At the pore scale, the interface separating one fluid patch from the next is a series of meniscii. Roughness on the grain surfaces keeps the contact lines of these meniscii pinned to the grain surfaces. Pride and Flekkoy (1999) argue that the contact lines of an air-water meniscus will remain pinned for fluid-pressure changes less than roughly 104 Pa which correspond to the pressure range induced by linear seismic waves. So as a wave passes, the meniscii will bulge and change shape but will not migrate away. This makes the problem vastly more simple to analyze theoretically.
One porous-continuum boundary condition is that all fluid volume that locally enters the interface from one side, must exit the other side so that (). Another boundary condition is that the difference in the rate at which energy is entering and leaving the interface is entirely due to the work performed in changing the miniscii surface area. Before the wave arrives, each miniscus has an initial mean curvature Ho fixed by the static fluid pressures initially present; where is the surface tension. During wave passage, one can demonstrate (Pride and Flekkoy, 1999) that the mean curvature changes as where H1 is of the same order as Ho and where is a dimensionless number called the capillary number. The capillary number is defined where is some estimate of the wave-induced Darcy flux and that is thus bounded as the wave strain times phase velocity; i.e., m/s. For typical interfaces (like air and water), we have Pa m and Pa s. Thus, for linear wave problems, and can be considered a very small number.
Writing the fluid pressures as and using the fact that is continuous, allows the conservation of energy at the interface to be expressed