The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Ludwig-Soret效应，也称为热扩散，是指在温度梯度下分离气体，液体或固体混合物的过程。混合物组分的运动由密度分数的非线性偏微分方程控制。在此，针对外部施加的指数温度场，讨论了二元混合物的非线性微分方程的解。在没有质量扩散影响的情况下，用于分离的运动方程式简化为哈密顿对，从中可以找到混合物各组分的空间分布。包含边界效应的分析计算表明会形成冲击。给出了运动方程的数值计算结果，其中包括热扩散和质量扩散。