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We report analytical results for the development of the viscous fingeringinstability in a cylindrical Hele-Shaw cell of radius a and thickness b. Wederive a generalized version of Darcy's law in such cylindrical background, andfind 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 influenceof cell's radius of curvature on the instability characteristics. Linear andslightly nonlinear flow regimes are studied through a mode-coupling analysis.Our analytical results reveal that linear growth rates and finger competitionare inhibited for increasingly larger radius of curvature. The absence oftip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte

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