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