Interface conditions for two-phase displacement in Hele-Shaw cells

Abstract

In displacing a viscous fluid from the gap between two closely spaced parallel plates, a thin film of the original fluid remains on the surface of each plate. Boundary conditions which connect the approximate equations in the region in front of the interface with the approximate solutions in the thin-film region are determined from local solutions of the equations in the vicinity of the interface edge. These interface conditions depend on both b/R (gap half-width/radius of curvature) and μUn/T, where μ is the viscosity of the original fluid, Un is the normal velocity of the interface edge, and T is the interfacial tension. These conditions are determined using perturbation method when μUn/T [Lt ] 1 and numerical methods when μUn/T is O(1). Though previous theories have shown qualitative agreement with experiments, it is hoped that these new boundary conditions improve the quantitative agreement.