GENERALIZED HYDRODYNAMICS AND LINEAR-STABILITY ANALYSIS OF CYLINDRICAL COUETTE-FLOW OF A DILUTE LENNARD-JONES FLUID

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 obtai ned by using the Navier-Stokes-Fourier equations for compressible flui ds and also for incompressible fluids. In the low Reynolds or Mach num ber regime, if the Knudsen number is sufficiently low, the marginal st ability curves calculated by the generalized hydrodynamic theory coinc ide, within numerical errors, with those based on the Navier-Stokes th eory. But there are considerable deviations between them in the regime s beyond those mentioned earlier, since nonlinear effects manifest the mselves in the laminar mean flow through the nonlinear dissipation ter m and normal stresses. There are three marginal stability curves obtai ned in contrast to the Navier-Stokes theory, which yields only two. Th e previously observed phase-transition-like behavior in fluid variable s and the slip phenomenon are found to occur beyond the hydrodynamic s tability 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 i ncreases and thereby the dynamic structure is progressively more organ ized.