The linear pressure dependence of the viscosity at high densities

Abstract

Over the years, experimental data of the viscosity coefficient of simple dense fluids at high pressures have been obtained both in our laboratory and elsewhere. These data show that, at high densities, i.e. roughly in the last third of the density range from vacuum to the melting transition, for constant temperature the viscosity coefficient is a linear function of the pressure in a few different but neighbouring ranges, each with different slope and intersection with the pressure axis. The slope appears to be a time of picoseconds. The intersection with the pressure axis can be considered to be a value for the internal pressure. Thus, the viscosity coefficient is directly proportional to the thermal pressure, i.e. the combination of the experimental pressure and the internal pressure, in these ranges. It is shown that such a linear pressure dependence of the viscosity occurs in large ranges of the liquid state and at high densities in the fluid state of simple molecules. We subsequently call attention to old ideas of Maxwell on the equivalence of elasticity and viscosity and the modern basis of it given by Zwanzig and Mountain. This concept leads to Maxwell’s relaxation time. On account thereof, the slope of the linear viscosity–pressure relation is interpreted as the relaxation time, i.e. the time in which a disturbance to the Maxwellian equilibrium state decreases to 1/e of its original value, and as the ideal collision interval. The similarity of the present solution and the case of electrical conductivity in an n-type semiconductor is also pointed out. This leads to a simple view on the transport mechanism and gives reason to consider the temperature dependence of the relaxation times.