Fick's Second Law Transformed: One Path to Cloaking in Mass Diffusion

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example in fluids. This theory is illustrated with finite element computations for a liposome particle surrounded by a cylindrical multilayered cloak in a water-based environment, and for a spherical multilayered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bio-engineering.