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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...

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Detalles Bibliográficos
Autores principales: Guenneau, S., Puvirajesinghe, T. M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3645418/
https://www.ncbi.nlm.nih.gov/pubmed/23536540
http://dx.doi.org/10.1098/rsif.2013.0106
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author Guenneau, S.
Puvirajesinghe, T. M.
author_facet Guenneau, S.
Puvirajesinghe, T. M.
author_sort Guenneau, S.
collection PubMed
description 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.
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spelling pubmed-36454182013-06-06 Fick's second law transformed: one path to cloaking in mass diffusion Guenneau, S. Puvirajesinghe, T. M. J R Soc Interface Reports 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. The Royal Society 2013-06-06 /pmc/articles/PMC3645418/ /pubmed/23536540 http://dx.doi.org/10.1098/rsif.2013.0106 Text en http://creativecommons.org/licenses/by/3.0/ © 2013 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Reports
Guenneau, S.
Puvirajesinghe, T. M.
Fick's second law transformed: one path to cloaking in mass diffusion
title Fick's second law transformed: one path to cloaking in mass diffusion
title_full Fick's second law transformed: one path to cloaking in mass diffusion
title_fullStr Fick's second law transformed: one path to cloaking in mass diffusion
title_full_unstemmed Fick's second law transformed: one path to cloaking in mass diffusion
title_short Fick's second law transformed: one path to cloaking in mass diffusion
title_sort fick's second law transformed: one path to cloaking in mass diffusion
topic Reports
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3645418/
https://www.ncbi.nlm.nih.gov/pubmed/23536540
http://dx.doi.org/10.1098/rsif.2013.0106
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