Design of Metamaterials for Mass Diffusion

In recent years it has been proved that Fick’s law of diffusion is invariant under coordinate transformations therefore this theory can be used to design metamaterials to control mass diffusion. The main limitation of the Fick’s law approach is that the concentration gradient is considered as the driving force rather than the chemical potential, which governs mass transport. As a result, an implicit assumption is that the solubility of the diffusing species is constant throughout the system. This assumption is not applicable to heterogeneous systems, thus imposing additional constraints in the design of mass diffusion metamaterials. In this work we discuss how general metamaterial theory and effective medium formulations based on the chemical potential allows for the relaxation of constant solubility assumptions enabling the use of materials with different solubilities in mass diffusion metamaterials. By using this novel formulation it is possible to design metamaterials that simultaneously control the diffusion of several chemical species independently. Our results show that the use of a general metamaterials theory can enhance membrane-based separations in chemical and biochemical processes with improvements in performance orders of magnitude larger than standard membranes.