Related Experiment Video
Updated: Jul 27, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Mathematical analysis of thermal diffusion shock waves
Vitalyi Gusev1, Walter Craig, Roberto LiVoti
1Université du Maine, av. Messiaen, 72085 LeMans, Cedex 09 France.
Abstract:
Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.
More Related Videos
10:52Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System
Published on: August 7, 2018
10:23A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
Published on: December 1, 2023
Related Concept Videos
Shock Waves
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
Joule-Thomson Effect
This experiment forces high-pressure gas through a throttle valve or a porous plug to a lower-pressure region. The gas expands as it passes through to...
Deriving the Speed of Sound in a Liquid
The speed of sound in fluids can be derived by considering a mechanical wave propagating...
Thin-Walled Hollow Shafts
Steady, Laminar Flow Between Parallel Plates
The Chain Rule: Problem Solving