Stability of thin liquid films: Theory and application to foam flow in porous media

Foam coalescence in porous media is governed by the behavior of individual lamellae flowing through pores of varying shape. Upon translating moving from a pore body to a pore constriction, a lamella is sequentially stretched and squeezed by the confining wall. Simultaneously, wetting liquid from surrounding pores fills or drains the lamella depending on the difference between the conjoining/disjoining pressure and the local capillary pressure of the porous medium. A hydrodynamic theory describes this process for a single lamella transporting through a sinusoidal pore and yields a periodic steady state for the film thickness.; To determine the dynamic coalescence threshold of the transporting lamella, we present a linear stability analysis about the time periodic base state. The resulting evolution equation for the lamella thickness is solved numerically via the Galerkin finite element method and a generalized eigenvalue problem. Long wavelength disturbances are amplified by the squeezing/filling flow, but are damped by the stretching/draining flow. When film rupture occurs, fascinating patterns of evolution at various capillary pressure levels are observed. Generally, at low capillary pressures moving lamellae tend to rupture at a point near the pore wall while lamellae flowing through media at high capillary pressure rupture closer to the film center.; The stability threshold for the moving lamella is established as a function of capillary number, the pore-body to pore-throat radius ratio, the film aspect ratio, and the conjoining/disjoining pressure isotherm. Successful comparison is made to available measurements of the capillary pressure necessary to initiate coalescence in porous media as a function of the velocity of foam flow.; Foam, emulsion, and pseudoemulsion films stabilized by surfactants above the critical micelle concentration also exhibit pronounced step-wise layer thinning under a constant capillary pressure. Removal of a layer is triggered by the formation and subsequent sheeting of a hole (or holes) at each step of the overall thinning. We present a nonlinear hydrodynamic stability analysis of a homogeneous base state accounting for repulsive double layer, attractive van der Waals, and oscillatory structural components to the disjoining pressure that models the dynamics of hole formation and sheeting.; Nucleation of a hole is attributed to the nonlinear growth of a hydrodynamic instability during film thinning under the action of a constant capillary pressure and an oscillatory disjoining pressure. Subsequent growth or sheeting of the hole is explained by outward fluid flow within the inhomogeneous thin film as radial pressure gradients develop from curvature gradients and viscous resistance to flow. Qualitative comparison is made between the proposed hydrodynamic theory and experimental observations. Numerical results show the correct trends with measured early-time expansion rates.