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Updated: Oct 3, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Analytical approximate solutions of the time-domain diffusion equation in layered slabs
Fabrizio Martelli1, Angelo Sassaroli, Yukio Yamada
1Dipartimento di Fisica dell'Università degli Studi di Firenze and Istituto Nazionale di Fisica della Materia, Italy.
Abstract:
Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.
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