Rheological properties of concentrated polymer solutions I. Growth of pressure fluctuations during prolonged shear flow

Rheological Properties of Concentrated Polymer Solutions L Growth of Pressure Fluctuations during Prolonged Shear Flow A. S. LODGE* A new apparatus, similar to the Weissenberg Rheogoniometer, has been developed for the determination o / t h e differences of normal stress components in steady shear flow. The liquid is sheared between a rotating cone and a fixed plate, the pressure distribution on the latter being measured by means o[ a diaphragm-capacity gauge having a response time (about 0"1 sec) considerably shorter than those (about 1 h) of the capillary gauges which have been used hitherto. Preliminary experiments reported here have revealed the unexpected result that with certain systems [poly(methyl methacrylate) in dimethylphthalate, polystyrene in dimethylphthalate] the observed pressure during prolonged shear flow (20 min at 20 sec -~) develops a random fluctuation with 'periods' of up to 0"4 sec and amplitudes up to about one third o[ the shear stress. A liquid mixture o/polydimethylsiloxanes showed no fluctuations under similar conditions. The growth of pressure fluctuations was accompanied by the development, in the [ree liquid surface near the rotating cone, of irregularities or ruffling visible to the naked eye. The observations may possibly be explained in terms o[ structural changes in the solutions leading to the growth of inhomogeneities or gel particles o[ dimensions (about 0"4 mm) comparable to the gap between cone and plate.

INTRODUCTION RHEOLOGICAL PROPERTIES of moderately concentrated polymer solutions are not completely characterized by values of the viscosity alone : in steady shear flow, it is also necessary to know the values of the differences of the three normal components of stress acting on the shearing planes, on planes normal to the lines of flow, and on planes normal to both these sets of planes 1. Following the work of Weissenberg 1 and others 2, 3, increasing attention is now being given to the problem of measuring these differences. Non-zero values for these differences give rise to characteristic pressures on the walls of viscometers: in a cone-and-plate rotational viscometer, for example, the pressure on the plate increases towards the axis of rotation, the rate of increase dp [ don r) (where p = pressure and r-- distance from the axis) being a constant (for a given shear rate) equal to one combination of the required differences of normal stress components. Such pressure distributions have been measured by means of capillary gauges 3. 4, but these usually take an hour or more to reach equilibrium owing to the appreciable viscosity of the solutions used, and therefore mask any effects which might arise from more rapid changes in the state or structure of the flowing solutions. A quick-response gauge has recently been developed 5 to replace the capillary gauges and is now being used for systematic measurements of pressure distributions in cone-and-plate and in *Present address: Department of Mathematics, The Manchester College of Science and Technology, Manchester, 1. 195

A. S. LODGE parallel plate rotational systems. The results of these measurements together with a detailed description of the apparatus used are to be published elsewhere. The present paper deals solely with certain new and unexpected effects which have been observed in preliminary measurements performed with a prototype cone-and-plate apparatus embodying a pressure gauge with a response time of the order of 0-1 sec. These effects appear to arise from reversible changes of structure induced by slow, steady flow. EXPERIMENTAL

Apparatus A schematic diagram of the apparatus used is given in Figure 1. The liquid under investigation is sheared in the narrow gap between a fixed horizontal duralumin plate and a wide-angled mild steel cone rotating about

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its axis which is vertical. The pressure on the plate is measured by means of a diaphragm-capacitance gauge connected to a small hole, 1 mm in diameter, in the plate. Values of pressure at different distances from the cone axis are obtained by moving the lower plate and pressure gauge horizontally. The pressure gauge consists of a chamber, filled from below with the liquid under test; one wall is a circular beryllium-copper diaphragm, 18 mm × 0"002 in. whose deflection in response to a change of pressure gives rise to a capacity change to an electrode about 0"001 in. away. The capacity change is measured by means of a Fielden Proximity Meter Type PM2 slightly modified so as to give an improved response to quick changes of input. The output (about 1 V for a pressure change of 130 d y n / c m 2) from the Fielden is fed through another d.c. amplifier to a Siemens-Ediswan pen oscillograph which gave the traces shown in Figures 2 and 3. The pressure gauge (and the rest of the apparatus) used here was of a provisional design used to give information on which a finalized design was prepared. A detailed description of the finalized design of pressure gauge has been published elsewhere 5 : this gauge differs only in minor details (e.g. in having a fixed instead of a movable electrode) from the gauge used in obtaining the results reported below. 196

C O N C E N T R A T E D P O L Y M E R SOLUTIONS

Calibration The whole pressure-measuring system was calibrated with regard to sensitivity and response time by applying and then suddenly removing a known air pressure to the electrode side of the diaphragm, the gauge and the gap between cone and plate being filled with liquid ready for measurement. The calibration traces obtained for each liquid used are included in Figures 2 and 3. From these traces it will be seen that the response times are of the order 0'02 sec to 0"1 sec, depending on the liquid used. It is to be expected that the response time, which is essentially determined by the movement of liquid through the small hole in the plate, will depend on the viscosity of the liquid used. The small oscillations observed in the

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Figure 2 - - G r o w t h of pressure fluctuations in solution A. Shear rate 20 sec -1. Times of shearing shown in minutes. First trace shows response to sudden change of pressure 160 d y n / c m L a b = l sec; e d = p e r i o d of rotation of cone. Distance between hole and cone axis=4"2 cm (cone radius=4-4 cm)

calibration traces for two of the three liquids used may be due to oscillations in air pressure induced by the sudden change, and are in any case unimportant for present purposes. (It should be noted that the time scale for the calibration traces of Figure 3 is expanded by a factor of 4 in comparison with the time scale for all the other traces of Figures 2 and 3.) It can also be seen that the response time is independent of the distance of the hole from the cone axis.

Materials Solution A contained 2 g of poly(methyl methacrylate) of number-average molecular weight l0 s in 100 ml of dimethylphthalate. Solution B contained 3 g of polystyrene of viscosity-average molecular weight 5 x 1 0 ~ in 100 ml of dimethylphthalate. Dimethylphthalate was a comparatively poor solvent for these polymers; dissolution of the polymer was accelerated by slow rotation of a flask with tilted axis in an oven at 60°C to 90°C for a few days. When cooled to room temperature, both solutions exhibited marked elasticity, as judged by the observed recoil of air bubbles following cessation of a sudden rotation of the solutions. Solution C was a mixture of two MS 200 (polydimethylsiloxane) fluids : 60 per cent (by weight) of the 12,500 CS fluid and 40 per cent of the 1000 CS fluid. This mixture was 197

A. S. LODGE chosen to give an inelastic liquid of viscosity roughly comparable to those of solutions A and B. The viscosities given in Table 1 were estimates made by the falling-ball method; the viscosity of B was (unfortunately) not measured, but appeared to be similar to that of A. RESULTS

Pressure fluctuations A sample of solution A which had been at rest for several days was subjected to a constant shear rate in the apparatus. Pressure records taken at various times after the commencement of shear flow are given in Figure 2. They show that the pressure is steady at first and begins to Table 1 Pressure)quctuations Solution

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fluctuate after a few minutes shearing; the fluctuations appear to be random and increase in amplitude and frequency during the first 30 min or so, after which they reach a more or less steady pattern. Some pressure records for solution A are reproduced in Figure 3 for comparison with pressure records taken under similar conditions for solutions B and C. It will be seen that similar fluctuations, t h o u g h somewhat smaller in amplitude, are obtained with solution B and that none are obtained with solution C. The two lower traces for solution C show periodic variations having the same period as the rotation of the cone; it is believed that these variations are an artefact of the apparatus, arising from small axial translations of the cone due to end-movement in its bearing. As is to be expected on this explanation, the amplitude of these variations is greater at points nearer the cone axis. A similar but smaller periodic variation is discernible in the lower traces for solutions A and B in Figure 3; the fact that this variation is smaller for A and B than for C is consistent with the fact that the viscosities of A and B are smaller than the viscosity of C. There is no difficulty in seeing that these periodic variations are quite separate effects from the random fluctuations.

Normal stress components The greatest amplitudes of the pressure fluctuations, estimated from the traces, are given in Table 1. It is desirable to have some other pressure value as a standard of comparison with these amplitudes, and for this purpose the values of dp/d(ln r) are also given in Table 1. These were obtained as the slopes of graphs of mean pressure p plotted as a function of In r, where r denotes distance from the cone axis; the graphs were substantially linear. As mentioned in the Introduction it can be shown that 198

CONCENTRATED POLYMER SOLUTIONS

(under suitable conditions) these values give a certain combination of differences of normal stress components in shear flow and represent a fundamental property (quite distinct from viscosity) of the liquids concerned 4.

Visible heterogeneities A further observation, qualitative but significant, was made. It was observed that, during the first 5 to 15 minutes shearing of solutions A and B, the appearance of the free liquid surface near the rim of the cone changed from smooth to rough as if small gel-like particles were being formed in the solution. The size of these particles or heterogeneities, estimated by eye, was of the order of ¼ or ½ mm. N o such effect was ever observed with solution C. Time dependence oJ mean pressure It was also observed that, during the first few minutes shearing of solutions A and B, the mean pressure at a point (i.e. the pressure with any fluctuations averaged out) increased to a maximum and then more slowly decreased to a more or less steady value. N o such effect was observed with solution C: indeed, the pressure variations with both time and position were barely significant for this liquid. A 38crn ~ 45 rain 1"6cm 45rain ~

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Figure 3--Pressure records for solutions A, B and C. Distances between hole and cone axis in centimetres. Times of shearing in minutes. Shear rate 20 see -1. Sensitivity ef=500 dyn/cm 2 for all traces. Time scale: a b = l sec for left-hand traces, ,~B=¼ sec for right-hand (response time) traces; c d = p e r i o d of rotation of cone

Reversibility When the shear flow was stopped for a short time (a few minutes), after prolonged shearing so that the pressure fluctuations had been developed, 199

A. S. LODGE and then started again, the pressure fluctuations and visual heterogeneities appeared at once, apparently unchanged. A rest period of 1 or 2 days, however, was sufficient to restore the solutions (A and B) to their original state, i.e. that in which pressure fluctuations and visual heterogeneities did not occur at the start of shear flow. DISCUSSION In view of the facts that pressure fluctuations occur (with solutions A and B) only after prolonged shearing, and that they never occur at all with solution C, it seems certain that the fluctuations must be regarded as arising from some material property of solutions A and B and that they cannot be dismissed as artefacts of the apparatus. It might be objected that the viscosity of C was in fact 2½ times larger than the viscosity of A and that in consequence the response time of the gauge when filled with C would be too long to resolve the fluctuations, but inspection of the calibration traces shows that this is not so : the response time with C though longer than those with A or B is still short enough to resolve fluctuations of the type found with A and B. In any case, fluctuations attributable to the apparatus may be seen in the ½ min trace of Figure 2 and are evidently very much smaller than those occurring after prolonged shearing. It should be aaoted that the rate of flow is very much too low for turbulence (in any accepted sense of the word) to occur. A possible explanation of the pressure fluctuations is that during prolonged shear flow the structure of the solution (or state of dispersion of the polymer) undergoes changes (by some mechanism as yet u n k n o w n ) i n such a manner that gel particles or regions of higher polymer concentration, surrounded by regions of lower concentration, are formed. When such a particle moves past the hole in the plate, it is reasonable to expect it to give rise to a transient change of pressure in She hole; the apparently random nature of the observed fluctuations would result from the super, position of pressure transients of various amplitudes and durations caused by particles not only of various sizes but also moving past the hole at various heights (and therefore at various speeds) above it. A simple calculation shows that the size of particle necessary to produce the widest peaks in the pressure records (a 0"4 mm diameter particle moving past the hole at a height of 0"2 mm above the plate) is not inconsistent with the sizes of surface irregularities (about 0" 1 to 0"5 mm) observed near the cone rim. The literature contains other evidence for the occurrence of timedependent changes of structure induced by steady flow: the shear stress for the rubber-decalin system, for example, increases to a maximum and then decreases to a steady value s. Some evidence (based on the diffusion of dye) also exists for the occurrence of heterogeneities ('rheologieal units') in the shear flow of raw rubberT; in this case the largest heterogeneities are only 0'01 mm in diameter. The evidence offered in the present paper appears to be rather more direct than any previously published and is, moreover, remarkable in that structural changes occur at a polymer concentration as low as 2 per cent and at a shear rate as low as 20 see-x. The effects described in this paper are considered to be important for the 200

CONCENTRATED POLYMER SOLUTIONS following reasons: they represent a new source of information concerning the structure of polymers in solution; they give renewed warning of fundamental difficulties s in rheological investigations of certain p o l y m e r solvent systems, viz. the occurrence of heterogeneity on a scale comparable with the apparatus dimensions; and, if they occur in fibre-forming systems (e.g. in the slow flow through feed pipes to a spinneret), they may influence the properties of the spun fibre. It is a pleasure to thank my former colleagues, Dr D. W. Saunders and Mr K. J. Butler, for their continual assistance in developing the apparatus used here. The British R a y o n Research Association, Heald Green Laboratories, Wythenshawe, Manchester, 22 (Received 18th November, 1960) REFERENCES 1 WEISSENBERG,K. Nature, Lond. 1947, 159, 310 2 JOBLING, A. and RDBFA~TS,J. E. J. Polym. Sci. 1959, 36, 421 3 GARNER, F. H., NISSAN, A. H. and WOOD,G. F. Phil. Trans. A, 1950, 243, 37 GREENSMITH, H. W. and RIVLIN, R. S. Phil. Trans. A, 1953, 245, 399 4 ROBERTS, J. E. Proceedings of 2nd International Congress on Rheology, Butterworths, London, 1954, pp. 91-98 LODGE, A. S. J. sci. lnstrum. 1960, 37, 401 TRAPEZN1KOV, A. A. and ASSONOVA,T. V. Colloid J. Voronezh, 1958, 20, 376 7 MOONEY, M. and V~;OLSTENHOLME,W . E. J. appl. Phys. 1954, 25, 1098 8 BONDI, A. Trans. Soc. Rheology, 1958, 2, 303

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