Viscous fingering patterns for Hele-Shaw flow in a doubly connected geometry driven by a pressure differential or rotation

Viscous fingering patterns that occur at the interface between two immiscible fluids of differing viscosities in a Hele-Shaw cell are normally studied mathematically via nonlinear moving boundary problem with single interface. Here we study more realistic model which involves doubly connected region viscous fluid bounded by interfaces. We simulate this numerically using level set method, supported linear stability analysis and some experiments. Various results presented for configurations flow is driven either pressure difference or rotating entire cell.