A boundary integral method to investigate pattern formation in a rotating Hele-Shaw cell with time dependent gap. (15th July 2022) - Barua, Amlan K.
Abstract: In this article we present a spectrally accurate boundary integral method to investigate the evolution of a Hele Shaw blob in a rotating, radial cell with time dependent gap. The blob of the viscous fluid is affected by the shearing forces induced by a changing gap distance, however the rotation also has significant influence on the shape of the blob. Using the method of complex moments, we characterize the solution of the moving boundary problem that models the evolution of the blob and investigate the morphology using linear analysis. The results of the linear analysis indicate the de-stabilizing influence of the rotation. In the numerical methods, we develop a spectrally accurate boundary integral technique to explore the complete nonlinear dynamics of the problem. Using the boundary integral simulations we demonstrate that, for a given strength of surface tension, the rotational effect causes a more complex pattern on the fluid interface that involves the formation of narrow fingers and more splitting of the interface. The effect is more pronounced if the angular speed increases. We also prescribe a method for controlling the viscous fingering using insights from linear analysis. Our numerical simulations validate the proposed controlling mechanism.