Capillarity

If molecules of certain liquid possess, relatively, greater affinity for solid molecules, or in other words the liquid has greater adhesion than cohesion, then it will wet a solid surface with which it is in contact and will tend to rise at the point of contact, with the result that the liquid surface is concave upward and the angle of contact θ is less than 90° as shown in Fig. 1. Capillary action is the result of adhesion and surface tension. Adhesion of water to the walls of a vessel will cause an upward force on the liquid at the edges and result in a meniscus which turns upward. The surface tension acts to hold the surface intact, so instead of just the edges moving upward, the whole liquid surface is dragged upward.

For example, if a glass tube of small diameter is partially immersed in water, the water will wet the surface of the tube and it will rise in the tube to some height, above the normal water surface, with the angle of contact θ, being zero. The wetting of solid boundary by liquid results in creating decrease of pressure within the liquid and hence the rise in the liquid surface takes place, so that the pressure within the column at the elevation of the surrounding liquid surface is the same as the pressure at this elevation outside the column.

Fig. 1 Capillarity in Circular Glass Tubes

On the other hand, if for any liquid there is less attraction for solid molecule or in other words the cohesion predominates, then the liquid will not wet the solid surface and the liquid surface will be depressed at the point of contact, with the result that the liquid surface is concave downward and the angle of contact θ is greater than 90° as shown in Fig. 1. For instance, if the same glass tube is now inserted in mercury, since mercury does not wet the solid boundary in contact with it, the level of mercury inside the tube will be lower than the adjacent mercury level, with the angle of contact θ equal to about 130°. The tendency of the liquids which do not adhere to the solid surface, results in creating an increase of pressure across the liquid surface, (as in the case of a drop of liquid). It is because of the increased internal pressure, the elevation of the meniscus (curved liquid surface) in the tube is lowered to the level where the pressure is the same as that in the surrounding liquid.

Such a phenomenon of rise or fall of liquid surface relative to the adjacent general level of liquid is known as capillarity. Accordingly, the rise of liquid surface is designated as capillary rise and the lowering of liquid surface as capillary depression and it is expressed in terms of m or mm of liquid in SI units, in terms of cm or mm of liquid in the metric system of units and in terms of inch or ft of liquid in the English system of units.

The capillary rise (or depression) can be determined by considering the conditions of equilibrium in a circular tube of small diameter inserted in a liquid. It is supposed that the level of liquid has risen (or fallen) by h above (or below) the general liquid surface when a tube of radius r is inserted in the liquid. For the equilibrium of vertical forces acting on the mass of liquid lying above (or below) the general liquid level, the weight of liquid column h (or the total internal pressure in the case of capillary depression) must be balanced by the force, at surface of the liquid, due to surface tension ‘σ’. Thus equating these two forces we have

where ‘w’ is the specific weight of water, ‘s’ is specific gravity of liquid, and ‘θ’ is the contact angle between the liquid and the tube. The expression for ‘h’ the capillary rise (or depression) then becomes

As stated earlier, the contact angle ‘θ’ for water and glass is equal to zero. Thus the value of cos θ is equal to unity and hence h is given by the expression

This equation for capillary rise (or depression) indicates that the smaller the radius r the greater is the capillary rise (or depression). The above obtained expression for the capillary rise (or depression) is based on the assumption that the meniscus or the curved liquid surface is a section of a sphere. This is, true only in case of the tubes of small diameters (r < 2.5 mm) and as the size of the tube becomes larger, the meniscus becomes less spherical and also gravitational forces become more appreciable. Hence such simplified solution for computing the capillary rise (or depression) is possible only for the tubes of small diameters.

However, with increasing diameter of tube, the capillary rise (or depression) becomes much less. It has been observed that for tubes of diameters 6 mm or more the capillary rise (or depression) is negligible. Hence in order to avoid a correction for the effects of capillarity in manometers, used for measuring pressures, a tube of diameter 6 mm or more should be used. Another assumption made in deriving this equation is that the liquids and tube surfaces are extremely clean. In practice, such cleanliness is virtually never encountered and h will be found to be considerably smaller than that given by the above equation.

If a tube of radius r is inserted in mercury (specific gravity s1) above which a liquid of specific gravity s2 lies, then by considering the conditions of equilibrium it can be shown that the capillary depression h is given by

in which ‘σ’ is the surface tension of mercury in contact with the liquid.

Further if two vertical parallel plates ‘t’ distance apart and each of width ‘l’ are held partially immersed in a liquid of surface tension σ and specific gravity ‘s’, then the capillary rise (or depression) ‘h’ may be determined by equating the weight of the liquid column h (or the total internal pressure in the case of capillary depression) (swhlt) to the force due to surface tension (2σl cos θ). Thus we have