In addition to being manipulated for medical and energy applications, capillary pressure is the cause behind various natural phenomena as well. For example, needle ice, seen in cold soil, occurs via capillary action. The first major contributions to the study of needle ice, or simply, frost heaving were made by Stephen Taber (1929) and Gunnar Beskow (1935), who independently aimed to understand soil freezing. Taber’s initial work was related to understanding how the size of pores within the ground influenced the amount of frost heave. He also discovered that frost heave is favorable for crystal growth and that a gradient of soil moisture tension drives water upward toward the freezing front near the top of the ground. In Beskow’s studies, he defined this soil moisture tension as “capillary pressure” (and soil water as “capillary water”). Beskow determined that the soil type and effective stress on the soil particles influenced frost heave, where effective stress is the sum of pressure from above ground and the capillary pressure.
In 1961, D.H. Everett elaborated on Taber and Beskow’s studies to understand why pore spaces filled with ice continue to experience ice growth. He utilized thermodynamic equilibrium principles, a piston cylinder model for ice growth and the following equation to understand the freezing of water in porous media (directly applicable to the formation of needle ice):
where:
: is the pressure of the solid crystal
: is the pressure in the surrounding liquid
: is the interfacial tension between the solid and the liquid
: is the surface area of the phase boundary
: is the volume of the crystal
: is the mean curvature of the solid/liquid interface
With this equation and model, Everett noted the behavior of water and ice given different pressure conditions at the solid-liquid interface. Everett determined that if the pressure of the ice is equal to the pressure of the liquid underneath the surface, ice growth is unable to continue into the capillary. Thus, with additional heat loss, it is most favorable for water to travel up the capillary and freeze in the top cylinder (as needle ice continues to grow atop itself above the soil surface). As the pressure of the ice increases, a curved interface between the solid and liquid arises and the ice will either melt, or equilibrium will be reestablished so that further heat loss again leads to ice formation. Overall, Everett determined that frost heaving (analogous to the development of needle ice) occurs as a function of the pore size in the soil and the energy at the interface of ice and water. Unfortunately, the downside to Everett's model is that he did not consider soil particle effects on the surface.