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

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

2002-01-31

arxiv.org/abs/cond-mat/0201589v1

Physical Review E 65, 026303 (2002)

Physics

Condensed Matter

Soft Condensed Matter

14 pages, 3 ps figures, Revtex

Scientific paper

10.1103/PhysRevE.65.026303

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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