Nonlinear effects due to gravity in a conical Hele-Shaw cell.

In this work we study the viscous fingering instability in a conical Hele-Shaw cell under the presence of gravity. We focus on understanding how the dynamical evolution of the fingering patterns is affected by the combined action of gravity and cell topology. Gravity-induced nonlinear effects are studied by a mode-coupling approach. Our results show that the interplay between gravity and cell topology leads to important effects, and profoundly modifies pattern evolution. We have found that the most dramatic consequences refer to finger tip behavior. Depending on the relative values of fluids' densities and viscosities, finger tip splitting reaches maximum intensity at well defined, preferred values of the cell opening angle. In fact, finger tip splitting can be completely replaced by finger tip sharpening as the cell angle is varied. Finger competition dynamics is also significantly changed: it is considerably enhanced (restrained) if the displaced fluid is more (less) dense.