Related Experiment Video
Updated: Jun 24, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab
Angelo Sassaroli1, Fabrizio Martelli, Sergio Fantini
1Department of Biomedical Engineering, Tufts University, 4 Colby Street, Medford, Massachusetts, USA. angelo.sassaroli@tufts.edu
Abstract:
We apply a previously proposed perturbation theory of the diffusion equation for studying light propagation through heterogeneous media in the presence of absorbing defects. The theory is based on the knowledge of (a) the geometric characteristics of a focal inclusion, (b) the mean optical path length inside the inclusion, and (c) the optical properties of the inclusion. The potential of this method is shown in the layered and slab geometries, where calculations are carried out up to the fourth order. The relative changes of intensity with respect to the unperturbed (heterogeneous) medium are predicted by the theory to within 10% for a wide range of contrasts dDeltamu(a) (up to dDeltamu(a) approximately 0.4-0.8), where d is the effective diameter of the defect and Deltamu(a) the absorption contrast between defect and local background. We also show how the method of Padé approximants can be used to extend the validity of the theory for a larger range of absorption contrasts. Finally, we study the possibility of using the proposed method for calculating the effect of a colocalized scattering and absorbing perturbation.
Related Concept Videos
Partial Differential Equations
Steady, Laminar Flow Between Parallel Plates
Boundary Layer Characteristics
The Electrical Double Layer
Theories of Dissolution: Diffusion Layer Model
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
Poisson's And Laplace's Equation

