Effects of Inertia, Rarefaction, and Reaction on Viscous Fingering

by Andong He (Nordita)

Wednesday 26 Sept 2012, 13:30 → 14:30 Europe/Stockholm

Nordita Astrophysics Seminar Room

Viscous fingering is an interfacial instability occurring in a Hele-Shaw cell when a less viscous fluid displaces a more viscous one. We investigate the effects of inertia and rarefaction of the flow, which are represented by the generalized Darcy’s equation and the boundary conditions. We apply a conformal-mapping method to transform the moving-free boundary problem into solving a differential equation in a fixed domain. A linear stability analysis shows that fluid inertia and rarefaction have a stabilizing effect. We also consider two fluids meeting and reacting in a Hele-Shaw cell. This reaction changes the local interfacial tension which dictates the stability of the interface. We treat the interface as an elastic membrane whose bending stiffness depends on the curvature. A dispersion relation is derived from the energy variation method. Our model can explain the occurrence of an anomalous fingering instability observed experimentally