2024/04/03 by Hongyu Liu, Liu, Hongyu, Zhi-Qiang Miao +3 · 1 citation
Engineering · Environmental Science · #Analysis of PDEs (math.AP) #Electrohydrodynamics and Fluid Dynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Water-Energy-Food Nexus Studies
paper · pdf · doi:10.48550/arxiv.2404.02773
openalex publication_date 2024/04/03 · openalex created_date 2024/04/06 · openalex updated_date 2026/07/28
In this paper, we develop a general mathematical framework for the electro-osmosis problem to design simultaneous microscale electric and hydrodynamic cloaking in a Hele-Shaw configuration. A novel approach to achieving simultaneously cloaking both the electric and flow fields through a combination of scattering-cancellation technology and an electro-osmosis effect is proposed. In the design, the electric field is manipulated with scattering-cancellation technology while the pressure with electro-osmosis effect. As proof of this concept, the perfect electric and hydrodynamic cloaking conditions are derived for the cloaks with the cross-sectional shape being annulus or confocal ellipses using the layer potential techniques. Furthermore, we also propose an optimization scheme for the design of approximate cloaks within general geometries and prove the well-posedness of the optimization problem. In particular, the conditions that can ensure the simultaneous occurrence of approximate cloaks for general geometries are also established. Our theoretical findings are validated by a variety of numerical results and guide efficiently designing electric-related multiphysics cloaking.