Generalized hydrodynamics and linear stability analysis of cylindrical Couette flow of a dilute Lennard–Jones fluid

Abstract

Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible fluids and also for incompressible fluids. In the low Reynolds or Mach number regime, if the Knudsen number is sufficiently low, the marginal stability curves calculated by the generalized hydrodynamic theory coincide, within numerical errors, with those based on the Navier–Stokes theory. But there are considerable deviations between them in the regimes beyond those mentioned earlier, since nonlinear effects manifest themselves in the laminar mean flow through the nonlinear dissipation term and normal stresses. There are three marginal stability curves obtained in contrast to the Navier–Stokes theory, which yields only two. The previously observed phase-transition-like behavior in fluid variables and the slip phenomenon are found to occur beyond the hydrodynamic stability point. The disturbance entropy production associated with the Taylor–Couette vortices is calculated to first order in disturbances in flow variables and is found to decrease as the number of vortices increases and thereby the dynamic structure is progressively more organized.