The potential energy per unit area of the surface film is called the surface energy.
It can also be described as the amount of work done in increasing the area of the surface film through unity. Thus,
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Assume that sliding wire is free to move on the horizontal U shaped wire frame and a thin film (of soap say) exists as shown. If we do not exert any force in -ve x direction the sliding wire would be pulled up by the film by a force = T * 2l = 2 T l .(2L because there are two surfaces exerting surface tension)
Now let us consider that we pull it by a constant force
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= 2Tl by a distance 'x' then work completed by this force
= 2Tlx. So increase in energy of this film = 2Tlx = TA ( A = 2lx)
Hence 'A' is the increased area of this film
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(A) Angle of Contact: The angle which the tangent to the liquid surface at the point of contact makes with the solid surface inside the liquid is called angle of contact. Those liquids which wet the walls of the container (say in case of water and glass) have meniscus concave upwards and their value of angle of contact is less than 90° (also called acute angle).
However, those liquids which don't wet the walls of the container (say in case of mercury and glass) have meniscus convex upwards and their value of angle of contact is greater than 90° (also called obtuse angle).
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The angle of contact of mercury with glass about 140°, whereas the angle of contact of water with glass is about 8°. But, for pure water, the angle of contact with glass is taken as 0°, therefore in a glass tube; the meniscus of water will be exactly hemispherical.
Case I: When θ < 90°:
The liquid surface curves up towards the solid. This occurred when the force of cohesion between two liquid molecules is less than force of adhesion between the liquid and the materials. If such a liquid is converted into a solid tube, it can have a concave meniscus.
Case II: When θ > 90°:
The liquids surfaces get curved downward in contact with a solid. In that type the force of cohesion is bigger than the force of adhesion. In such types, solids do not take "wet". When such liquids are place into a hard tube, a convex meniscus is obtained.
(B) Capillarity: Before start operating the process of capillarity, let us analyze the difference between the two sides of a curved liquid surface.
A tube of very small bore is known as a capillary (hair-like) tube.
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It is found that when capillary tubes open at both the ends is dipped in a liquid (which wets the walls of the tube), the liquid rises up in the tube [fig.]. On the other hand, when the capillary tube is dipped in a liquid, which does not wet the sides of the tube, the liquid depresses under the free surface of the liquid in the container [Fig.].
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This fall or rise of a liquid in a tube of very fine bore is called capillarity.
It has been seen that the extent to which a liquid rises or depresses depends upon the radius of the bore of the glass. The smaller the bore of the tube, the larger is the rise or fall of the liquid in the tube.
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Consider a capillary tube open at both ends dipped in a beaker of water as given. The contact angle is acute and is same toq, say. Let T be the surface force for the glass water interface and r the radius of the glass tube.
We have
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,
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It is easy to see that if q > 90° we have a dip rather than rise.
The free surface of a liquid always has a tendency to contract and possess minimum surface area. If we want to increase the surface area of the liquid, work has to be completed. This work done is saved in the surface film of the liquid as its potential energy.
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