Rheological properties of concentrated polymer solutions II. A cone-and-plate and parallel-plate pressure distribution apparatus for determining normal stress differences in steady shear flow

Abstract

For non-Newtonian liquids in steady rectilinear shear flow in which liquid planes x2 constant move parallel to the x-axis of a rectangular Cartesian co-ordinate system 0x, x2x3, the three normal components of stress p11, p22, p33 are in general not all equal. Their differences can be determined from the radial distributions of pressure (-p22) on the plate of a cone-and-plate system (‘ cp’)or of a pair of parallel plates (‘pp’) in relative rotation: (a) the quantity p11+p22-2p33 is equal to the pressure gradient d/>22/d In r)cp (b) the quantity p22 — p33 is (under suitable conditions) equal to the value of the pressure —p22 at the rim of the rotating member in either system and ( c) the quantity -p22 can alternatively be determined from the differences in the values of the pressure gradient d/>22/d In r obtained (over a range of shear rates) in the two systems. The object of the present paper is to describe a new apparatus for measuring the necessary pressure distributions and in particular to compare the values ofobtained by the two methods (b), (c). In the new apparatus (a development of the Roberts—Weissenberg Rheogoniometer), the liquid is sheared in the narrow gap between a rotating member (cone or plate) of diameter 8.8 cm and a stationary flat plate, 20.2 cm x 12.6 cm. Pressures up to 2 x 10 dyn/cm2 are measured to within about 5 dyn/cm2 at each of three holes, 0.05 cm in diameter, by means of diaphragm-capacitance gauges which have a response time of a few seconds when used with a test liquid of viscosity 10 P. The apparatus is used with the free liquid boundary either vertical (at the rim of the rotating member) or horizontal (so that the rotating member rotates in a ‘ sea ’ of liquid filling the lower plate). In the latter case, the radial distribution of pressure can be studied in greater detail by moving the lower plate and its attached pressure gauges horizontally. The alinement of both stationary and rotating members is adjustable. Using a silicone fluid of viscosity 10 P as a Newtonian control liquid in a systematic investigation of the effects of small tilts of the stationary plate about horizontal axes, it is found that a cone-and-plate system is about 12 times more sensitive to tilt than a parallel plate system having the same value of rim gap, and that in neither system can the effect of tilt be completely eliminated by the usual procedure of averaging the pressures recorded with the two senses of rotation. Measurements on two polymer solutions (polymethylmethacrylate in dimethyl phthalate, polyisobutylene in dekalin) having viscosities in the range 10 to 30 P have been made at shear rates in the range 5 to 100s-1. Both quantities p n 2 — an<l a are found to be positive Pn > b for a tensile stress) for a tensile stress) and to increase steadily with shear rate. Values obtained by methods ( b) and (c) are different, being up to seven times greater for method (c). It is not possible, with the solutions used, to assess the accuracy of method (c) owing to uncertainties involved in an extrapolation to zero shear rate. When a constant shear rate is first applied to solutions which have been at rest for 1 or 2 days, records of pressure against time of shearing show two pronounced maxima for the first solution and no maxima for the second solution.