# Surface tension

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Surface tension

:"For the work of fiction, see Surface Tension (short story)."Surface tension is a property of the surface of a liquid that causes it to behave as an elastic sheet. It allows insects, such as the water strider (pond skater, UK), to walk on water. It allows small objects, even metal ones such as needles, razor blades, or foil fragments, to float on the surface of water, and it is the cause of capillary action. An everyday observation of surface tension is the formation of water droplets on various surfaces or raindrops.

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 with another substance.

Applying Newtonian physics to the forces that arise due to surface tension accurately predicts many liquid behaviors that are so commonplace that most people take them for granted. Applying thermodynamics to those same forces further predicts other more subtle liquid behaviors.

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.

Cause

Surface tension is caused by the attraction between the liquid's molecules by various intermolecular forces. In the bulk of the liquid, each molecule is pulled equally in all directions by neighbouring liquid 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 and are not attracted 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 subject to an inward force of molecular attraction which is balanced only by the liquid's resistance to compression, meaning there is no net inward force. However, there is a driving force to diminish the surface area, and in this respect a liquid surface resembles a stretched elastic membrane. Thus the liquid squeezes itself together until it has the locally lowest surface area possible.

Another way to view it is that a molecule in contact with a neighbour is in a lower state of energy than if it wasn't in contact with a neighbour. The interior molecules all have as many neighbours as they can possibly have. But the boundary molecules have fewer neighbours 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 must therefore minimize its surface area.cite book|last=White|first=Harvey E.|title=Modern College Physics|publisher=van Nostrand|year=1948|isbn=0442294018]

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. Consequently 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

Where the two surfaces meet, they form a contact angle, $scriptstyle heta$, 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, $scriptstyle gamma_\left\{mathrm\left\{ls - gamma_\left\{mathrm\left\{sa$, is less than the liquid-air surface tension, $scriptstyle gamma_\left\{mathrm\left\{la$, but is nevertheless positive, that is

:$gamma_\left\{mathrm\left\{la > gamma_\left\{mathrm\left\{ls - gamma_\left\{mathrm\left\{sa > 0$

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point. The horizontal component of $scriptstyle f_mathrm\left\{la\right\}$ is canceled by the adhesive force, $scriptstyle f_mathrm\left\{A\right\}$.

:$f_mathrm\left\{A\right\} = f_mathrm\left\{la\right\} sin heta$

The more telling balance of forces, though, is in the vertical direction. The vertical component of $scriptstyle f_mathrm\left\{la\right\}$ must exactly cancel the force, $scriptstyle f_mathrm\left\{ls\right\}$.

:$f_mathrm\left\{ls\right\} - f_mathrm\left\{sa\right\} = -f_mathrm\left\{la\right\} cos heta$

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

:$gamma_mathrm\left\{ls\right\} - gamma_mathrm\left\{sa\right\} = -gamma_mathrm\left\{la\right\} cos heta$

where:* $scriptstyle gamma_mathrm\left\{ls\right\}$ is the liquid-solid surface tension,:* $scriptstyle gamma_mathrm\left\{la\right\}$ is the liquid-air surface tension,:* $scriptstyle gamma_mathrm\left\{sa\right\}$ is the solid-air surface tension,:* $scriptstyle heta$ 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°.Sears, Francis Weston; Zemanski, Mark W. "University Physics 2nd ed." Addison Wesley 1955]

This means that although the difference between the liquid-solid and solid-air surface tension, $scriptstyle gamma_mathrm\left\{ls\right\} - gamma_mathrm\left\{sa\right\}$, is difficult to measure directly, it can be inferred from the easily measured contact angle, $scriptstyle heta$, if the liquid-air surface tension, $scriptstyle gamma_mathrm\left\{la\right\}$, is known.

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:

:$gamma_mathrm\left\{la\right\} > 0 > gamma_mathrm\left\{ls\right\} - gamma_mathrm\left\{sa\right\}$

pecial contact angles

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. Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.

:$gamma_\left\{mathrm\left\{la = gamma_\left\{mathrm\left\{ls - gamma_mathrm\left\{sa\right\} > 0qquad heta = 180^circ$

Methods of measurement

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimum 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.
* A miniaturized 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.cite web|url=http://www.ksvinc.com/surface_tension1.htm|title=Surface and Interfacial Tension|accessdate=2007-09-08|publisher=Langmuir-Blodgett Instruments]

* 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.

* 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.cite web|url=http://lauda.de/hosting/lauda/webres.nsf/urlnames/graphics_tvt2/\$file/Tensio-dyn-meth-e.pdf|title=Surfacants at interfaces|accessdate=2007-09-08|publisher=lauda.de]

* 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.cite web|url=http://mysite.du.edu/~jcalvert/phys/surftens.htm|title=Surface Tension (physics lecture notes)|author=Calvert, James B.|accessdate=2007-09-08|publisher=University of Denver]

* 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).cite web|url=http://www.dataphysics.de/english/messmeth_sessil.htm|title=Sessile Drop Method|accessdate=2007-09-08|publisher=Dataphysics]

Effects

Liquid in a vertical tube

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Toricelli'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.

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 aggressively 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.

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:

::$h = frac \left\{2gamma_mathrm\left\{la\right\} cos heta\right\}\left\{ ho g r\right\}$

where

:* $scriptstyle h$ is the height the liquid is lifted,:* $scriptstyle gamma_mathrm\left\{la\right\}$ is the liquid-air surface tension,:* $scriptstyle ho$ is the density of the liquid,:* $scriptstyle r$ is the radius of the capillary,:* $scriptstyle g$ is the acceleration due to gravity,:* $scriptstyle heta$ is the angle of contact described above. Note that if $scriptstyle heta$ is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.

Puddles on a surface

thumb|374px|right|Profile curve of the edge of a puddle where the contact angle is 180°. The curve is given by the formula">:$scriptstyle x - x_0 = frac \left\{1\right\} \left\{2\right\} H cosh^\left\{-1\right\}left\left(frac \left\{H\right\}\left\{h\right\} ight\right) - H sqrt\left\{1 - frac\left\{h^2\right\} \left\{H^2$ where $scriptstyle H = 2 sqrt\left\{frac \left\{gamma\right\} \left\{g ho$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 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, but only on a surface made of 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 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:cite book|title=Capillary and Wetting Phenomena -- Drops, Bubbles, Pearls, Waves|author=Pierre-Gilles de Gennes, Françoise Brochard-Wyart, David Quéré|publisher=Springer|year=2002|translator=Alex Reisinger|isbn=0-387-00592-7]

::$h = 2 sqrt\left\{frac\left\{gamma\right\} \left\{g ho$

where

:

* Anti-fog
* Capillary wave &ndash; short waves on a water surface, governed by surface tension and inertia
* Cheerio effect &ndash; the tendency for small wettable floating objects to attract one another.
* Dortmund Data Bank &ndash; contains experimental temperature-dependent surface tensions.
* Eötvös rule &ndash; a rule for predicting surface tension dependent on temperature.
* Electrowetting
* Electrodipping force
* Hydrostatic Equilibrium &ndash; the effect of gravity pulling matter into a round shape.
* Meniscus &ndash; surface curvature formed by a liquid in a container.
* Mercury beating heart &ndash; a consequence of inhomogeneous surface tension.
* Specific surface energy &ndash; same as surface tension in isotropic materials.
* Surface tension values
* Sessile drop technique
* Surfactants &ndash; substances which reduce surface tension.
* Tears of wine &ndash; the surface tension induced phenomenon seen on the sides of glasses containing alcoholic beverages.
* Tolman length &ndash; leading term in correcting the surface tension for curved surfaces.
* Wetting and dewetting
* James Blish, author of the short story "Surface Tension" (1957).
* Weber number

References

* [http://www.ramehart.com/goniometers/surface_tension.htm Concise overview of surface tension]
* [http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html On surface tension and interesting real-world cases]
* [http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/ MIT Lecture Notes on Surface Tension]
* [http://www.kruss.info/techniques/surface_tension_e.html Theory of surface tension measurements]
* [http://www.kayelaby.npl.co.uk/general_physics/2_2/2_2_5.html Surface Tensions of Various Liquids]
* [http://www.scientistlive.com/elab/20061201/analyticallab-equipment/2.1.282.286/16974/understanding-the-interaction-between-gases-and-liquids.thtml Understanding the interaction between gases and liquids] Scientist Live

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### Look at other dictionaries:

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