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 consider...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Royal Society interface 2013-06, Vol.10 (83), p.20130106-20130106
Main Authors: Guenneau, S., Puvirajesinghe, T. M.
Format: Article
Language:English
Subjects:
Anisotropy
Cloaking
Condensed Matter
Effective Medium
Finite Elements
Liposomes - chemistry
Mass Diffusion
Models, Chemical
Physics
Temperature
Thermal Diffusion
Thermodynamics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1742-5689
1742-5662
DOI:10.1098/rsif.2013.0106