Estimating the viscosity of liquids under pressure

This dossier follows on from the and . In , we have shown the influence of pressure on fluid viscosity by means of a few characteristic figures for water, carbon dioxide and propane. In , we presented some methods for calculating the viscosity of pure gases as a function of temperature and pressure or density. In this paper, we propose a few methods for calculating the viscosity of pure liquids as a function of temperature and pressure or density. We recall that the liquid domain is the region of the phase diagram that extends above the liquid-vapor transition curve.

All methods for calculating the effect of pressure on viscosity are empirical. For the most part, they are based on corresponding states. The numerical coefficients used in these relationships are adjustable parameters, sometimes determined from phase diagrams of reference fluids, representing viscosity as a function of temperature and pressure or volume. Deviations between experimental data and those calculated by the various equations described in this dossier are rarely less than 10%. The effect of pressure on liquid viscosity is masked by the much greater effect of temperature. In that liquid viscosity increases exponentially with decreasing temperature, while viscosity varies almost linearly with pressure. The effect is greater at temperatures close to the critical temperature than at low temperatures, when we consider the variation of the ratio of viscosity at pressure P to that of viscosity at saturation pressure and at the same temperature, as a function of reduced pressure. Roughly speaking, the variation is twice as great for reduced temperatures of 0.95 than for those of 0.5.

Increasing pressure on a liquid leads to an increase in viscosity. The correlations reported in this dossier will cover most pressure ranges, from pressures close to saturation pressures, to pressures extending over several hundred MPa. In this region, data at very high pressures suggest that the logarithm of viscosity is proportional to pressure, and that the structural complexity of the molecule plays an important role. Several empirical or semi-empirical expressions have been proposed to represent experimental liquid viscosity data as a function of temperature and pressure. Often, the logarithm of viscosity is developed according to isothermal polynomial equations as a function of pressure or mass.

Tables showing viscosity as a function of temperature and pressure, for several inorganic and organic compounds, in the liquid and gaseous domains, are the subject of a separate dossier.