Since the shear rate of a non‐Newtonian fluid is of importance in fixing the rheological or viscometric behavior of such a material, the present study has been concerned with the development of a general relationship between impeller speed and the shear rate of the fluid. The resulting relationship was then used to interpret and correlate power‐consumption data on three non‐Newtonian fluids by use of a generalized form of the conventional power‐number–Reynolds‐number plot for Newtonians. Flat‐bladed turbines from 2 to 8 in. in diameter were used exclusively. Tank diameters ranged from 6 to 22 in. and power inputs from 0.5 to 176 hp./1,000 gal. The study encompassed a 130‐fold range of Reynolds numbers in the laminar and transition regions. The results to date indicate that power requirements for the rapid mixing of non‐Newtonian fluids are much greater than for comparable Newtonian materials.

In spite of the great range of the available experimental data, further work is necessary in the transition and turbulent-flow regions. No data at all were available on thixotropic, rheopectic, and dilatant fluids, and extension of the correlation to these materials should prove most illuminative from both theoretical and practical viewpoints.

This paper reviews the flow behavior of concentrated suspensions as may be of interest in the processing of composites and similar polymeric materials. Succinct synopses are arranged at the end of each section. In general, the state of the art is a good one: a small number of experiments on a new formulation frequently suffice for a general prediction of flow behavior when solids are suspended in viscous molten polymers, and in many instances, even a priori predictions of the viscosity are possible. Less viscous systems are much more difficult; several remaining problems and research areas are identified.

A theoretical analysis for turbulent flow of non-Newtonian fluids through smooth round tubes has been performed for the first time and has yielded a completely new concept of the attending relationship between the pressure loss and mean flow rate. In addition, the analysis has permitted the prediction of non-Newtonian turbulent velocity profiles, a topic on which the published literature is entirely silent.To confirm the theoretical analysis, experimental data were taken on both polymeric gels and solid-liquid suspensions under turbulent-flow conditions. Fluid systems with flow-behavior indexes between 0.3 and 1.0 were studied at Reynolds numbers as high as 36,000. All the fully turbulent experimental data supported the validity of the theoretical analysis. The final resistance-law correlation represents a generalization of von Karman's equation for Newtonian fiuids in turbulent flow and is applicable to all non-Newtonians for which the shear rate depends only on shear stress, irrespective of rheological class& cation. All the turbulent experimental data for the non-Newtonian systems were correlated by this _.. .-..-ship with a mean deviation of 1.9%. THEORYNon-Newtonian fluids are defined as materials which do not conform to a direct proportionality between shear stress and shear rate. Because of this negative definition of non-Newtonian behavior, essentially an infinite number of possible rheological relationships exist for this class of fluids, and as yet no single equation has been proved to describe exactly the shear-stress-shearrate relationships of all such materials over all ranges of shear rates. If such a general equation could be developed, it seems probable that its complexity would be too great for general engineering utility. Although it is desirable that the following theoretical analysis be universally applicable to all time-dependent, nonelastic fluids, irrespective of any arbitrary rheological classifications such as Bingham plastic, pseudoplastic, or dilatant, this consideration is much too broad to be handled in the initial phases of the development. Therefore a particular rheological model will be selected for use initially, and application of the resulting development to fluids deviating from the assumed model will be considered subsequently.I t has been found experimentally (7, 11,19,20) that the relationship between shear stress and shear rate for a great many non-Newtonian fluids, possibly the majority, may be represented closely over wide ranges of shear rate (ten-to one-thousand-fold) by a twoconstant power function of the form D. W. Dodge is with E.

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