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arXiv · 1901.03754

Stability Results on Radial Porous Media and Hele-Shaw Flows with Variable Viscosity Between Two Moving Interfaces

Craig Gin·Prabir Daripa
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Abstract

We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients and eigenvalue-dependent boundary conditions. We study this eigenvalue problem and find upper bounds on the spectrum. We also give a characterization of the eigenvalues and prescribe a measure for which the eigenfunctions are complete in the corresponding $L^2$ space. The limit as the viscous gradient goes to zero is compared with previous results on multi-layer radial flows. We then numerically compute the eigenvalues and obtain, among other results, optimal profiles within certain classes of functions.

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Craig Gin, Prabir Daripa. 2019-01-11. Stability Results on Radial Porous Media and Hele-Shaw Flows with Variable Viscosity Between Two Moving Interfaces. https://arxiv.org/abs/1901.03754

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