On the Limitations of the Diffusion Equation

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Abstract
This paper identifies the physical limitations inherent in the laws of Fickian diffusion by critically examining various derivations of the diffusion equation. Particle transport theory, statistical mechanics, and thermodynamic principles are utilized for this purpose. It is rigorously demonstrated that diffusion describes a quasi‐equilibrium and nearly isotropic process at regions away from external boundaries and sources or sinks of the transported quantity. It is also proven that the diffusion equation is not applicable to transport within a void, or when the vector flux changes rapidly with time.