title: Fick's second law transformed: one path to cloaking in mass diffusion.
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.
authors.affiliation: Institut Fresnel, UMR CNRS 7249, Aix Marseille Université, Campus de St Jérôme, Marseille Cedex 20, France. guenneau@liverpool.ac.uk
authors.forename: S
authors.initials: S
authors.lastname: Guenneau
authors.forename: T M
authors.initials: TM
authors.lastname: Puvirajesinghe
mesh_terms: D016880:Anisotropy; D008081:Liposomes / Q000737:chemistry; D008956:Models, Chemical; D013696:Temperature; D055471:Thermal Diffusion; D013816:Thermodynamics
chemical_list: D008081:Liposomes
references.citation: Phys Rev Lett. 2013 May 10;110(19):195901
references.pmid: 23705719
references.citation: Science. 2006 Jun 23;312(5781):1780-2
references.pmid: 16728597
references.citation: Opt Express. 2007 May 14;15(10):6314-23
references.pmid: 19546935
references.citation: Nat Neurosci. 2011 Aug 30;14(11):1481-8
references.pmid: 21878933
references.citation: Science. 2006 Jun 23;312(5781):1777-80
references.pmid: 16728596
references.citation: Int J Nanomedicine. 2007;2(4):595-607
references.pmid: 18203427
references.citation: Science. 2010 Sep 24;329(5999):1616-20
references.pmid: 20929839
references.citation: Science. 2001 Nov 30;294(5548):1929-32
references.pmid: 11729319
references.citation: Biophys J. 2003 Sep;85(3):1734-40
references.pmid: 12944288
references.citation: Eur J Nucl Med Mol Imaging. 2006 Oct;33(10):1196-205
references.pmid: 16763815
references.citation: Opt Express. 2012 Mar 26;20(7):8207-18
references.pmid: 22453491
references.citation: Science. 2006 Nov 10;314(5801):977-80
references.pmid: 17053110
references.citation: Biol Reprod. 1998 Dec;59(6):1506-14
references.pmid: 9828199
references.citation: Phys Rev Lett. 2012 May 25;108(21):214303
references.pmid: 23003263