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Fick's second law transformed: one path to cloaking in mass diffusion
S Guenneau1, T M Puvirajesinghe
1Institut Fresnel, UMR CNRS 7249, Aix Marseille Université, Campus de St Jérôme, Marseille Cedex 20, France. guenneau@liverpool.ac.uk
Journal of the Royal Society, Interface
|March 29, 2013
Summary
This study extends transformational thermodynamics to mass transport, controlling concentration flux using anisotropic diffusion. Finite-element models demonstrate applications in bioengineering, like cloaking liposomes.
Area of Science:
- Physics
- Chemical Engineering
- Materials Science
Background:
- Transformational thermodynamics controls heat flux using anisotropic diffusivity.
- Mass transport is governed by Fick's equation, a parabolic partial differential equation.
- Anisotropic heterogeneous diffusivity presents challenges in modeling mass concentration transport.
Purpose of the Study:
- To adapt transformational thermodynamics principles for mass concentration diffusion and transport.
- To analyze the n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation.
- To explore potential bioengineering applications of this adapted theory.
Main Methods:
- Adaptation of transformational thermodynamics for mass transport.
- Consideration of the n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation.
- Finite-element computations for multi-layered cloak models.
Main Results:
- Demonstration of controlling mass concentration flux via anisotropic heterogeneous diffusivity.
- Successful modeling of liposome cloaking with cylindrical and spherical multi-layered structures.
- Validation of the effective medium approach for isotropic homogeneous diffusivity in fluid layers.
Conclusions:
- The adapted transformational thermodynamics framework is effective for modeling anisotropic mass transport.
- Finite-element analysis provides a viable method for simulating complex multi-layered systems.
- This approach holds promise for advancements in bioengineering, particularly in drug delivery and cellular encapsulation.
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