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February 22, 1894.

The LORD KELVIN, D.C.L., LL.D., President, in the Chair.

A List of the Presents received was laid on the table, and thanks ordered for them.

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The Bakerian Lecture was delivered as follows:

BAKERIAN LECTURE.—“ On the Relations between the Vis

cosity (Internal Friction) of Liquids and their Chemical
Nature.” By T. E. THORPE, D.Sc., F.R.S., and J. W.
RODGER, Assoc. R.C.S. Received February 22, 1894.

The parpose of this paper is to throw light upon the relations be-
tween the viscosity of homogeneous liquids and their chemical nature.
It is divided into three parts.

Part I contains a summary of the attempts which have been made, more particularly by Poiseuille, Graham, Rellstab, Guerout, Pribram and Handl, and Gartenmeister, to elucidate this question. Although it is evident from the investigations of these physicists that relationships of the kind under consideration do exist, it must be admitted that they are as yet not very precisely defined, mainly for the reason that the conditions by which truly comparable results can alone be obtained bave received but scant consideration. For example, it seems futile to expect that any

definite stoichiometric relations would become evident by comparing observations taken at one and the same temperature. Practically, nothing is known of a quantitative character concerning the influence of temperature on viscosity.

From the time which a liquid takes to flow through a capillary tube under certain conditions, which are set out at length in the paper, a measure of the viscosity of the liquid can be obtained.

An apparatus was, therefore, designed on this principle which admitted of the determination in absolute measure of the viscosity, and for a temperature range extending from 0° up to the ordinary boiling point of the liquid examined. In this way instead of finding, as has been the usual custom, relative times of flow in the same apparatus under the same external conditions of temperature and pressure, and which

might or might not be taken as measures of a single physical magni. tude of the substance, i.e., its viscosity, the physical magnitude itself could be measured, and the various influences which are found to affect its value could be allowed for. The physical constants thus obtained could then be treated from the point of view of the chemist, and the comparison would then be of the same kind as that employed in connexion with other physical magnitudes.

Full details of the conditions determining the dimensions of the apparatus and of the modes of estimating these dimensions, together with the methods of conducting the observations, are given in the paper.

The corrections to be applied to the direct results are then discussed.

The question of the mathematical expression of the relation of viscosity of liquids to temperature is considered, and reasons are given for preferring the formula of Slotte-

n = c/(1+bt)", n is here the coefficient of viscosity in dynes per square centimetre, and c, b, and n are constants varying with the liquid.

With a view of testing the conclusions set out at length in the bistorical section of the paper, and, in particular, of tracing the influence of homology, substitution, isomerism, and, generally speaking, of changes in the composition and constitution of chemical compounds upon viscosity, a scheme of work was arranged which involved the determination, in absolute measure, of the viscosity of some seventy liquids, at all temperatures between 0o (except where the liquid solidified at that temperature) and their respective boiling points.

Part II of the memoir is concerned with the origin and modes of establishing the purity of the several liquids ; it contains the details of the measurements of the viscosity coefficients, together with the data required to express the relation of viscosity coefficients to temperature by means of Slotte's formula, and tables are given showing the agreement between the observed aud calculated values.

In Part III the results are discussed. In the outset the factors upon which the magnitude of the viscosity probably depends are dealt with. The influence of possible molecular aggregations, as indicated by observations of vapour densities, boiling points, and critical densities, and, more especially, by measurements of surface energy, made by Eötvös in 1886, and more recently by Ramsay and Shields, are taken note of.

The deductions which may be made by considering the graphical representation of the results, showing the variations of viscosity coefficients with temperature, are then set forth.

For liquids which probably contain simple molecules, or for which VOL. LY.


there is little evidence of association of molecules at any temperature, the following conclusions may be drawn :

1. In homologous series the coefficient of viscosity is greater, the greater the molecular weight.

2. An iso-compound has always a smaller viscosity coefficient than the corresponding normal compound.

3. An allyl compound has, in general, a coefficient which is greater than that of the corresponding isopropyl compound, but less than that of the normal propyl compound.

4. Substitution of halogen for hydrogen raises the viscosity coeffi. cient by an amount which is greater, the greater the atomic weight of the halogen; successive substitutions of hydrogen by chlorine in the same molecule bring about different increments in the viscosity coefficients.

5. In some cases, as in those of the dichlorethanes, substitution exerts a marked influence on the viscosity, and in the case of the dibromides and benzene, it may be so large that the compound of higher molecular weight has the smaller viscosity.

6. Certain liquids, which probably contain molecular complexes, do not obey these rules. Formic and acetic acids are exceptions to Rule 1. The alcohols at some temperatures, but not at all, are exceptions to Rule 2; at no temperatures do they conform tó Rule 3.

7. Liquids containing molecular complexes have, in general, large valnes of dn/dt.

8. In both classes of liquids the behaviour of the initial members of homologoas series, snch as formic acid and benzene, is in some cases exceptional when compared with that of higher homologues.

As regards the influence of temperature on viscosity, it is found that the best results given by Slotte's formula are in cases where the slope of the curve varies but little with the temperature. From the mode in wbich the values of the constants n and b are derived, it cannot be expected that their magnitudes will be related in any simple manner to chemical nature. With the exception of ccrtain liquids, such as water and the alcohols, which are character. ised by large temperature coefficients, and in which there is reason to expect the existence of molecular aggregates, the formula

n= c/(1+Bt+y), obtained from Slotte's expression by neglecting terms in the denominator involving higher powers of t than t, gives a close agreement with the observed results, and in this formula the magnitude of B and y are definitely related to the chemical nature of the substances.

In order to obtain quantitative relationships between viscosity and chemical nature, and to compare one group of substances with another, it is necessary to fix upon particular temperatures at which the liquids may be taken as being in comparable conditions as regards viscosity, and to compare the values of the viscosities at those temperatures.

The first comparable temperature which suggested itself was the boiling point.

A second comparable temperature was obtained by calculating values of corresponding tenperatures by the method of van der Waals with such data as could be obtained.

The third basis of comparison consisted in using temperatures of equal slope, i.e., temperatures at which the rate of change of the viscosity coefficient is the same for all liquids.

At each of the different conditions of comparisons, the experimental results have been expressed according to the same system, in order to show at a glance relationships between the magnitudes of the viscosity constants and the chemical nature of the substances. The liquids are arranged so that chemically related substances are groaped together. Tables are constructed which give the values of the three different magnitudes derivable from measurements of the viscosity of the substances.

1. Values of viscosity coefficients (n). 2. Values of n x molecular area, i.e., molecular viscosity. 3. Values of n x molecular volume, i.e., molecular viscosity work.

The coefficient n is the force in dynes which has to be exerted per unit-area of a liquid surface in order to maintain its velocity relative to that of another parallel surface at unit distance equal to unity. It seemed, however, that relations between viscosity and chemical nature would best be brought to light if, instead of adopting merely unit-areas, areas were selected upon which there might be assumed to be the same number of molecules. The molecular viscosity is propor. tional to the force exerted on a liquid molecule in order to maintain its velocity equal to unity under the unit conditions above defined. With the units chosen it is the force in dynes exerted on the molecular area in square centimetres uuder unit conditions. The molecular viscosity work may be regarded as proportional to the work spent in moving a molecule through the average distance between two adjacent molecules ander unit conditions. In ordinary units it is the work in ergs required to move a surface equal to the molecular area in square centimetres through the molecular length in centimetres.

In the case of the comparison of the viscosity coefficients at the boiling point, it is found :

1. As an homologous series is ascended, in a few cases the viscosity coefficient remains practically the same, but in the greater number of series the coefficients diminish. In one series the coefficients increase ; in the case of the alcohols the coefficients vary irregularly with ascent of the series.

2. Of corresponding compounds, the one having the highest molecular weight has in general the highest coefficient (the aliphatic acids, and to a much greater extent the alcohols, do not conform with this rule).

3. Normal propyl compounds have, as a rule, slightly higher values than allyl compounds; in the case of the alcohols, propyl compounds have much the higher value.

4. The effect of molecular weight in some cases may be more than counterbalanced by that of constitution, or of complexity.

5. The lowest members of homologous series frequently exhibit deviations from the regularity shown by higher members.

6. An iso-compound has in general a larger coefficient than a normal compound, and the differences reach their maximum in the case of the alcohols.

7. In the case of other metameric substances, branching in the atomic chain and the symmetry of the molecule influence the magni. tudes of the coefficients; the ortho-position, in the case of aromatic compounds, appears to have a more marked effect on the coefficient than either the meta- or para-position. Acetone and ether have coefficients that are less than half the values given by the isomeric alcohols.

8. One of the most striking points thus brought to light is the peculiar behaviour of the alcohols, and to some extent of the acids, as contrasted with that of other liquids.

Comparisons of molecular viscosity at the boiling point show

1. That, with the exception of the alcohols, dibromides, and the lowest members of homologous series, an increment of CH, in chemical composition corresponds with an increase in molecular viscosity.

2. With the above exceptions, it is also apparent that the corresponding compound having the highest molecular weight has the highest molecular viscosity: the difference in molecular viscosity between the corresponding members of two correlated series is fairly constant.

3. The relationships shown in the other tables are substantially of the same nature as those given by the viscosity coefficients.

The comparisons which give the largest deviation from regularity contain those substances which, as already shown, exhibit a pecaliar behaviour, namely, the alcohols, acids, propylene dibromide, ethylene dichloride, &c.

In order to indicate how molecular viscosity at the boiling point is quantitatively connected with chemical nature, attempts were made to calculate the probable partial effects of the atoms on the molecular

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