Reinterpreting diffusive constraints: Concentration cloaking via homogenization and pseudoconformal mapping.

Abstract

The manipulation of mass diffusion is crucial for applications spanning biotechnology to chemical engineering. However, established methods for designing diffusion metadevices are often constrained by high background diffusivity, inherent anisotropy, or implementation complexity. Here we present a unified theoretical framework for isotropic mass diffusion control that bridges transformation optics and convective transport. By applying homogenization theory to established convection-enhanced diffusion mechanisms, we demonstrate that a rotating fluid core effectively emulates the behavior of a near-zero-index medium in optics and thermotics. By combining this effective description with pseudoconformal mapping, we design an isotropic concentration cloak that remains applicable even in high-diffusivity environments. Numerical simulations validate that the cloak maintains robust performance for arbitrary target shapes in high-diffusivity regimes. Notably, the cloaked region remains sensitive to the external environment, allowing the internal concentration to track background changes in real time. A feasible experimental suggestion using perforated structures is also proposed. This work provides a diffusion-based reinterpretation of near-zero-index-inspired concepts and a synthesis of fluid mechanics and pseudoconformal mapping, offering a unified and practically accessible framework for engineering diffusive fields.