Influence of a drag force on linear transport in low-density gases. Stability analysis

Abstract

The transport coefficients of a dilute classical gas in the presence of a drag force proportional to the velocity of the particle are determined from the Boltzmann equation. The viscous drag force could model the friction of solid particles with a surrounding fluid (interstitial gas phase). First, when the drag force is the only external action on the state of the system, the Boltzmann equation admits a Maxwellian solution f0(v,t) with a time-dependent temperature. Then, the Boltzmann equation is solved by means of the Chapman–Enskog expansion around the local version of the distribution f0 to obtain the relevant transport coefficients of the system: the shear viscosity η, the thermal conductivity κ, and a new transport coefficient μ (which is also present in granular gases) relating the heat flux with the density gradient. The results indicate that while η is not affected by the drag force, the impact of this force on the transport coefficients κ and μ may be significant. Finally, a stability analysis of the linear hydrodynamic equations with respect to the time-dependent equilibrium state is performed, showing that the onset of instability is associated with the transversal shear mode that could be unstable for wave numbers smaller than a certain critical wave number.