Abstract

In this talk, we discuss the recent progress on microscale hydrodynamic cloaking and shielding for electro-osmotic model, which contain single-field cloaking and shielding, enhanced near-cloaking and multi-field cloaking. Based on asymptotic analysis, layer potential techniques and optimal control theory, the core-shell structure contains annulus, confocal ellipses, slightly deformed annulus or confocal ellipses and more general geometry are considered. Especially, the conditions that can ensure the occurrence of above microscale hydrodynamic cloaking and shielding are established. Our theoretical findings are validated and supplemented by a variety of numerical results.