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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2013
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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. |
format | Online Article Text |
id | pubmed-3645418 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT guenneaus fickssecondlawtransformedonepathtocloakinginmassdiffusion AT puvirajesinghetm fickssecondlawtransformedonepathtocloakinginmassdiffusion |