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On the approach to local equilibrium and the stability of the uniform density stationary states of a Van der Waals gas Le, Dinh Chinh

Abstract

Some equilibrium and non-equilibrium properties of a gas of hard spheres with a long range attractive potential are investigated by considering the properties of an equation, proposed by deSobrino (1967), for a one-particle distribution function for the gas model considered. The solutions of this equation obey an H-theorem indicating that our gas model approaches local equilibrium. Equilibrium solutions of the kinetic equation are studied; they satisfy an equation for the density η(r) for which space dependent solutions exist and correspond to a mixture of gas and liquid phases. The kinetic equation is next linearized and the linearized equation is applied to the study of the stability of the uniform density stationary states of a Van der Waals gas. A brief asymptotic analysis of sound propagation in dilute gases is presented in view of introducing an approximation of the linearized Boltzmann collision integral due to Gross and Jackson (1959). To first order, the dispersion in the speed of sound at low frequencies is the same as the Burnett and Wang Chang-Uhlenbeck values while the absorption of sound is slightly less than the Burnett value and slightly greater than the Wang Chang-Uhlenbeck value; all three are in good agreement with experiment. Finally, using the method developed in the previous section, an approximation for the linearized Enskog collision integral is obtained; a dispersion relation is derived and used to show that the uniform density states which correspond to local minima of the free energy and traditionally called metastable, are in fact stable against sufficiently small perturbations.

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