Surface Tension

The surface tension , or energy of interface , or energy of surface , is the tension which exists with the Surface of separation of two Milieu X.

This effect makes it possible for example the insects to go on water, the dew not to be spread out over the petals of flowers, and explains the Capillarité. The surface tension explains also the formation of the bubbles of soap.

Mechanism

Liquid interface/gas

Within a Fluid (Liquid or Gas), the Molécule S exert between them forces of attraction or repulsion: Force of Van der Waals (attraction), electrostatic Force (attraction or repulsion). One speaks about “intermolecular forces”.

If one considers a pure Substance liquid, composed of only one type of molecules, the molecules attract each other (if not, they would not form a phase). Within the liquid, each molecule is drawn in all the directions by the molecules close to liquid: the resultant of the forces is null.

In the vacuum, a molecule, is on the other hand attracted per nothing. Therefore, at the liquid border/vacuum, the molecules are attracted liquid side but not empty side; the resultant of the forces being exerted on the molecules of surface east thus directed towards the interior of the liquid. This tightens surface.

In the case of a liquid interface/vacuum, it is thus an effect within a liquid which leads surface to become deformed like an elastic membrane.

But it is known that subjected to the vacuum, part of the liquid evaporates (see the article saturating Steam pressure ). If this gas pressure is low, the liquid is subjected to a weak compression, and the molecules of surface are also subjected to a weak attraction on behalf of their pairs of the gas phase; but the density of gas being much lower than that of the liquid, this attraction is negligible.

So now there is another gas above (for example of the air), the phenomenon is similar. The liquid is subjected to the pressure of gas, and the molecules on the surface of the liquid are subjected to attraction or the repulsion on behalf of the molecules of gas. Because of weak density of gas compared to the liquid, one neglects this last contribution in general.

The form of surface thus results from balance between the pressure of gas, attraction by the interior of the liquid, and the Poids if one is in the presence of gravity.

Let us note that the liquid can be in the shape of a film; this film is then subjected to the pressure of gas on the two sides. If the attraction forces within the liquid are weak, the film does not hold. Contrary, if these forces are strong, the film holds well and has an elastic behavior (soap bubble).

Liquid interface/liquid

When two liquids has and B is miscible, it form only one phase. On the other hand, if they are nonmiscible, they form two separate phases.

If they are nonmiscible, it is that the molecules are pushed back. The molecules located at the interface are thus subjected:

• for the molecules of has :
• with an attraction towards the interior of the liquid has ;
• with a repulsion on behalf of the molecules of B ;
• for the molecules of B :
• with an attraction towards the interior of the liquid B ;
• with a repulsion on behalf of the molecules of has .

It is thus seen that the resultant of the forces is located towards the interior of each liquid in all the cases.

The form of the interface is thus determined by

• the attraction forces within the liquids, has / has and B / B ;
• the force of repulsion between has and B ;
• gravity if necessary.

It is the case of the Eau and the Huile, of the Vinaigrette:

• is oil forms a layer above water;
• is oil forms droplets within water (emulsion).

Interface triple: The solid-liquid contact - vapor

One is often in the presence of an interface triples solid/liquid/gas, for example

• drop posed on a solid;
• drop suspended with a solid;
• edge of glass.

Interactions liquid/gas one described above.

In the same way, the molecules of the liquid can be attracted or pushed back by the molecules of the solid. The form of the interface on the level of the triple point thus will be given by:

• the attraction force within the liquid;
• attraction or the repulsion on behalf of the solid;
• pressure of gas, and possibly attraction or the repulsion by gas;
• gravity.

If there is attraction between the liquid and the solid:

• the drop posed on the solid will tend to be spread out;
• the suspended drop will be retained;
• the liquid will go up along glass (meniscus, Capillarité).

If there is repulsion between the liquid and the solid:

• the drop posed on the solid will tend “to gather”, to take a spherical form;
• the suspended drop will fall;
• the liquid will curve upwards.

Compounds make it possible to decrease the surface tension, they are Tensioactif S.

Modeling

The surface tension is measured in newtons per meter (NR·m^-1). It is defined as the force which it is necessary to apply to the unit of length along a line perpendicular to the surface of a liquid in balance to cause the extension of this surface, or like the work exerted by this force per unit of area. The unit of surface tension (NR·m^-1) is equivalent to joules per square meter (J·m^-2), which corresponds to a unit of energy of surface. One can define this energy of interface as being the surplus of energy chemical compared to the case where the molecules of surface would be inside the liquid.

The system tends to minimize the energy of surface.

Nonmiscible liquids

In the case of a drop of a liquid has within a liquid B , energy is minimal when surface is minimal. However the form corresponding to smallest possible surface is a sphere. Therefore the water drops have a circular form.

If two drops meet, they will amalgamate and thus form only one drop (Coalescence), always to minimize the surface tension. Indeed, two spheres of volume $\{V\; \backslash \; over\; 2\}$ have a surface larger than only one sphere of volume V :

a sphere of volume $\{V\; \backslash \; over\; 2\}$a a ray checking $\{V\; \backslash \; over\; 2\}\; =\; \{4\; \backslash \; over\; 3\}\; \backslash \; cdot\; \backslash \; pi\; \backslash \; cdot\; r\_1^3$, R being the ray; surface is thus $4\; \backslash \; cdot\; \backslash \; pi\; \backslash \; cdot\; r\_1^2$, and surfaces it of the two drops

$S\_1\; =\; 8\; \backslash \; cdot\; \backslash \; pi\; \backslash \; cdot\; r\_1^2\; =\; \backslash \; sqrt\; \{8\; \backslash \; cdot\; \backslash \; pi\}\; \backslash \; cdot\; (3\; \backslash \; cdot\; V)\; ^\; \{2\; \backslash \; over\; 3\}\; =\; 2\; \backslash \; cdot\; \backslash \; sqrt\; \{\backslash \; pi\}\; \backslash \; cdot\; (3\; \backslash \; cdot\; V)\; ^\; \{2\; \backslash \; over\; 3\}$

a sphere of volume V has a ray checking $V\; =\; \{4\; \backslash \; over\; 3\}\; \backslash \; cdot\; \backslash \; pi\; \backslash \; cdot\; r\_2^3$, and a surface $4\; \backslash \; cdot\; \backslash \; pi\; \backslash cdot\; r\_2^2$, either

$S\_2\; =\; 4\; \backslash \; cdot\; \backslash \; pi\; \backslash \; cdot\; r\_2^2\; =\; \backslash \; sqrt\; \{4\; \backslash \; cdot\; \backslash \; pi\}\; \backslash \; cdot\; (3\; \backslash \; cdot\; V)\; ^\; \{2\; \backslash \; over\; 3\}$

or

$S\_2\; =\; \backslash \; sqrt\; \{2\}\; \backslash \; cdot\; S\_1$

In this case, the total energy of the interface depends only on the surface of the interface. If one calls σ the surface tension (density of energy of surface), then energy necessary to create the interface is:

W_S = σ· S .

Liquid on a solid

If the energy of interface between a solid and a liquid is strong, then the liquid is not spread out and remains in the form of droplet.

Experiments

A certain number of simple experiments make it possible to highlight the surface tension

• Ménisque of water in glass: when one puts water in glass, water goes up approximately millimetre along the wall; this is particularly visible in the case of test a Tube (approximately 1 cm diameter); or, contrary, one can make exceed the water surface of the edge of glass without it not running out apart from this one.
• drop which hangs without falling: it is the surface tension which retains the drop with the support; the mass of the drop which falls from a account-drop is given by the Loi of Touches
• propulsion with oil or the soap;
• a liquid can go up in a fine tube: Law of Jurin
• fountain of Soda: in a soda, the molecules of the Carbonic gas dissolves are solvatées, the molecules of water form a shield around CO₂; if the bottle is shaken, one overcomes the surface tension of the shield and the molecules of CO₂ gather to form bubbles; or by using a powder, the small grains lower the surface tension, one can for example put Chewing-gum S (see also Menthos fountain).
• milk psychedelic - to see the experiment in video on Wikidébrouillard

Values

The following values drawn from are duplicated from Broch:

• Water
• 0 °C: σ = 7,6·10^-2 NR·m^-1;
• 20 °C: σ = 7,3·10^-2 NR·m^-1;
• 37 °C : σ = 7,0·10^-2 NR·m^-1;
• Blood plasma, 37 °C: σ = 7,3·10^-2 NR·m^-1;
• water + Surfactant pulmonary: 2,5·10^-2 NR·m^-1;
• mercury, 20 °C: σ = 4,36·10^-1 NR·m^-1.

Source: Flow Science Inc.

• water + oil with 20 °C: σ = 2,0·10^-2 NR·m^-1;

See too

Related articles

• Effect lotus

• Gerridés (Spider of water)
• Law of pulmonary Laplace
• Surfactant

External bonds

• surface Tension: drops, capillarity, bubbles and superfusion

• Duplicated of mechanics of the fluids, Henri Broch, p.13

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