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Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell

Jose A. Miranda
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Abstract

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.

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Jose A. Miranda. 2002-01-31. Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell. https://doi.org/10.1103/physreve.65.026303

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