Microscale Hydrodynamic Cloaking via Geometry Design in a Depth-Varying Hele-Shaw Cell

We theoretically and numerically demonstrate that hydrodynamic cloaking can be achieved by simply adjusting the geometric depth of a region surrounding an object in microscale flow, rendering the external flow field undisturbed. Using the depth-averaged model, we develop a theoretical framework based on analytical solutions for circular and confocal elliptical cloaks. For cloaks of arbitrary shape, we employ an optimization method to determine the optimal depth profile within the cloaking region. Furthermore, we propose a multi-object hydrodynamic cloak design incorporating neutral inclusion theory. All findings are validated numerically. The presented cloaks feature simpler structures than their metamaterial-based counterparts and offer straightforward fabrication, thus holding significant potential for microfluidic applications.