Enhanced microscale hydrodynamic near-cloaking using electro-osmosis

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the relationship of shapes is quantified more accurately by recursive formulas. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking. Additionally, the concept of cloaking has efficient applications in the field of microfluidics, including drag reduction, microfluidic manipulation, and biological tissue coculture.