Instability and fingering in a rotating Hele–Shaw cell or porous medium

The simplified mathematical model for two‐phase displacement in a Hele–Shaw cell, i.e., slow flow between closely spaced parallel plates, has been extended to include effects arising from a constant rate of rotation of the system. A linear stability analysis for an initially concentric circular drop reveals that it is unstable both to translation and, depending on the rotation rate, to a number of fingering modes. The nonlinear evolution with time of two of these modes is traced using a boundary‐integral numerical scheme. Ultimately, the liquid mass will break up into a number of drops. Apart from small distortion due to the Coriolis force, the patterns formed are essentially independent of both the liquid viscosity and the cell plate spacing or porous‐medium permeability. Potential application areas include certain aspects of coating flows, mold filling, and a class of liquid‐filled spinning projectiles with permeable packing.