Applications of regime-switching in the nonlinear double-diffusivity (D-D) model

The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled Fick-type partial differential equations and a mass exchange term connecting the diffusivities, is a paradigm in modeling mass transport in inhomogeneous media, e.g., fissures or fractures. Uncoupling of these equations le...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied physics 2024-01, Vol.135 (2)
Main Authors: Chattopadhyay, Amit K., Aifantis, Elias C.
Format: Article
Language:English
Subjects:
Diffusivity
Exact solutions
Fourier transforms
Fractures
Inhomogeneous media
Mass transport
Mathematical models
Partial differential equations
Spinodal decomposition
Switching
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled Fick-type partial differential equations and a mass exchange term connecting the diffusivities, is a paradigm in modeling mass transport in inhomogeneous media, e.g., fissures or fractures. Uncoupling of these equations led to a higher order partial differential equation that reproduced the non-classical transport terms, analyzed independently through Barenblatt’s pseudoparabolic equation and the Cahn–Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction–diffusion (R–D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models.
ISSN:0021-8979
1089-7550
DOI:10.1063/5.0188904