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

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 f 0 ( 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 f 0 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.