Capillary action

Capillary Action:

A tube having a very fine bore ( ~ 1 mm) and open at both ends is called a capillary tube. If one end of a capillary tube is dipped in a liquid which partially or completely wets the surface of the capillary the level of liquid in the capillary rises. On the other hand, if the capillary tube is dipped in a liquid which does not wet its surface the level of liquid in the capillary drops. The phenomenon of rise or fall of a liquid inside a capillary tube when it is dipped in the liquid is called capillarity.

Capillarity is in action when

• Oil rises up the wick of a lamp

• Cloth rag sucks water

• Water rises up the crevices in rocks

• Sap and water rise up to the top most leaves in a tree

• Blotting paper absorbs ink

When a capillary is dipped in a liquid, two effects can be observed,

a) The liquid level can rise in the capillary (water in a glass capillary),

b) The liquid level can fall in the capillary (mercury in glass capillary).

a) Capillary fall:

Consider a capillary tube dipped in a liquid which does not wet the surface, for example, in mercury. The shape of mercury meniscus in the capillary is upper convex. Consider the points A, B, C, and D such that

i) Point A is just above the convex surface and inside the capillary

ii) Point B is just below the convex surface inside the capillary

iii) Point C is just above the plane surface outside the capillary

iv) Point D is just below the plane surface and outside the capillary, and below the point C. 

Let pA, pB, pC, and pD be the values of the pressures at the points A, B, C, and D respectively. As discussed previously, the pressure on the concave side is always greater than that on the convex side. As the points A and C are at the same level, the pressure at both these points is the same, and it is the atmospheric pressure.

pA = pC

Between the points C and D, the surface is plane.

pC = pD = pA

pB > pD

But the points B and D are at the same horizontal level. Thus, in order to maintain the same pressure, the mercury in the capillary rushes out of the capillary. Because of this, there is a drop in the level of mercury inside the capillary as shown in the figure.

Capillary rise: 

This follows the same explanation as above in reverse.

Expression for capillary rise or fall:

a) Method (I): Using pressure difference:

The above equation gives the expression for capillary rise (or fall) for a liquid. Narrower the tube, the greater is the height to which the liquid rises (or falls). 

b) (Method II): Using forces: