# Capillary pressure

Capillary pressure refers to the deviation in pressure across the interface between two immiscible fluids. The difference in pressure varies proportionately with the surface tension and is inversely proportional to the effective radius of the interface. It also depends upon the wetting angle of the liquid that is on the surface of the capillary.

## The 'wetting' characteristics of liquids

A liquid has a tendency to wet the surface of a solid if the molecules of the liquid have a stronger attraction to the molecules of the solid. The wetting characteristics of a liquid can be quantified by measuring the angle of contact of a drop of liquid that is placed on the surface of an object. The wetting characteristics of a liquid also determine the fact whether it can penetrate a void in a solid and fill it.

## Equation of capillary pressure

The equation of capillary pressure is given by the following expression:

pc = (2γcosθ)/r

where

• pc stands for capillary pressure,
• γ stands for surface tension of the liquid,
• θ stands for the wetting angle of the liquid against the capillary through which it rises,
• r stands for the effective radius of the interface.

The capillary pressure can be denoted as pc = pg – pw , in case one of the phase is gaseous with pressure of pg and the other is water with its pressure being pw.

The equation for capillary pressure in liquids is valid only under capillary equilibrium. This implies that there is no possibility of flowing phases.

A penetrant liquid will continue to fill a void until there is an opposing force that balances the capillary pressure. The balance in pressure is normally ensured by gas trapped at the void.