Characteristic time scales for diffusion processes through layers and across interfaces

Physical Review. E
Elliot J Carr

Abstract

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the...Continue Reading

References

Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adam J ElleryRuth E Baker
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adam J ElleryRuth E Baker
Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adam J ElleryRuth E Baker
Jun 12, 2016·International Journal of Pharmaceutics·Laurent Simon, Juan Ospina
Nov 7, 2017·Mathematical Biosciences·Kristinn GudnasonFjola Jonsdottir
Jan 8, 2018·Computers in Biology and Medicine·Badr KaouiGiuseppe Pontrelli

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Citations

Aug 21, 2021·Physical Review. E·Tadeusz Kosztołowicz, Aldona Dutkiewicz

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