Numerical simulation of an off-centered fluid drop in a rotating Hele-Shaw cell

In standard rotating Hele-Shaw cell flows, an initially circular fluid drop, surrounded by an outer fluid of negligible density and viscosity, is centered at the rotation axis of the cell. The interplay of centrifugal and surface tension forces leads to the emergence of intricate interfacial patterns, markedly characterized by intense competition among the inward-moving fingers of the outer fluid as they penetrate the inner one. In this work, we study a variation of this traditional rotating flow problem, considering that the center of the initially circular drop is at a distance d from the cell's rotation axis. We explore this off-centered situation by employing numerical simulations based on the level set method. Our numerical results show that, at fully nonlinear stages of the flow, the off-center parameter d plays a key role in determining the morphology and dynamic competition among fingers, leading to the development of asymmetric interfacial patterns that drift away from the rotation axis of the cell. The impact of the effective surface tension parameter B (measure of the relative strength of centrifugal and capillary effects) on the main features of these complex, centrifugally driven translating patterns is also discussed.