In fluid statics, capillary pressure () is the pressure between two immiscible fluids in a thin tube (see capillary action), resulting from the interactions of forces between the fluids and solid walls of the tube. Capillary pressure can serve as both an opposing or driving force for fluid transport and is a significant property for research and industrial purposes (namely microfluidic design and oil extraction from porous rock). It is also observed in natural phenomena. Definition Capillary pressure is defined as: where: is the capillary pressure is the pressure of the non-wetting phase is the pressure of the wetting phase The wetting phase is identified by its ability to preferentially diffuse across the capillary walls before the non-wetting phase. The "wettability" of a fluid depends on its surface tension, the forces that drive a fluid's tendency to take up the minimal amount of space possible, and it is determined by the contact angle of the fluid. A fluid's "wettability" can be controlled by varying capillary surface properties (e.g. roughness, hydrophilicity). However, in oil-water systems, water is typically the wetting phase, while for gas-oil systems, oil is typically the non-wetting phase. Regardless of the system, a pressure difference arises at the resulting curved interface between the two fluids. Equations 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