Mass transport in a strongly sheared binary mixture of Maxwell molecules

TL;DR

This paper derives exact expressions for mass transport coefficients in a sheared binary Maxwell molecule mixture, revealing anisotropic diffusion tensors and their dependence on shear rate, with implications for non-equilibrium transport phenomena.

Contribution

It provides the first exact analytical determination of mass flux transport tensors in a sheared binary Maxwell mixture, including effects of shear rate and external thermostats.

Findings

Diffusion tensors depend on shear rate and mixture parameters.

Shear flow induces anisotropy in mass transport.

Deviations from equilibrium transport coefficients are significant.

Abstract

Transport coefficients associated with the mass flux of a binary mixture of Maxwell molecules under uniform shear flow are exactly determined from the Boltzmann kinetic equation. A normal solution is obtained via a Chapman--Enskog-like expansion around a local shear flow distribution that retains all the hydrodynamics orders in the shear rate. In the first order of the expansion the mass flux is proportional to the gradients of mole fraction, pressure, and temperature but, due to the anisotropy induced in the system by the shear flow, mutual diffusion, pressure diffusion and thermal diffusion tensors are identified instead of the conventional scalar coefficients. These tensors are obtained in terms of the shear rate and the parameters of the mixture (particle masses, concentrations, and force constants). The description is made both in the absence and in the presence of an external thermostat introduced in computer simulations to compensate for the viscous heating. As expected, the analysis shows that there is not a simple relationship between the results with and without the thermostat. The dependence of the three diffusion tensors on the shear rate is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their equilibrium forms is in general quite important. Finally, the generalized transport coefficients associated with the momentum and heat transport are evaluated from a model kinetic equation of the Boltzmann equation.