The viscosity of simple gases
Keywords: simple gases
viscosity
rare gases
gases

Over the last few years considerable doubt has been cast on the accuracy of the values of the transport properties of the inert gases available in the literature (1,2,3). Barker and Pompe in a careful analysis (2) have shown that the high temperature transport data of argon are inconsistent with potential energy functions obtained by reference to molecular beam experiments, second virial coefficient measurements and direct theoretical calculation. Similar considerations have led Hanley and Childs (3) to suggest that the published tables of inert gas viscosities may be incorrect by as much as 10 percent above 600°K.
This thesis reports a new determination of the low pressure viscosity coefficients up to high temperatures for all the rare gases and nitrogen. The determination was made using a specially designed capillary viscometer capable of making measurements up to 1600°K.
Accurate viscometry requires numerous corrections to be applied to the basic Poiseuille formula. The apparatus was designed to allow these corrections to be made simply and accurately. Thus the effects due to gas imperfection and the kinetic energy of the gas accelerating along the capillary (Hagenbach correction) were usually reduced to less than 0.1%. To maintain the capillary at a uniform temperature it was necessary to wind it in a close helix. However at high flow rates extra resistance due to centrifugal forces on the molecules, the so-called curved pipe flow effect, occurs. A separate study of curved pipe flow was made and the results and conclusions are given in the final chapter.
The viscosity coefficients were determined from an analysis of the times of flow, in practice the time for a mercury surface to pass between electrical contacts, at various mean pressures in the capillary. Thus the slip factor, which arises from the finite velocity of the gas at the wall surface, can be eliminated by a suitable analysis, since it is dependent on the mean free path in the gas, which itself is inversely proportional to the pressure. It is shown that the slip coefficient, widely thought to be constant, in fact can vary with the thermal history, composition and temperature of the capillary.
Two comparative methods of calculating the viscosities were employed; the so-called RELATIVE method where the ratio of one gas to a standard gas at the same temperature is determined, and the so-called STANDARD method where the viscosity of a gas at a given temperature Is taken as a standard and the viscosity at another temperature calculated relative to it. This method requires accurate measurement of the temperature of the capillary. The results were fitted to polynomials of the form,
Log10(Ratio) = A log10 T+ B/T + C/T2 + D
and are presented in the Summary tables (4-1) to (4-3). These ratios are believed accurate to within 0.5% and the standard deviations of the observed ratios from the smooth curves given by the polynomials are less than 0.2%.
The viscosities were calculated from these ratios using standard values taken from the literature and are given in Summary tables (4-4) and (4-5). The absolute accuracy of the results depends on the choice of a suitable standard viscosity. It is believed that the standards of viscosity are accurate to within our experimental error but the results in Summary tables (4-4) and (4-5) can easily be recalculated should the accepted values be proved to be in error. The viscosities of the inert gases given in our Tables are believed to be accurate to within 1%. The literature has been surveyed and the data of other workers for both viscosity and thermal conductivity coefficients are presented in an appendix. The results of this work are critically compared with the earlier data. For the Inert gases the thermal conductivity coefficient is directly proportional to the viscosity coefficient and interconversion is straightforward. The widely quoted viscosity data of Trautz et al. (4) and Vesilesco (5) are shown to be In error by over 5% at the highest temperatures.
The new data in this thesis have been examined carefully to see if they give better agreement with intermolecular potential functions derived from other sources. It is shown that the new data satisfy the law of corresponding states within experimental error and that much of the discrepancy between viscosity data and other sources of information is reconciled.
(1) E.A, Mason and W.E. Rice, J. Chem. Phys. 22 843 (1954) (2) J.A. Barker and A, Pompe, private communication to be published: see E.B. Smith Ann, Rep.Chem.Soc. (London) 83 13 (1966) (3) H.J.M. Hanley and G.E. Childs, Science 159 1114 (1968) (4) M. Trautz and R. Zink, Ann. Physik 7 427 (1930) (5) V. Vasliesco, Ann. Physique (Paris) 20 137, 292 (1945)