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Updated: Jul 19, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Subdiffusion with particle immobilization process described by a differential equation with Riemann-Liouville-type
1Institute of Physics, Jan Kochanowski University, Uniwersytecka 7, 25-406 Kielce, Poland.
Abstract:
An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann-Liouville type which is a differential-integral operator with the kernel defined by the Laplace transform; the kernel controls the immobilization process. We propose a method for calculating the inverse Laplace transform providing the kernel in the time domain. In the long time limit the subdiffusion-immobilization process reaches a stationary state in which the probability density of a particle distribution is an exponential function.
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