| Abstract: |
| In this talk, 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 boundary integral method where a coupled integral equation system is formulated. Our nonlinear results reveal that positive currents restrain finger ramification and promote 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 flux 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. |
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