The Viscosity of Polymeric Fluids J. E. Perrin and G. C. Martin Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13210
Fluid viscosity is a property of fundamental importance in most engineering applications involving the flow of fluids. For many fluids such ax water or air, the viscosity or the resistance of the fluid to flow depends primarily on the temperature of the fluid. These fluids are termed Newtonian while in anonNewtonian fluid the viscosity also depends on the nature of the shearing process applied to the fluid. Such fluids are of great commercial significance and include most polymer solutions and melts, slurries and suspensions, and paints and inks. One of the first experiments performed in the undergraduate chemical engineering laboratory is the determination of the concentration of an aqueous sucrose solution, which is Newtonian, by measuring its viscosity using a Brookfield viscometer. In order to illustrate the behavior of polymeric fluids, and in what respects they differ from Newtonian liquids, an experiment has been developed to account for the shear-rate dependence of non-Newtonian fluids. This experiment can be used in association with an introductory course in transport processes, fluid mechanics, or with a course on the physical chemistry of polymers.
Figure 1. Viscosity behavior of pseudoplastic, Newtonian, and dilatant fluids.
Theory The viscosity of a fluid is defined as the ratio of the shear stress T to the shear rate j.: 7 = TI?
where 7 is the fluid viscosity. For a Newtonian fluid, there is a linear relationship between .r and j.,hence 7 is a constant and independent of j..In the case of nun-Newtonian fluids this relation is nonlinear and the character of this relation can he used to classify several types of fluids. One such classification is the power law model. Here, where K and n are constants which are properties of the fluid and the temperature. The viscosity may be expressed by combining eqns. (1)and (2) t o give When n = 1,eqn. (3) reduces to the case of aNewtonian fluid. For n < 1,the viscosity decreases with increasing shear rate and the fluid is termed "shear-thinning" or pseudoplastic, whereas, for n > 1,the viscosity increases with shear rate and the fluid is "shear-thickening" or dilatant. These types of behavior are shown in Figure 1in which the viscosity is plotted as a function of shear rate for Newtonian, pseudoplastic, and dilatant fluids. Most polymer solutions and melts are pseudoplastic; quicksand is a dilatant fluid. The properties of non-Newtonian fluids are described in detail by Bird et al. ( I ) , Lodge ( Z ) , and Middleman ( 3 ) . A large number of instruments are available for the measurement of solution viscosity. One of the most widely used and relatively inexpensive instruments is the Brookfield Synchro-Lectric Viscometer (4). The Brookfield viscometer measures the torque M required to rotate a suspended spindle a t a constant rotational speed S l through the fluid. The resistance of the fluid to the rotation of the spindle is registered on a dial via a beryllium-copper spring. The torque M is calculated from the dial reading and the spring constant and the rotational velocity from the rate of rotation of the spindle (4-6). 516
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( b l Discoid01 Spidle Figure 2. Schematic diagram of the cylindrical and discoidal spindles for the Brookfield Synchro-Lectric Viscometer.
If the fluid is Newtonian, a chart, provided by the manufacturer (41, may be used to determine the viscosity directly from the dial reading and the rate of rotation of the spindle. If the fluid is non-Newtonian, the viscosity is shear-rate dependent, and it is necessary to relate r and j.to M and 12 by analyzing the flow geometry in order to obtain the viscosity. Two types of spindle geometries, a cylinder and a disk, which can be utilized in the experiment are illustrated in Figure 2.