| Abstract: | We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw
cell subject to an in-plane applied electric field. We develop a spectrally accurate numerical method for solving a coupled integral equation system. Although the stiffness
due to the high order spatial derivatives can be removed using a small scale decomposition technique, the long-time simulation is still expensive since the evolving velocity of the interface drops dramatically as the interface expands. We remove this
physically imposed stiffness by employing a rescaling scheme, which accelerates the
slow dynamics and reduces the computational cost. Our nonlinear results reveal that
positive currents restrain finger ramification and promote the overall stabilization of
patterns. On the other hand, negative currents make the interface more unstable and
lead to the formation of thin tail structures connecting the fingers and a small inner
region. When no fluid is injected, and a negative current is utilized, the interface tends
to approach the origin and break up into several drops. We investigate the temporal
evolution of the smallest distance between the interface and the origin and find that it
obeys an algebraic law $(t_??t)^b,$ where $t_?$ is the estimated pinch-off time. |
