2021/11/04 by Anjos, Pedro H. A., Zhao, Meng, Lowengrub, John +1
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2111.03102
Time-dependent injection strategies are commonly employed to control the number of viscous fingers emerging at the interface separating two fluids during radial displacement in Hele-Shaw flows. Here we demonstrate theoretically that such a usual controlling method is significantly improved by taking advantage of an electro-osmotic flow generated by applying an external electric field. More specifically, under the coupled action of time-varying electric currents and injection rates, we design a strategy capable of controlling not only the number of fingers emerging at the interface but also when (and if) the self-similar evolution occurs. In addition, the level of instability of the n-fold fingered patterns can also be tuned. This improved control over the interfacial features cannot be realized by the sole consideration of a time-varying injection rate. Perturbative second-order mode-coupling analysis and boundary integral simulations confirm that the validity and effectiveness of the controlling protocol go beyond the linear regime.