Saffman-Taylor problem on a sphere - art. no. 036307

The Saffman-Taylor problem addresses the morphological instability of an in terface separating two immiscible, viscous fluids when they move in a narro w gap between two flat parallel plates (Hele-Shaw cell). In this work, we e xtend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface pertur bation amplitudes and study both linear and nonlinear flow regimes. The eff ect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger ti p-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.