P.S. van der Gulik

Compressible laminar flow in a capillary

An equation based on the hydrodynamical equations of change is solved, analytically and numerically, for the calculation of the viscosity from the mass-flow rate of a steady, isothermal, compressible and laminar flow in a capillaiy. It is shown that by far the most dominant correction is that due to the compressibility of the fluid, computable from the equation of state. The combined correction for the acceleration of the fluid and the change of the velocity profile appears to be 1.5 times larger than the correction accepted to date.

The thermal conductivity of carbon dioxide in the critical region: II. Measurements and conclusions

Abstract Experimental data for the thermal conductivity coefficient of CO2 at elevated densities including the critical region are presented. It is shown that the thermal conductivity coefficient exhibits a pronounced maximum in the critical region. The behaviour of the thermal conductivity is compared with that of the specific heat and the viscosity.

The thermal conductivity of carbon dioxide in the critical region: I. The thermal conductivity apparatus

Abstract In this paper, the first of a series of three, a description is given of an apparatus adapted to the measurement of the thermal conductivity coefficient of gases in the critical region, where the probability for the occurrence of convection is very high. The apparatus is a modification of a parallel plate method described earlier.

The viscosity of argon at very high pressure, up to the melting line

Abstract The viscosity of argon has been measured as a function of pressure at 223.15 K, 301.15 K and 323.15 K by means of a vibrating wire viscometer. The measurement of the 223.15 K isotherm has been carried out right up to the melting pressure (7790 bar).

Viscosity of carbon dioxide in the liquid phase

The viscosity coefficient of liquid carbon dioxide has been measured along isotherms from the triple-point temperature (217 K) up to the critical temperature (304 K) at temperatures of 220, 230, 240, 260 and 280 K by means of a vibrating-wire viscometer. The measurements extended beyond both phase-transition lines into the coexistence region (superheated liquid) and into the solid range (undercooled liquid). The accuracy of the measurements is estimated to be 1%. The agreement with data of other authors is rather good. For the most part, the results show a linear pressure dependence in three neighbouring pressure ranges for the various isotherms with a common intersection with the negative pressure axis pi. The fluidity, the reciprocal of the viscosity, shows a linear dependence of the molar volume in adjacent density ranges. After reduction of the molar volume with the volumes of close packing, three sets of linear functions result with common intersections of the axis VB.

The viscosity of methane at 25°C up to 10 kbar

Abstract The viscosity coefficient of methane at 25°C has been measured at pressures from 1 to 10 000 bar by means of the vibrating wire viscometer. The same behaviour has been found for methane as for argon with earlier measurements, except at the very highest pressures from 8 to 10 kbar. In this range the viscosity coefficient η of methane deviates from the expected behaviour, presumably due to hindered rotation of the molecules. This appears in the Batschinski-Hildebrand representation as a third linear relation between the fluidity and the molar volume in the high density range. The comparison of the results with molecular dynamic computations for hard spheres shows a similar deviation from the expected behaviour.

The viscosity of argon at high densities

The viscosity coefficient of argon has been measured at 174.45 K as a function of pressure from 161 up to 4707 bar, including the melting point at 4637 bar and one data point in the supercooled region. Use was made of a vibrating wire viscometer described in a previous paper. The reduced data have been compared with results obtained from molecular dynamics calculations and the agreement is found to be satisfactory. Following the Batschinski-Hildebrand representation it was found that the present results, as well as earlier reported data measured at higher temperatures, can be described by three different linear relations between the fluidity and the molar volume, corresponding to three adjacent volume ranges, covering half the experimental density range. A further analysis shows that, while at intermediate densities the viscosity may be described by the Enskog formalism, at higher densities the behaviour of η is markedly influenced by correlated motions of the molecules.

Thermal effects in compressible viscous flow in a capillary

The thermal effects for a compressible viscous flow in a capillary have been calculated by solving the equation of energy, where a parabolic profile is assumed for the axial flow velocity. It is shown that, in general, the temperature changes are small (a few millikelvins), consistent with the current assumption of an isothermal flow, except in the case of a critical, i.e., very compressible, fluid where the cooling can be substantial. This effect is demonstrated numerically on the basis of a flow of ethylene in nearly critical circumstances.

The working equations of a vibrating wire viscometer

A convenient set of working equations has been developed, together with their limits of validity, for the computation of the viscosity coefficient from the experimental data obtained with a vibrating wire viscometer. These equations are applicable for both a forced damped oscillation as well as a free damped oscillation. In the latter, non-stationary case a correction is incorporated in the equations which accounts for the corresponding difference in the fluid flow pattern.

The viscosity of the refrigerant 1,1-difluoroethane along the saturation line

The viscosity coefficient of the refrigerant R152a (1,1-difluoroethane) has been measured along the saturation line both in the saturated liquid and in the saturated vapor. The data have been obtained every 10 K from 243 up to 393 K by means of a vibrating-wire viscometer using the free damped oscillation method. The density along the saturation line was calculated from the equation of state given by Tamatsu et al. with application of the saturated vapor-pressure correlation given by Higashi et al. An interesting result is that in the neighborhood of the critical point, the kinematic viscosity of the saturated liquid seems to coincide with that of the saturated vapor. The results for the saturated liquid are in satisfying agreement with those of Kumagai and Takahashi and of Phillips and Murphy. A comparison of the saturatedvaport data with the unsaturated-vapor data of Takahashi et al. shows some discrepancies.