Rational design of mass diffusion metamaterial concentrators based on coordinate transformations

Recent advances in coordinate transformations of Fick's equation have paved the way for the design of metamaterial devices that can manipulate mass diffusion flux. The control of diffusion paths has a great potential for the design of novel catalytic and separation systems in chemical and biomolecular engineering. In order to explore these new applications, it is necessary to understand mass diffusion in coordinate transformation metamaterial devices. In this work, we present a comprehensive study on the impact of structure and material properties on the resultant physical properties of mass concentrator metamaterial shells. The concentration gradient at the core, the total mass flow rate towards the core, and the disturbance of the external concentration field are systematically examined in order to provide guidelines for the rational design and fabrication of metamaterial mass concentrators. A practical case is also presented where the concentration of oxygen diffusing in a polymeric system is studied.