Finger competition in lifting Hele-Shaw flows with a yield stress fluid.

A weakly nonlinear approach is used to investigate interfacial pattern formation in a lifting Hele-Shaw cell containing a yield stress fluid surrounded by a fluid of negligible viscosity. By considering the onset of nonlinear effects and the regime in which viscous effects dominate over yield stress, we study how the system responds to changes in two controlling dimensionless parameters: (i) the geometric aspect ratio (ratio of the initially circular radius of the fluid-fluid interface to the initial Hele-Shaw cell plate spacing), and (ii) a yield stress parameter (relative measure of yield stress to viscous forces). Within this context, we discuss how these key factors influence interface stability and finger competition dynamics during early linear and intermediate stages of pattern evolution.