Slow heat-driven flow in a gas of hard disks

We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel.

The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a low-Mach-number, nearly isobaric evolution.

In the dilute limit, the corresponding isobaric hydrodynamic theory reduces to a previously known ideal-gas description.

We extend this theory to finite densities by incorporating a non-ideal equation of state of a hard-disk fluid, and solve the resulting one-dimensional equations numerically.

Finite-density effects produce appreciable deviations from the ideal-gas prediction.

We then test the theory directly against event-driven molecular dynamics simulations of hard disks and find very good agreement in both the dilute and finite-density regimes.

The results provide, to our knowledge, the first particle-level test of isobaric gas dynamics of a strongly inhomogeneous cooling flow.