  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.
