Fick's second law transformed: one path to cloaking in mass diffusion
Open Access
- 6 June 2013
- journal article
- research article
- Published by The Royal Society in Journal of The Royal Society Interface
- Vol. 10 (83), 20130106
- https://doi.org/10.1098/rsif.2013.0106
Abstract
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 multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.Keywords
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