Gradient-field-dependent transformation theory: Metamaterial cloaks of non-Newtonian fluids
Phys. Rev. Applied 23, 064007 – Published 4 June, 2025
DOI: https://doi.org/10.1103/g7zs-6gxz
Abstract
The control of fluids is a crucial aspect of modern engineering, where hydrodynamic metamaterials have emerged as transformative solutions for flow manipulation. However, until now, the design of hydrodynamic metamaterials has been limited to Newtonian fluids, lacking exploration of non-Newtonian fluids. In this study, we explore cloak designs for power-law and Bingham fluids within a Hele-Shaw cell using transformation theory. We establish a generalized transformation framework enabling anisotropic and isotropic material cloaks for power-law and Bingham fluids in Hele-Shaw configurations. The derived tensor-invariance conditions reveal unidirectional cloaking capability dictated by a pressure-gradient-orientation dependence. Simulations validate our findings. In contrast to traditional nonlinear transformation theories centered on potential-dependent diffusion systems, our theory extends to gradient-field-dependent scenarios and offers insights into the design of systems across various physical domains.
