Viscous fingering via the Saffman-Taylor instability is perhaps the most well-known and studied
phenomenon among a family of phenomena that exhibit interfacial instabilities. This hydrodynamic instability arises when a fluid displaces another of higher viscosity in the narrow gap separating two flat, parallel glass plates of an experimental device known as Hele-Shaw cell. The interplay of viscous and surface tension forces is responsible for the formation of highly intricate interfacial patterns and is sensitive to noise. A variety of mechanisms have been developed in the past several years to influence the patterning dynamics, including manipulation of the Hele-Shaw cell geometry, usage of elastic-walled cells, and time-dependent injection fluxes and gap widths. In this talk, we use mathematical modeling and computer simulations to investigate how electro-osmotic flows generated by external electric fields affect the patterning morphologies. In particular, our nonlinear results reveal that electro-osmotic flows can oppose or assist the pressure-driven flow. Positive currents restrain shape ramification and promote the overall stabilization of patterns. On the other hand, negative currents make the interface more unstable and promote ramification. Our study paves the way for other explorations that exploit the rich physics behind “multi-field” driven interfacial dynamics.
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