure in that region. The effect of these components is

opposite the effects of the radius of the stream itself.

The two effects, in general, do not exactly cancel. One of them will have greater magnitude than the other, depending upon wave number and the initial radius of

the stream. When the wave number is such that the radius of curvature of the wave dominates that of the radius of the stream, such components will decay over

time. When the effect of the radius of the stream dominates that of the curvature of the wave, such components grow exponentially with time.

When all the math is done, it is found that unstable components (that is, components that g row over time) are only those where the product of the wave number

with the initial radius is less than unity ( ). The component that grows the fastest is the one whose wave number satisfies the equation : [3]

Thermodynamics

Thermodynamic definition

As stated above, the mechanical work needed to increase a surface is . Hence at constant temperature and pressure, surface tension equals Gibbs free

energy per surface area: [1]

where is Gibbs free energy and is the area.

Thermodynamics requires that all spontaneous changes of state are accompanied by a decrease in Gibbs free energy.

From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous ( ), provided it is not coupled to any other

energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.

Gibbs free energy is defined by the equation, [13] , where is enthalpy and is entropy. Based upon this and the fact that surface tension is

Gibbs free energy per unit area, it is possible to obtain the following expression for entr opy per unit area:

By rearranging the previous equations, Kelvin's Equation I

is obtained. It states that surface enthalpy or surface energy (different from surface free energy) depends both on surface tension and its derivative with

temperature at constant pressure by the relationship [14]

Influence of temperature

Surfacetension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated.

The general trend is that surface tension decreases with the increase of temperature, reach ing a value of 0 at the critical temperature. For further details see

Eötvös rule. There are only empirical equations to relate surface tension and temperature:

Eötvös: [8][14]

Temperature dependency of

the surface tension of benzene

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is the molar volume of that substance

is the critical temperature

is a constant for each substance.

For example for water k = 1.03 erg/°C (103 nJ/K), V = 18 ml/mol and TC = 374 °C.

A variant on Eötvös is described by Ramay and Shields: [13]

where the temperature offset of 6 Kelvins provides the formula with a better fit to reality at lower temperatures.

Guggenheim-Katayama: [14]

is a constant for each liquid and n is an empirical factor, whose value is 11/9 for organi c liquids. This equation was also proposed by van der Waals, who

further proposed that could be given by the expression, , where is a universal constant for all liquids, and is the critical pressure of the liquid

(although later experiments found to vary to some degree from one liquid to another). [14]

Both Guggenheim-Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to

match reality at this endpoint.

Influence of solute concentration

Solutes can have different effects on surface tension depending on their structure:

No effect, for example sugar

Increase of surface tension, inorganic salts

Decrease surface tension progressively, alcohols

Decrease surface tension and, once a minimum is reached, no more effect: surfactants

What complicates the effect is that a solute can exist in a different concentration at the surface of a solvent than in its bulk. This difference varies from one

solute/solvent combination to another.

Gibbs isotherm states that: [13]

is known as surface concentration, it represents excess of solute per unit area of the surface over what would be present if the bulk concentration

prevailed all the way to the surface. It has units of mol/m 2

is the concentration of the substance in the bulk solution.

is the gas constant and the temperature

Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applie d to ideal (very dilute) solutions with two components.

Influence of particle size on vapour pressure

Starting from Clausius-Clapeyron relation, another equation, attributed to Kelvin, is obtained. It explains why, because of surface tension, the vapor pressure for

small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is

forming small droplets, the equilibrium concentration of its vapor in its surroundings is g reater. This arises because the pressure inside the droplet is greater than

outside. [13]

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is the standard vapor pressure for that liquid at that temperature and pressure.

is the molar volume.

is the gas constant

rk is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation of vapors. In the absence of nucleation sites, tiny droplets must form before they

can evolve into larger droplets. This requires a vapor pressure many times the vapor pressu re at the phase transition

point. [13]

This equation is also used in catalyst chemistry to assess mesoporosity for solids. [15]

The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).

The table shows some calculated values of this effect for water at different drop sizes:

P/P0 for water drops of different radii at STP [14]

Droplet radius

(nm)

1000 100 10 1

P/P0 1.001 1.011 1.114 2.95

The effect becomes clear for very small drop sizes, as a drop of 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a

quantum mechanics analysis.

Gallery of effects

Breakup of a moving

sheet of water

bouncing off of a

spoon.

See also

A soap bubble

balances surface

tension forces against

internal pneumatic

pressure.

Wikimedia Commons has media related to:

Surfacetension

Surfacetension

prevents a coin from

sinking: the coin is

indisputably denser

than water, so it cannot

be floating due to

buoyancy alone.

A daisy. The flower is

under the water level,

which has risen gently

and smoothly. Hence

surface tension

prevents the water

from submerging the

flower.

Anti-fog

Cheerios effect – the tendency for small wettable floating objects to attract one another

Dortmund Data Bank – contains experimental temperature-dependent surface tensions

Eötvös rule – a rule for predicting surface tension dependent on temperature

Hydrostatic Equilibrium – the effect of gravity pulling matter into a round shape.

Meniscus – surface curvature formed by a liquid in a container

Mercury beating heart – a consequence of inhomogeneous surface tension

Specific surface energy – same as surface tension in isotropic materials.

Surfacetension values

Surfactants – substances which reduce surface tension

Tolman length – leading term in correcting the surface tension for curved surfaces

Wetting and dewetting

References

Molecules on the surface of a tiny droplet

(left) have, on average, fewer neighbors

than those on a flat surface (right). Hence

they are bound more weakly to the droplet

than are flat-surface molecules.

^ a b c d e f g h i j k 1.

Pierre-Gilles de Gennes, Françoise Brochard-Wyart, David Quéré (2002). Capillary and Wetting Phenomena -- Drops, Bubbles,

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Surfacetension - Wikipedia, thefreeencyclopedia file:///C:/Documents%20and%20Settings/Mara/User/d/user/mara/course...

Pearls, Waves. Springer. ISBN 0-387-00592-7.

^ a b c 2. White, Harvey E. Modern College Physics, van Nostrand 1948

^ a b c d 3. John W. M. Bush (May 2004). MIT Lecture Notes on Surface Tension, lecture 5

(http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture5.pdf) . Massachusetts Institute of Technology. Retrieved on April 1, 2007.

^ a b c d e f g h i j 4.

Sears, Francis Weston; Zemanski, Mark W. University Physics 2nd ed. Addison Wesley 1955

5. ^ John W. M. Bush (April 2004). MIT Lecture Notes on Surface Tension, lecture 1 (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture1.pdf)

. Massachusetts Institute of Technology. Retrieved on April 1, 2007.

6. ^ John W. M. Bush (May 2004). MIT Lecture Notes on Surface Tension, lecture 3 (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture3.pdf)

. Massachusetts Institute of Technology. Retrieved on April 1, 2007.

7. ^ Aaronson, Scott, "NP-Complete Problems and physical reality." (http://www.scottaaronson.com/papers/npcomplete.pdf) , SIGACT News

^ a b 8. Surface Tension by the Ring Method (Du Nouy Method) (http://www.nikhef.nl/%7Eh73/kn1c/praktikum/phywe/LEP/Experim/1_4_05.pdf) (pdf).

PHYWE. Retrieved on 2007-09-08.

^ a b 9. Surface and Interfacial Tension (http://www.ksvinc.com/surface_tension1.htm) . Langmuir-Blodgett Instruments. Retrieved on 2007-09-08.

10. ^ Surfacants at interfaces (http://lauda.de/hosting/lauda/webres.nsf/urlnames/graphics_tvt2/$file/Tensio-dyn-meth-e.pdf ) . lauda.de. Retrieved on

2007-09-08.

11. ^ Calvert, James B.. Surface Tension (physics lecture notes) (http://mysite.du.edu/%7Ejcalvert/phys/surftens.htm) . University of Denver. Retrieved on

2007-09-08.

12. ^ Sessile Drop Method (http://www.dataphysics.de/english/messmeth_sessil.htm) . Dataphysics. Retrieved on 2007-09-08.

^ a b c d e 13. Moore, Walter J. (1962). Physical Chemistry, 3rd ed.. Prentice Hall.

^ a b c d e 14. Adam, Neil Kensington (1941). The Physics and Chemistry of Surfaces, 3rd ed.. Oxford University Press.

15. ^ G. Ertl, H. Knözinger and J. Weitkamp; Handbook of heterogeneous catalysis, Vol. 2, page 430; Wiley-VCH; Weinheim; 1997

External links

Concise overview of surface tension (http://www.ramehart.com/goniometers/surface_tension.htm)

On surface tension and interesting real-world cases (http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html)

MIT Lecture Notes on Surface Tension (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/)

Theory of surface tension measurements (http://www.kruss.info/techniques/surface_tension_e.html)

Understanding the interaction between gases and liquids

(http://www.scientistlive.com/elab/20061201/analyticallab-equipment/2.1.282.286/16974/unders tanding-the-interaction-between-gases-and-liquids.thtml)

Scientist Live

General subfields within physics

[hide] [hide]

Classical mechanics · Electromagnetism · Thermodynamics · Statistical mechanics · Quantum mechanics · Relativity · High energy physics · Condensed matter physics ·

Atomic, molecular, and optical physics

Retrieved from "http://en.wikipedia.org/wiki/Surface_tension"

Categories: Continuum mechanics | Fundamental physics concepts | Fluid mechanics | Surface chemistry

This page was last modified 15:29, 9 September 2007.

All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.)

Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) tax-deductible nonprofit charity.

12 of 12 9/14/2007 9:39 AM

<strong>Surface</strong> <strong>tension</strong> - <strong>Wikipedia</strong>, <strong>the</strong> <strong>free</strong> <strong>encyclopedia</strong> file:///C:/Documents%20and%20Settings/Mara/User/d/user/mara/course... <strong>Surface</strong> <strong>tension</strong> From <strong>Wikipedia</strong>, <strong>the</strong> <strong>free</strong> <strong>encyclopedia</strong> In physics, surface <strong>tension</strong> is an effect within <strong>the</strong> surface layer of a liquid that causes that layer to behave as an elastic sheet. This effect allows insects (such as <strong>the</strong> water strider) to walk on water. It allows small metal objects such as needles, razor blades, or foil fragments to float on <strong>the</strong> surface of water, and causes capillary action. The physical and chemical behavior of liquids cannot be understood without taking surface <strong>tension</strong> into account. It governs <strong>the</strong> shape that small masses of liquid can assume and <strong>the</strong> degree of contact a liquid can make wi th ano<strong>the</strong>r substance. Continuum mechanics Key topics Conservation of mass Conservation of momentum Navier-Stokes equations Classical mechanics Stress · Strain · Tensor Solid mechanics Solids · Elasticity Plasticity · Hooke's law Rheology · Viscoelasticity Fluid mechanics Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids <strong>Surface</strong> <strong>tension</strong> Scientists Newton · Stokes · o<strong>the</strong>rs When a liquid makes a contact with ano<strong>the</strong>r liquid (oil with water, for example), <strong>the</strong> same e ffect is observed, but in this case is called interface <strong>tension</strong>. Contents 1 The cause 2 Effects in everyday life 3 Basic physics 3.1 Definition 3.2 Water striders 3.3 <strong>Surface</strong> curvature and pressure 3.4 Liquid surface as a computer 3.5 Contact angles 4 Methods of measurement 5 Effects 5.1 Liquid in a vertical tube 5.2 Puddles on a surface 5.3 The break up of streams into drops 6 Thermodynamics 6.1 Thermodynamic definition 6.2 Influence of temperature 6.3 Influence of solute concentration 6.4 Influence of particle size on vapour pressure 7 Gallery of effects 8 See also 9 References 10 External links The cause Help Your us continued improve donations <strong>Wikipedia</strong> keep by supporting <strong>Wikipedia</strong> it running! financially. • Ten things • Learn you didn't more about know about citing <strong>Wikipedia</strong> • 1 of 12 9/14/2007 9:39 AM

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Surface-tension values

This is a table of surface tension values[1] for some interfaces at the indicated temperatures. Note that the SI units millinewtons per meter (mN·m−1) are equivalent to the cgs units dynes per centimetre (dyn·cm−1).

References[edit]

  1. ^A. W. Adamson, A. P. Gast.; Physical chemistry of surfaces; 6Ed, Wiley, 1997)
  2. ^ abColloids and Surfaces (1990)43,169–194, Pallas,N.R. and Harrison,Y
  3. ^"Surface Tension of Hexane from Dortmund Data Bank". ddbst.com. Retrieved 13 October 2020.
  4. ^Geoffrey Taylor (1964). "Disintegration of Water Droplets in an Electric Field". Proceedings of the Royal Society A. 280 (1382): 383–397. Bibcode:1964RSPSA.280..383T. doi:10.1098/rspa.1964.0151. JSTOR 2415876. S2CID 15067908.
  5. ^ abcdSmirnov, Evgeny; Peljo, Pekka; Scanlon, Micheál D.; Gumy, Frederic; Girault, Hubert H. (2016). "Self-healing gold mirrors and filters at liquid–liquid interfaces"(PDF). Nanoscale. 8 (14): 7723–7737. doi:10.1039/c6nr00371k. hdl:10344/8369. ISSN 2040-3364. PMID 27001646.
  6. ^Smirnov, Evgeny; Peljo, Pekka; Girault, Hubert (2017). "Self-assembly and redox induced phase transfer of gold nanoparticles at the water-propylene carbonate interface"(PDF). Chem. Commun. 53 (29): 4108–4111. doi:10.1039/c6cc09638g. ISSN 1364-548X. PMID 28349148.

External links[edit]

More values on

Sours: https://en.wikipedia.org/wiki/Surface-tension_values


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