Viscosity

As mentioned, Bridgman determined the viscosities at 3o° and at 75° ; at the same pressure the viscosity at the higher tem perature is always smaller than at the lower. The liquid at the higher tem perature, however, occupies a greater vol ume than at the lower, when the pressures are equal, and since it is very natural to assume that the change in viscosity caused by either temperature or pressure is merely a consequence of the accompanying change in volume, it is of great interest to com pare the viscosities at equal volumes. The volumes corresponding to different pres sures up to 12,000 atmospheres were de termined by Bridgman in an earlier investi gation; they are plotted in fig. 8 as abscis sae and the viscosities at 3o° and 75° cor responding to them as ordinates. The vis cosity at 3o° is always higher than that at 75° and at the same volume ; in other words, the viscosity is not determined by the volume alone, as has been assumed in several theories. The point is of funda mental importance and still awaits ex planation.

Water behaves anomalously, as it does in respect of other physical properties. At temperatures below about 3o° the viscosity at first decreases with increasing pressure and shows a minimum at about i,000 atmos pheres, which is the more marked the lower the temperature. At temperatures above 3o° water behaves like other liquids, i.e., the viscosity increases with the pressure throughout the whole range.

Viscosity and Chemical Constitution.

Thomas Graham, the founder of colloid chemistry, who carried out a great number of viscosity measurements by Poiseuille's method, was the first to suggest that the viscosity of compounds of similar constitu tion might increase in a regular manner with the number of mole cules or groups contained in them. Several investigations have been directed towards establishing such a connection, the best known of which was carried out by Thorpe and Rodger. They found that in any homologous series the viscosity increased with the molecular weight, the increase being fairly regular with the higher members, while the first two or three behaved anoma lously—as they do in regard to other physical properties. Series like the alcohols and the fatty acids show considerable irregulari ties which are ascribed to association, i.e., to their consisting, not of single molecules, but of complexes of such, which break up with rising temperature. There is other evidence of association, and the anomalies of water are ascribed to the same cause.

Viscosity of Solutions and Mixtures.

The investigations on both these have been extremely numerous. Solutions of all non electrolytes and of electrolytes with certain well-known excep tions have viscosities higher than that of the solvent, the increase for equal increments of dissolved substance becoming higher at high concentrations. The exceptions are solutions of certain salts of potassium, ammonium, rubidium and caesium in water or alcohol, which, between certain limits of temperature and con centration, have viscosities lower than that of the solvent.

The viscosity of all solutions, like that of pure liquids, decreases with rising temperature; the effect is even more marked than in the latter, especially at high concentration. This is well shown in

fig. 9, in which the viscosities of 4o and 6o% cane sugar solutions are plotted against the temperature; the viscosity of the 6o% solution at o° is over 7o times, and that of the 4o% solution about 15 times the respective values at for water this ratio is about 6.3.

It has so far been impossible to find the law connecting the viscosity of a solution with its concentration, and none of the empirical formulae which have been proposed fits more than a limited number of solutions. There are hardly any mixtures the viscosity of which is the mean calculated from the viscosities and percentages of the two components; if the viscosity of a mixture of chemically quite indifferent liquids is plotted against the per centage of one component, a slightly sagged curve (fig. 1o) is the nearest approach to the straight line (dotted) which would repre sent the viscosity of the "ideal" mixture. It frequently happens, however, that the curve has a maximum (fig. ) or a minimum (fig. 12); in other words, the viscosity of the mixture, at certain ratios of the components, is greater or smaller than the viscosity of either alone. The maximum or minimum may occur at the same concentration at all temperatures (fig. 1) or it may shift with changing temperature (fig. 12). Maxima and minima fre quently occur at ratios, at which other physical constants, like the specific volume or the boiling point, also show extreme values ; thus Poiseuille and Graham already observed, that the viscosity maximum of the alcohol-water mixture occurred at the same ratio as the greatest contraction on mixing.

It has not so far been possible to formulate any molecular theory of the viscosity of liquid which accounts even qualitatively for the variations with temperature and pressure. The kinetic theory of gases, on the other hand, led to some very striking conclusions regarding the viscosity of gases, which were subse quently verified by experiment and must now be described briefly.

The Viscosity of Gases.

A few years after the publication of Poiseuille's paper Thomas Graham investigated very carefully the flow of gases through capillaries. The times in which equal volumes of different gases passed through the same tubes under the same pressure were different and were expressed as "tran spiration coefficients," the time for oxygen being taken as unity. Graham found the same transpiration coefficients with different tubes, so that they represented a constant characteristic of the gas itself. Maxwell in developing the kinetic theory of gases deduced an expression from which it follows immediately that (I) the viscosity of a gas is independent of the pressure, and (2) investigators. The viscosity coefficients of a few gases at o° are given below in centipoises; it will be noticed that the viscosity coefficient of air at that temperature is almost exactly of that of water at o°.