Physics Definition of Surface Tension

[show]

[show]

[show]

Continuum mechanics

Conservation of mass

Conservation of momentum

Navier–Stokes equations

Tensors

Solid mechanics

Fluid mechanics

Scientists

From New World Encyclopedia

In physics, surface tension is an effect within the surface layer of a liquidthat causes that layer to behave as an elastic sheet. This effect allowsinsects (such as the water strider) to walk on water. It allows small metalobjects such as needles, razor blades, or foil fragments to float on thesurface of water, and causes capillary action. Interface tension is the nameof the same effect when it takes place between two liquids.

1 The cause of surface tension2 Surface tension in everyday life3 Physics definition of surface tension4 Water strider physics5 Liquid in a vertical tube6 Pool of liquid on a nonadhesive surface7 Liquid surfaces as minimization solver8 Measuring methods9 Surface tension and thermodynamics

9.1 Thermodynamic definition9.2 Influence of temperature on surface tension9.3 Influence of solute concentration on surface tension9.4 Pressure jump across a curved surface9.5 Influence of particle size on vapor pressure

10 Surface tension values11 See also12 Notes13 References14 External links15 Credits

Surface tension - New World Encyclopedia http://www.newworldencyclopedia.org/entry/Surface_tension

1 of 11 10/10/2009 22:50

Diagram of the forces on amolecule of liquid.

Water beading on a leaf

Water drop animation

Surface tension is caused by the attraction between the molecules of theliquid by various intermolecular forces. In the bulk of the liquid eachmolecule is pulled equally in all directions by neighboring liquid molecules,resulting in a net force of zero. At the surface of the liquid, the moleculesare pulled inwards by other molecules deeper inside the liquid but they arenot attracted as intensely by the molecules in the neighboring medium (be itvacuum, air or another liquid). Therefore, all of the molecules at the surfaceare subject to an inward force of molecular attraction which can bebalanced only by the resistance of the liquid to compression. Thus, theliquid squeezes itself together until it has the locally lowest surface areapossible.

Another way to think about it is that a molecule in contact with a neighboris in a lower state 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 moleculeshave fewer neighbors than interior molecules and are therefore in a higher state of energy. For the liquid tominimize its energy state, it must minimize its number of boundary molecules and therefore minimize its

surface area.[1]

As a result of this minimizing of surface area, the surface will want to assume the smoothest flattest shape itcan (rigorous proof that "smooth" shapes minimize surface area relies on use of the Euler-LagrangeEquation). Since any curvature in the surface shape results in higher area, a higher energy will also result.Consequently, the surface will push back on the disturbing object in much the same way a ball pushed uphillwill push back to minimize its gravitational energy.

Some examples of the effects of surfacetension seen with ordinary water:

Beading of rain water on thesurface of a waxed automobile.Water adheres weakly to wax andstrongly to itself, so water clustersin drops. Surface tension givesthem their near-spherical shape,because a sphere has the smallestpossible surface area to volumeratio.

Formation of drops occurs whena mass of liquid is stretched. Theanimation shows water adhering tothe faucet gaining mass until it isstretched to a point where the surface tension can no longer bind it to the faucet. It then separates andsurface tension forms the drop into a sphere. If a stream of water were running from the faucet, thestream would break up into drops during its fall. This is because of gravity stretching the stream, and

surface tension then pinching it into spheres.[2]

Surface tension has a big influence on other common phenomena, especially when certain substances,surfactants, are used to decrease it:

Soap Bubbles have very large surface areas for very small masses. Bubbles cannot be formed from


2 of 11 10/10/2009 22:50

Diagram shows, in crossection, a needle floating on thesurface 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 horizontalcomponents of the two arrows point in oppositedirections, so they cancel each other, but the vertical

components point in the same direction and therefore add

up.[1]

pure water because water has very high surface tension, but the use of surfactants can reduce thesurface tension more than tenfold, making it very easy to increase its surface area.Colloids are a type of solution where surface tension is also very important. Oil will not spontaneouslymix with water, but the presence of a surfactant provides a decrease in surface tension that allows theformation of small droplets of oil in the bulk of water (or vice versa).

Surface tension is represented by the symbol σ, γor T and is defined as the force along a line ofunit length where the force is parallel to thesurface but perpendicular to the line. One way topicture this is to imagine a flat soap film boundedon one side by a taut thread of length, L. Thethread will be pulled toward the interior of thefilm by a force equal to γL. Surface tension istherefore measured in newtons per meter

(N·m-1), although the cgs unit of dynes per cm is

normally used.[3]

A better definition of surface tension, in order totreat its thermodynamics, is work done per unitarea. As such, in order to increase the surfacearea of a mass of liquid an amount, δA, aquantity of work, γδA, is needed. Sincemechanical systems try to find a state ofminimum potential energy, a free droplet ofliquid naturally assumes a spherical shape. This isbecause a sphere has the minimum surface area for a given volume. Therefore surface tension can be also

measured in joules per square meter (J·m-2), or, in the cgs system, ergs per cm2.

The equivalence of both units can be proven by dimensional analysis.

A related quantity is the energy of cohesion, which is the energy released when two bodies of the sameliquid become joined by a boundary of unit area. Since this process involves the removal of a unit area ofsurface from each of the two bodies of liquid, the energy of cohesion is equal to twice the surface energy. Asimilar concept, the energy of adhesion, applies to two bodies of different liquids. Energy of adhesion islinked to the surface tension of an interface between two liquids.

See also Cassie's law.


3 of 11 10/10/2009 22:50

Suta Vijaya

Underline

Suta Vijaya

Underline

Water striders using water surface tensionwhen mating.

Diagram of a MercuryBarometer

The photograph shows water striders standing on the surface of apond. It is clearly visible that its feet cause indentations in thewater's surface. And it is intuitively evident that the surface withindentations has more surface area than a flat surface. If surfacetension tends to minimize surface area, how is it that the waterstriders are increasing the surface area?

Recall that what nature really tries to minimize is potentialenergy. By increasing the surface area of the water, the waterstriders have increased the potential energy of that surface. Butnote also that the water striders' center of mass is lower than itwould be if they were standing on a flat surface. So theirpotential energy is decreased. Indeed when you combine the twoeffects, the net potential energy is minimized. If the waterstriders depressed the surface any more, the increased surfaceenergy would more than cancel the decreased energy of lowering the insects' center of mass. If theydepressed the surface any less, their higher center of mass would more than cancel the reduction in surface

energy.[4]

The photo of the water striders also illustrates the notion of surface tension being like having an elastic filmover the surface of the liquid. In the surface depressions at their feet it is easy to see that the reaction of thatimagined elastic film is exactly countering the weight of the insects.

An old style mercury barometer consists of a vertical glass tube about 1 cm indiameter partially filled with mercury, and with a vacuum in the unfilledvolume (see diagram to the right). Notice that the mercury level at the centerof the tube is higher than at the edges, making the upper surface of themercury dome-shaped. The center of mass of the entire column of mercurywould be slightly lower if the top surface of the mercury were flat over theentire cross-section of the tube. But the dome-shaped top gives slightly lesssurface area to the entire mass of mercury. Again the two effects combine tominimize the total potential energy. Such a surface shape is known as a convexmeniscus.

The reason people consider the surface area of the entire mass of mercury,including the part of the surface that is in contact with the glass, is becausemercury does not adhere at all to glass. So the surface tension of the mercuryacts 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 bevery different. Mercury aggressively adheres to copper. So in a copper tube,the level of mercury at the center of the tube will be lower rather than higherthan at the edges (that is, it would be a concave meniscus). In a situationwhere the liquid adheres to the walls of its container, we consider the part ofthe fluid's surface area that is in contact with the container to have negative surface tension. The fluid thenworks to maximize the contact surface area. So in this case increasing the area in contact with the containerdecreases rather than increases the potential energy. That decrease is enough to compensate for theincreased potential energy associated with lifting the fluid near the walls of the container.


4 of 11 10/10/2009 22:50

Concave meniscus withcontact angle of less than

90°

Convex meniscus withcontact angle of greater than

90°

Image:2006-01-15 coin onwater.jpg

Surface tension prevents a coinfrom sinking: The coin is

indisputably denser than water,so it cannot be floating due to

buoyancy alone.

Surface tension prevents this flower fromsinking

The angle of contact of the surface of the liquidwith the wall of the container can be used todetermine the surface tension of theliquid-solid interface provided that the surfacetension of the liquid-air interface is known. Therelationship is given by:

where

is the liquid-solid surfacetension,

is the liquid-air surfacetension,

is the contact angle, where aconcave meniscus has contactangle less than 90° and a convexmeniscus has contact angle of

greater than 90°.[5]

If a tube is sufficiently narrow and the liquid adhesion to its walls issufficiently strong, surface tension can draw liquid up the tube in aphenomenon known as capillary action. The height the column is lifted to is

given by:[5]

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 of gravity, is the angle of contact described above. Note that

if is greater than 90°, as with mercury in a glasscontainer, the liquid will be depressed rather thanlifted.

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness (donot try this except under a fume hood. Mercury vapor is a toxic hazard). The puddle will spread out only tothe point where it is a little under half a centimeter thick, and no thinner. Again this is due to the action ofmercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury toas 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 of a substancethat the water does not adhere to. Wax is such a substance. Water poured onto a smooth, flat, horizontalwax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.


5 of 11 10/10/2009 22:50

The thickness of a puddle of liquid on a nonadhesive horizontal surface is given by

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/s2 or 9.8 m/s2

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

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

In reality, the thicknesses of the puddles will be slightly less than these calculated values. This is due to thefact that surface tension of the mercury-glass interface is slightly less than that of the mercury-air interface.Likewise, the surface tension of the water-wax interface is less than that of the water-air interface. Thecontact angle, as described in the previous subsection, determines by how much the puddle thickness isreduced from the theoretical.

To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictlymathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it insoap-solution, an approximately minimal surface will appear in the resulting soap-film within seconds.Without a single calculation, the soap-film arrives at a solution to a complex minimization equation on its

own.[5] [6]

Du Noüy Ring method: The traditional method used to measure surface or interfacial tension. Wettingproperties of the surface or interface have little influence on this measuring technique. Maximum pullexerted on the ring by the surface is measured.

Wilhelmy plate method: A universal method especially suited to check surface tension over long timeintervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting ismeasured.

Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter ofa 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 atelevated temperatures and pressures. Geometry of a drop is analyzed optically.


6 of 11 10/10/2009 22:50

Surface Tension can be measured using the pendantdrop method on a ramé-hart goniometer.

Temperature dependency of thesurface tension of benzene

Bubble pressure method (Jaeger's method): Ameasurement technique for determining surfacetension at short surface ages. Maximum pressureof each bubble is measured.

Drop volume method: A method for determininginterfacial tension as a function of interface age.Liquid of one density is pumped into a secondliquid of a different density and time betweendrops produced is measured.

Capillary rise method: The end of a capillary isimmersed into the solution. The height at whichthe solution reaches inside the capillary is relatedto the surface tension by the previously discussedequation.

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

Thermodynamic definition

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

energy per surface area:

, where is Gibbs free energy and is the area.

Influence of temperature on surface tension

Surface tension depends on temperature; for that reason, when a value isgiven for the surface tension of an interface, temperature must be explicitlystated. The general trend is that surface tension decreases with the increaseof temperature, reaching a value of 0 at the critical temperature. There areonly empirical equations to relate surface tension and temperature.

Influence of solute concentration on surface tension

Solutes can have different effects on surface tension depending on theirstructure:

No effect, for example sugarIncrease of surface tension, inorganic saltsDecrease surface tension progressively, alcoholsDecrease surface tension and, once a minimum is reached, no more effect: Surfactants

Pressure jump across a curved surface

If viscous forces are absent, the pressure jump across a curved surface is given by the Young-LaplaceEquation, which relates pressure inside a liquid with the pressure outside it, the surface tension and the


7 of 11 10/10/2009 22:50

geometry of the surface.

.

This equation can be applied to any surface:

For a flat surface so the pressure inside is the same as the pressure outside.For a spherical surface

For a toroidal surface , where r and R are the radii of the toroid.[7]

The table shows an example of how the pressure increases, showing that for not very small drops the effectis subtle but the pressure difference becomes enormous when the drop sizes approach the molecular size (adrop with a 1 nm radius contains approximately 100 water molecules), this can be attributed to the fact thatat a very small scale the laws of continuum physics cannot be applied anymore.

ΔP for water drops of different radii at STPDroplet radius 1 mm 0.1 mm 1 μm 10 nmΔP (atm) 0.0014 0.0144 1.436 143.6

Influence of particle size on vapor pressure

Starting from Clausius-Clapeyron relation Kelvin Equation II can be obtained; it explains that because ofsurface tension, vapor pressure for small droplets of liquid in suspension is greater than standard vaporpressure of that same liquid when the interface is flat. That is to say that when a liquid is forming smalldroplets, the concentration of vapor of that liquid in the surroundings is greater, this is due to the fact thatthe pressure inside the droplet is greater than outside.

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.

This equation is used in catalyst chemistry to assess mesoporosity for solids.[8]

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

Droplet radius(nm)

1000 100 10 1

P/P0 1.0011 1.0106 1.1115 2.8778

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


8 of 11 10/10/2009 22:50

Surface tension values for some interfaces

Interface Temperature γ in (mN·m–1)

Water - air 20º C 72.86±0.05[9]

Water - air 21.5º C 72.75

Water - air 25º C 71.99±0.05[9]

Methylene iodide - air 20º C 67.00Methylene iodide - air 21.5º C 63.11Ethylene glycol - air 25º C 47.3Ethylene glycol - air 40º C 46.3

Dimethyl sulfoxide - air 20º C 43.54Propylene carbonate -

air20º C 41.1

Benzene - air 20º C 28.88Benzene - air 30º C 27.56Toluene - air 20º C 28.52

Chloroform - air 25º C 26.67Propionic acid - air 20º C 26.69Butyric acid - air 20º C 26.51

Carbon tetrachloride -air

25º C 26.43

Butyl acetate - air 20º C 25.09Diethylene Glycol - air 20º C 30.09

Nonane - air 20º C 22.85Methanol - air 20º C 22.50Ethanol - air 20º C 22.39Ethanol - air 30º C 21.55Octane - air 20º C 21.62Heptane - air 20º C 20.14

Ether - air 25º C 20.14Mercury - air 20º C 486.5Mercury - air 25º C 485.5Mercury - air 30º C 484.5

NaCl - air 1073º C 115KClO3 - air 20º C 81

Water - 1-Butanol 20º C 1.8Water - Ethyl acetate 20º C 6.8

Water - Heptanoic acid 20º C 7.0Water - Benzaldehyde 20º C 15.5

Water - Mercury 20º C 415Ethanol - Mercury 20º C 389

Surface tension values[10] for some interfacesat the indicated temperatures. Note that the SI

units millinewtons per meter (mN·m–1) areequivalent to the cgs units, dynes per centimeter

(dyn·cm–1).

Contact angle, the angle the surface makes with the wall of a container.


9 of 11 10/10/2009 22:50

Cheerios effect, the tendency for small wettable floating objects to attract one anotherWater striders, insects that rely on the surface tension of water to walk on top of itWetting and dewettingMeniscus, surface curvature formed by a liquid in a containerTolman length, leading term in correcting the surface tension for curved surfacesSurfactants, substances which reduce surface tensionEötvös rule, a rule for predicting surface tension dependent on temperatureThe Dortmund Data Bank contains experimental temperature-dependent surface tensions

↑ 1.0 1.1 Harvey E. White, Modern College Physics (van Nostrand, 1948).1.↑ MIT, MIT Lecture Notes on Surface Tension, lecture 5. (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture5.pdf) Retrieved April 1, 2007.

2.

↑ MIT, Lecture Notes on Surface Tension, lecture 1. (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture1.pdf) Retrieved April 1, 2007.

3.

↑ MIT, MIT Lecture Notes on Surface Tension, lecture 3. (http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture3.pdf) Retrieved April 1, 2007.

4.

↑ 5.0 5.1 5.2 Francis Weston Sears and Mark W. Zemanski, University Physics, 2nd ed. (AddisonWesley, 1955).

5.

↑ Scott Aaronson, NP-Complete Problems and physical reality. (http://www.scottaaronson.com/papers/npcomplete.pdf) Retrieved November 14, 2008.

6.

↑ Sir Horace Lamb, Hydrodynamics, 6th ed. (Dover, 1932).7.↑ G. Ertl, H. Knözinger, and J. Weitkamp, Handbook of Heterogeneous Catalysis, Vol. 2 (Weinheim:Wiley-VCH, 1997).

8.

↑ 9.0 9.1 Colloids and Surfaces (1990)43,169-194,Pallas,N.R. and Harrison,Y9.↑ A. W. Adamson and A. P. Gast, Physical Chemistry of Surfaces, 6th ed. (Wiley, 1997).10.

Adamson, Arthur W., and Alice P. Gast. 1997. Physical Chemistry of Surfaces, 6th ed. New York:John Wiley. ISBN 0471148733.Savino, Raffaele. 2006. Surface Tension-Driven Flows and Applications. Research Signpost. ISBN8130800659.Venables, John A. 2000. Introduction to Surface and Thin Film Processes. Cambridge, UK:Cambridge University Press. ISBN 0521785006.Zangwill, Andrew. 2001. Physics at Surfaces. Cambridge, UK: Cambridge University Press. ISBN0521347521.

All links retrieved November 14, 2008.

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)[1] (http://www.surface-tension.de/) (Surface tension values.)


10 of 11 10/10/2009 22:50

General subfields within physics

Atomic, molecular, and optical physics | Classical mechanics | Condensed matterphysics | Continuum mechanics | Electromagnetism | General relativity | Particle

physics | Quantum field theory | Quantum mechanics | Special relativity | Statisticalmechanics | Thermodynamics

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordancewith New World Encyclopedia standards. This article abides by terms of the New WorldEncyclopedia:Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminatedwith proper attribution. Credit is due under the terms of this license that can reference both the New WorldEncyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite thisarticle click here (http://www.newworldencyclopedia.org/entry/Special:Cite?page=Surface_tension) for a listof acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchershere:

Surface_tension (http://en.wikipedia.org/w/index.php?title=Surface_tension&oldid=128895510) (May

8, 2007) history (http://en.wikipedia.org/w/index.php?title=Surface_tension&action=history)

Surface_tension_values (http://en.wikipedia.org/w/index.php?title=Surface_tension_values&

oldid=109444551) (May 8, 2007) history (http://en.wikipedia.org/w/index.php?title=Surface_tension_values&

action=history)

Note: Some restrictions may apply to use of individual images which are separately licensed.

Retrieved from http://www.newworldencyclopedia.org/entry/Surface_tensionCategories: Continuum mechanics | Physical sciences | Physics | Physical chemistry | Credited

This page was last modified on 14 November 2008, at 20:52.

Content is available under Creative Commons Attribution/Share-Alike License; additional terms mayapply. See Terms of Use for details.


11 of 11 10/10/2009 22:50

Documents

Physics Definition of Surface Tension