On the Kinetic Theory of the Enskog Fluid. Viscosity and Viscoelasticity, Heat Conduction and Thermal Pressure

Abstract

The moment method is applied to the linearized Enskog-Boltzmann equation for a dense gas. Thus an enlarged set of equations of thermo-hydrodynamics is obtained which allows to go beyond ordinary hydrodynamics. The resulting expressions for the density dependent viscosity and heat conductivity coincide with those previously obtained with the help of the ChapmanEnskog solution procedure. In addition, however, the frequency dependence of the viscosity is treated and it is demonstrated that the thermal pressure does not vanish in a dense fluid.

On the Shock Front Thickness in Water and other Molecular Liquids

“…4 and 5, H = L dp, in units of Z/ re fPref» is plotted versus (bp/p re f) 2 for water and methanol. The points represent the same data as shown in Figs Cause 1), referred to as the "Burnett" contribution in connection with gases [6], can be ruled out because the characteristic length involved there is of the order of a mean free path in gases, or of the order of a molecular size in liquids [7] and, even more important, because of an opposite sign in front of t 1 in (5). Burnett-like terms would imply a decrease of the shock width with increasing driving pressure difference rather than the observed increase.…”

The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition

“…for w see (3). The quantity A as given by (15) stems from the boundary condition at the point of contact (/-=1 + ). Equation 14is an expression for the Newtonian viscosity at small shear rates.…”

“…Due to (3) and (15), the condition A = 0 corresponds to for the volume fraction .v at the fluid-solid phase transition as inferred from the divergence of the viscosity. The theoretical value (17) is remarkably close to the computer results [1] which are x ~ 0.494 and A" ~ 0.545 for the volume fractions of the fluid and the coexisting fee solid of hard spheres; the densest packing corresponds to 0.7405.…”

“…1, the "KS-viscosity" given by 14is plotted as function of the volume fraction A. For comparison, the kinetic (direct momentum transfer: DMT) and collisional transfer (CT) contributions of the Enskog viscosity [14,15] are also shown. All viscosity coefficients are in units of mc §d~2, where d is the diameter of a hard sphere and c 0 = (k B T) U2 m~u 2 .…”

“…The (reference) relaxation time r 0 occurring in (14) was specified as . The quantity / [14,15], which modifies the collision frequency in the Enskog-Boltzmann theory was identified with g eq (l + ). At intermediate densities (A ^ 0.3), our "collisional transfer" contribution based on the KS equation does not differ much from the Enskog result.…”