Dynamics of Forced Imbibition in Interacting Pores

Imbibition of viscous fluids in capillaries is important in diagnostics, design of microfluidic devices and enhanced oil recovery. The imbibition of a viscous wetting fluid in a capillary follows Lucas-Washburn law. The Lucas-Washburn regime is only observed when the viscous forces are balanced by the capillary forces. This has been previously described for capillary driven flow as a function of the Ohnesorge number (Oh), the length imbibed by the fluid (x) and the radius (r), for a capillary initially filled with fluid of negligible viscosity, i.e., Ohxr∼1. We show using VOF simulations that, in a capillary of length L initially filled with a viscous fluid, the modified Lucas-Washburn law is observed only if the criterion OhLr∼1 is fulfilled. We use VOF simulations to show the deviation of capillary driven flow from the classical Lucas-Washburn behavior for OhLr∼0.1. VOF simulations for forced imbibition in the regime preceding the Lucas-Washburn regime for a single capillary show that with increase in the applied pressure, the advancement of the meniscus is faster. Forced imbibition dynamics in the interacting capillary geometry are also investigated in this study using VOF simulations. We observe that the leading meniscus in the interacting capillaries is significantly dependent on the applied pressures. We also show using VOF simulations that the wettability of the imbibing fluid plays a crucial role in determining the dynamics in an interacting capillary system.