Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow

7kg (or dry) soil sample, then the capillary pressure is in(m s) 1 . In addition, recently developed pore-scale models that simulate interface dynamics within a network of pores can also be used creased (or decreased) incrementally, and at each step to estimate the appropriate dynamic coefficients. Analyses of experi- the water content is measured after equilibrium is ments reported in the literature, and of simulations based on pore- reached. The time to equilibrium after each imposed scale models, indicate a range of dynamic coefficients that spans about pressure increment ranges from a few hours to many three orders of magnitude. To examine whether these coefficients days, depending on the soil type and saturation degree have any practical effects on larger-scale problems, continuum-scale (see, e.g., Elrick, 1963; Stephens, 1995, p. 189). The simulators may be constructed in which the dynamic effects are in- typical time needed to construct a complete capillary cluded. These simulators may then be run to determine the range of pressure–saturation curve is weeks or longer. Now, the coefficients for which discernable effects occur. Results from such question arises whether such curves adequately describe simulations indicate that measured values of dynamic coefficients are the relationship between P n –P w and S in drainage or within one order of magnitude of those values that produce significant effects in field simulations. This indicates that dynamic effects may imbibition events with a time scale in the order of hours. be important for some field situations, and numerical simulators for In fact, there is ample theoretical and experimental eviunsaturated flow should generally include the additional term(s) asso- dence that this simple relationship is not unique, but it ciated with dynamic capillary pressure. depends on the flow dynamics—it depends on both the history and the rate of change of saturation. The dependence of capillary pressure–saturation curves on the his