A simple derivation of an upper bound in the presence of a viscosity gradient in three-layer Hele-Shaw flows
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An upper bound on the growth rate of disturbances in three-layer Hele-Shaw flows with the middle layer having a smooth viscous profile is obtained using a weak formulation of the disturbance equations. A recently reported approach for the derivation of this bound is tedious, cumbersome, and requires numerical analysis. In contrast, the present approach is very simple, elegant, and requires no numerical analysis. The interpretation and limiting cases of this bound are also addressed in this paper. © IOP Publishing Ltd.
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