59 On the Anomalous Flow of Colloidal Systems By Colloid Science Laboratory, Arthur Stuart Clark Lawrence, Cambridge (' Communicated by Eric K. Rideal, F.R.S.—Received May 30, 1934) [Plates 3-5] Part I— The N ature of A nomalous Flow The flow of many solutions, most of them colloidal, is now known to be anomalous since they do not obey the linear Poiseuille relation connecting volume efflux with pressure applied. Under small pressure heads, the rate is disproportionately small compared with that under higher pressures so that the “ viscosity coefficient ” calculated from these rates is not a constant but becomes larger as the rate of flow decreases. This was first established by Hess in 1906; although in 1903 it had been found that the oscillating disc method gave 66 viscosities ” for colloidal systems which varied with the amplitude of the oscillation. In 1913 Hatschek* found similar effects in many colloidal systems using the Couette co-axial cylinder viscometer. Most lyophilic colloids show anomaly to a greater or less extent; and for these systems particularly viscosity has always been regarded as a characteristic property and used as an indicator of lyotropic changes.
The Anomalous Flow of Colloidal Systems 61 flow, ill which a narrow stream of coloured liquid drawn into the liquid in flow retains its linear identity so long as the critical turbulence velocity is not reached.* In this work, the coloured stream was wide enough to fill the whole flow tube and its profile was observed as it advanced along the tube. Coloured liquid introduced into the clear stream as a right cylinder is drawn out, in Newtonian flow, to a paraboloid. Photography of its profile will, therefore, confirm, or give a measure of the deviations from, Newtonian flow. After a short time, the form of the coloured stream approximates to a cylinder whose diameter is that of the aperture from which it emerges or the diameter of the flow tube, whichever is the smaller. For measurement of velocity distribution it is, therefore, Stop Fig. 1 essential that the coloured stream shall start with its surface a plane normal to the tube and photographs must be taken before the eccentricity of the paraboloid has become too great. For this purpose, various methods were tried for introducing the coloured liquid into the clear stream and, finally, a two-way stopcock was designed for the purpose. Its apertures had to be at least as large as the diameter of the flow-tube, which itself was required as large as possible. It was also essential that operation of the cock should cause the minimum discontinuity in the flow. The design used is shown in fig. 1. It was made of brass and was of solid construction. The apertures were very slightly larger than the diameter of the flow-tube which was 1 • 33 cm. One half was fixed Reynolds, “ Collected Papers,” pp. 51, 105, 524.
62 A. S. C. Lawrence to the flow-tube by a brass sleeve soldered to the cock and cemented to the glass by sealing-wax. The two tubes had been ground off square and the wax, pushed into the inside, removed so that there was no internal discontinuity in the flow tube. This half of the cock was fixed rigidly to the bench and the other half rotated by a handle. The liquids were supplied by rubber tubing whose internal diameter was a little larger than that of the flow-tube. Seizing of the two faces of the cock was prevented by a leather ring in a groove in one of them. The ring was not complete and projected a little so that when the second face was screwed down upon it and rotated, the gap provided the necessary take-up and the faces could approach closely enough to be water-tight while seizing was prevented. The groove and leather ring were lubricated Coloured Clear EboniteX //>'■-, Brass M M - Springs Spring Stop / Brass Ebonite Fig. 2 with graphite before assembly. This cock worked efficiently for more than a year without alteration or repair; but a modified type was designed for higher speeds, fig. 2. High speed of change-over was effected by a spring released by a trigger. This design has the advantage that the two faces can be ground flat separately whereas in the former type only one can be, the final grinding having to be carried out one against the other in situ. In the second type the moving block was of ebonite so that no lubricant other than water was required against brass. This cock was also designed that clear and coloured liquid were flowing through twin flow-tubes before the coloured liquid was shunted into the clear so that discontinuity due to setting the coloured one into flow from rest was avoided. However, work with the first type showed that this precaution is not necessary at low flow speeds.
The Anomalous Flow of Colloidal Systems 63 The critical rate of flow, taking the Reynolds’ number as 1400, is 50 cc per sec. The highest employed was 10 cc per sec. The Reynolds’ number is lower in colloidal systems than in ordinary liquids. Hatschek* found turbulence at an angular velocity of 70 to 90 degrees/sec in ammonium oleate solution where water remained normal up to 120°, Andrade and Lewisf found the critical velocity of a colloidal system to be about two-thirds of that calculated with the usual Reynolds’ number.
64 A. S. C. Lawrence here ali that is necessary is that both clear and coloured supplies should have the same temperature. That of the flow tube is reduced by the preliminary flushing. Any small difference of temperature of the two supplies shows itself as curvature of the coloured stream.
66 A. S. C. Lawrence water which shows that the method of working does not introduce deviations from Newtonian flow so that when these are found they are due to the liquid itself. (See also figs. 10 and 12.) From the results plotted in this manner, the viscosity coefficient is easily derived, since From the graph, differences of distance are read off directly at two different widths squared (these latter must be divided by four to reduce them to radii squared) and converted to velocities by dividing by the time interval between the curves used. The time interval between con secutive flashes was 10/7 sec. The distances are in real centimetres from the photographed linear scale, but the widths need to be multiplied by a correction factor which is the square of the ratio of the true width of tube to the width of its image on the negative.