Imagine an imaginary line AB on a liquid surface. The surface on either side of this line exerts a pulling force on the other side, lying in the plane of the surface and perpendicular to AB. The surface tension of the liquid is measured by the force per unit length of AB. If F is the total force on either side of line AB of length l, the surface tension T is given by T=F/l. Hence, surface tension is defined as the force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn in that surface. Its unit is Newton/meter, with dimensions [MT-2].
The value of surface tension depends on the liquid's temperature and the medium on the other side of the surface. It decreases with rising temperature and becomes zero at the critical temperature.
Increasing the surface area of a liquid requires work against the force of attraction among molecules, which is stored as potential energy in the new surface. Additionally, there is cooling due to the increased surface area, so heat from the surroundings is added to maintain constant temperature. This additional energy per unit area of the surface is called surface energy.
Consider a liquid film between a bent wire ABC and a straight, movable wire PQ. As the film tends to contract, PQ moves upward, requiring a downward force F to keep it in equilibrium. F is directly proportional to the length l of the film in contact with PQ. Since there are two free surfaces, F∝2l or F=T×2l, where T is the surface tension.
If PQ is moved downward by a small distance Δx, increasing the film's surface area, the work done by the force F is W = F × Δx = T × 2l × Δx. Since 2l × Δx is the total increase in area (ΔA), W = T × ΔA. Thus, the surface tension T equals the work required to increase the liquid film's surface area by unity at constant temperature, expressed in joules per square meter.
Let us consider a spherical drop of liquid of radius R. If the drop is small, the effect of gravity may be neglected and shape may be assumed to be spherical.
If the pressure just outside the surface is P1 and just inside the surface is P2.
P2 - P1 = 2T/R
The pressure inside the surface is greater than the pressure outside the surface.
Note:
The pressure on the concave side is greater than the pressure on the convex side.
If there is an air bubble inside the liquid as shown in the figure, is single surface is formed. There is air on the concave side and liquid on the convex side. The pressure in the concave side is greater than the pressure in the convex side, by an amount 2T/R.
P2 - P1 = 2T/R
Let the pressure of the air outside the bubble be P1, within the soap solution be P′ and that in the air inside the bubble be P2.
P′ - P1 = 2T/R
Similarly, looking at the inner surface,
P2 - P′ = 2T/R
Adding these two equations,
P2 - P1 = 4T/R
The angle between the tangent to the solid surface and the tangent to the liquid surface at the point of contact is the angle of contact. For liquids that wet the solid, the angle is acute; for those that do not, it is obtuse. For example, pure water and clean glass have an angle of zero, ordinary water and glass have about 8°, and mercury and glass have 135°. For water and silver, it is 90°, keeping the water surface horizontal in a silver vessel.
Explanation:
The phenomenon of capillarity arises due to the surface tension of liquids. When a capillary tube is dipped in water, the water meniscus inside the tube is concave. The pressure just below the meniscus is less than the pressure just above it by 2T/R, where T is the surface tension of water and R is the radius of curvature of meniscus.
The pressure of the surface of water is atmospheric pressure P. The pressure just below plane surface of water outside the tube is also P, but that just below the meniscus inside the tube is P – (2T/R). We know that pressure at all points in the same level of water must be the same.
Therefore, to make up the deficiency of pressure, 2T/R, below the meniscus, water begins to flow from outside into the tube. The rising force water in the capillary stops at a certain height h. In this position the pressure of the water-column of height h becomes equal to 2T/R, that is,
hρg = 2T/R
where ρ is the density of water and g is the acceleration due to gravity. If r be the radius of the capillary tube and θ the angle of contact of water-glass, then the radius of curvature R of the meniscus is given by R = r/cosθ.
∴ hρg = 2T/r/cosθ
or h = 2Tcos θ/rρg
This shows that as r decreases, h increases, that is, narrower the tube, greater is the height to which the liquid rises in the tube.
Rising of liquid in a capillary tube of insufficient length:
Suppose a liquid of density ρ and surface tension T rises in a capillary tube to a height h.
Then hρg = 2T/R
where R is the radius of curvature of the liquid meniscus in the tube. From this we may write
hR = 2T/ρg = constant (for a given liquid)
When the length of the tube is greater than h, the liquid rises in the tube to a height so as to satisfy the above relation. But if the length of the tube is less than h, say h′, then the liquid rise up to the top of the tube and then spreads out until its radius of curvature R increases to R′, such that h′R′ = hR = 2T/ρg
It is clear that liquid cannot emerge in the form of a fountain from the upper end of a short capillary tube.
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1. What is surface tension? |
2. How is surface tension related to surface energy? |
3. How does surface tension affect the work done in increasing surface area? |
4. What is excess pressure inside a drop and how is it related to surface tension? |
5. How does the angle of contact affect capillarity? |
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