Radial viscous fingering: wetting film effects on pattern-forming mechanisms

We consider the interfacial motion between two immiscible viscous fluids in the confined geometry of a radial Hele-Shaw cell. In this framework, we investigate the influence of a thin wetting film trailing behind the displaced fluid on the linear and weakly nonlinear dynamics of the system. More specifically, we examine how the interface instability and the pattern formation mechanisms of finger tip splitting and finger competition are affected by the presence of such a film in the low capillary number limit. Our theoretical analysis is carried out by employing a mode-coupling theory, which allows analytic assess to wetting-induced changes in pattern morphology at the onset of nonlinearities.