118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. J. A. J. BENNETT 31' THE LAW OF CAPILLARY FLOW IN THE CASE OF COLLOIDS.BY PROFESSOR ALFRED W. PORTER, 4ND P. A. M. RAO. Received I 2 th April, I 9 2 7. I t is well known that Poiseuille's equation for the flow of liquids in a capillary tube is not applicable to the case of sols and suspensions ; that is to heterogeneous systems in general. Various arbitrary modifications have been proposed in order to accommodate the equation to the experimental facts. These are not all satisfactory because they are not founded on an312 LAW OF CAPILLARY FLOW IN CASE OF COLLOIDS scientific basis and, in some cases, they da not even satisfy the principle of dimensions. I n order to extend our knowledge it is of doubtful use to introduce modifications into Poiseuille's equation itself; we must go further back to the mechanical basis on which that equation depends.I n deriving the equation the viscous force per unit area at any inter- face is taken as being a constant times the gradient of velocity ( - &) at right angles to the surface : the constant being the (coefficient of) viscosity (p). I t is the constancy of p that is in question when we are dealing with hetero- geneous media. There is no fundamental reason why it should be a constant. I t has been found to be so for simple liquids, but it may not be so in general. Nearly all physical factors (such as thermal conductivity, elastic constants, etc.) are found, in the long run, to be variables. I t is apparently insufficient, in general, to take the viscous force per unit area as being a constant x - and some other more complicated function of the rate of sheer must be assumed ; for example the constant may be replaced by po + a - where po and a are constants; or by such other function as may satisfy ex- periments.I n order to obtain sets 'I of data obtained as nearly a5 possible under similar con- ditions we have made de- terminations by the capillary tube method of the flow under various pressure-gradients of various sols, in particular sols of starch of three concentra- The horizontal capillary tube (about 35 crns. long) was completely immersed in a constant temperature tank. The pressure was applied by means of a large gas cylinder in which air was compressed to the pressure required; the value of the pressure was determined by a liquid manometer. The back pressure due to surface tension at the exit of the capillary was eliminated by the exit being made just to touch the surface of the liquid collected ; this adjustment could be maintained owing to the collecting vessel being rnounted on a levelling table,' the length of which was altered throughout the course of an experiment.The capillary tube was carefully calibrated ; the radius given is half the mean of 12 diameters. The liquids used were, in the main, very viscous and therefore it was not thought necessary to introduce any correction for the kinetic energy of flow. The final data for starch sols are given in the following tables A, B, C. I n each case the capillary tube was 37.5 crns. long and of radius 0.0376 cms. The starch (pure soluble starch) was mixed with a small quantity of cold distilled water to form a thick paste.Boiling distilled water was then added until the required dilution was obtained. The sol was finally filtered through a close-textured piece of cloth. An interval of 48 hours was dV 3 Zf ar av Q ar 'I5 '05 104 2 x 10' tions. FIG. I.-Starch sols. A IO'/,,, B So/,, C 6'1,.A. W. PORTER AND P. A. M. RAO 313 allowed to elanse before the sol was used in the case of A and 24 hours in the case of B i n d C. A. Starch Sol., 10 per cent. (C=WI), Temp. 12.3" C., Density 1.025 €3. Starch Sol., 8 p e ~ cent. (c=.oS), Temp. 15'95~ C., Density I*OO; C. Starch Sol., 6 per cent. (c=*06), Temp. 14'13' C., Density 1-00 - Wt. dected ?rams). - 1.127 4.2 I 10'35 1894 29.66 44'57 56-49 55'38 2.354 6'133 10'739 21.286 40.947 55'869 57'238 53'737 3.86 6.36 14.85 19-54 19-07 31'52 34-25 39.12 -- Time cconds). ___ 759 624'4 6082 610'4 613.4 615% 607.7 433'3 776'5 713'0 711.4 715'4 720% 543'6 424'1 375'2 607'6 603.0 605.5 425'5 303'5 304'6 251.6 242% Volume Time -__ - i x 108).1'449 6'579 16.61 30'28 47-18 70.62 90.69 124'9 3'264 8'547 15-00 29'50 56.44 134'1 142.3 102'1 6'320 10'49 24'39 45'66 62'48 102.9 135'4 160'3 __ 'ressure Drop, n. of Hg. - 6'74 12-47 19-65 2@46 34'17 4 1'89 48-84 59'50 2.28 5'24 8.24 13'49 33'89 41'53 43'61 2-15 4-13 7'74 13.18 18-26 28.99 37'10 43-12 21'21 Pnsswe Gradient, G. Dyneelem. Interpretation. To interpret these curves we may assume that the viscosity is a function of the rate of shear-diminishing as that rate increases. The value of the viscosity cannot always be directly determined from the curves of flow.The observed flow (Q) is only obtained by a double integration from the original equation in which the dependence of the viscosity upon the rate of shear is expressed and by these integrations the transverse rate of shear is eliminated. The simplest assumption to make is that the viscosity (p) varies as an inverse power of the rate of shear Consider the case of uniform straight-line motion of the fluid in a capillary tube of radius R. Let G equal the longitudinal pressure gradient ( - $). Divide up the tube into coaxial cylinders. Select one of radius Y. Then the assumption of uniform flow requires that ( - 5). or314 NOTE ON THE SORET EFFECT and R m R m t 3 0 Q = j arvrdr = (8) =. In this case the dependence of Q upon the pressure gradient determines This form i5 found to satisfy the experimental points very fairly with m and consequently n. the following values :- C m n A *I 2 '5 B *08 1.3 2 5 C *a6 1.1 -091. If further we endeavour to make the curves fit in with the value for '011 f 6*4[1or]12 pure water we get finally, P = - 2 4 4 9 0 ~ ~ These numbers must not be taken to indicate more than the approximate laws of dependence of p upon the concentration. Universip CoZZege, London.