Capillary pressure formulas are derived from the pressure relationship between two fluid phases in a capillary tube in equilibrium, which is that force up = force down. These forces are described as:
These forces can be described by the interfacial tension and contact angle of the fluids, and the radius of the capillary tube. An interesting phenomena, capillary rise of water (as pictured to the right) provides a good example of how these properties come together to drive flow through a capillary tube and how these properties are measured in a system. There are two general equations that describe the force up and force down relationship of two fluids in equilibrium.
The Young–Laplace equation is the force up description of capillary pressure, and the most commonly used variation of the capillary pressure equation:
where:
: is the interfacial tension
: is the effective radius of the interface
: is the wetting angle of the liquid on the surface of the capillary
The force down formula for capillary pressure is seen as:
where:
: is the height of the capillary rise
: is the density gradient of the wetting phase
: is the density gradient of the non-wetting phase