Fick's second law transformed: one path to cloaking in mass diffusion

Sebastien Guenneau (1) , Tania Puvirajesinghe (2)

1 EPSILON - EPSILON
2 CRCM - Centre de Recherche en Cancérologie de Marseille

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.

Mots clés: cloaking; effective medium; finite elements; mass diffusion

Domaines: Matière Condensée [cond-mat]

Sebastien Guenneau, Tania Puvirajesinghe. Fick's second law transformed: one path to cloaking in mass diffusion. Journal of the Royal Society Interface, 2013, 10 (83), pp.20130106. ⟨10.1098/rsif.2013.0106⟩. ⟨hal-01451387⟩