Equivalent-Radius Method for Determination of Non-Newtonian Flow Curves from Viscometric Data

Abstract

A rapid and precise method is presented for approximating absolute flow curves (shear rate vs shear stress) of non-Newtonian liquids from data obtained with rotational or capillary viscometers. It is shown that the apparent Newtonian flow curve computed from a single measurement (i.e., a single flow rate) in either type of viscometer crosses the true flow curve at a shear stress corresponding to some intermediate radius between the bob and cup radii or less than the capillary radius. If shear rate and stress are computed at the common point using the ordinary Newtonian relations for shear stress and shear rate, the point so calculated will lie on the absolute flow curve. An ``equivalent radius'' rather than a wall radius is used in the conventional Newtonian equations. The position of the equivalent radius is fairly insensitive to changes in the form of the flow curve, particularly in the case of the rotational viscometer. A method for determining the proper intermediate radius is developed and graphs are presented to facilitate this determination and permit estimation of the accuracy of the method. An example is given using data from the literature [I. M. Krieger and S. H. Maron, J. Appl. Phys. 25, 72 (1954)] for a 62.2 percent GR-S Latex slurry. Within the range of the data (slope of the log-log flow curve varying from 1.5 to 3.0), the maximum error incurred by use of a single equivalent radius for each of two rotational viscometers was 0.1 percent for the instrument with a cup/bob radius ratio of 1.064, and 0.4 percent for the instrument with a ratio of 1.113. Accuracy can be increased by use of an iterative procedure. The method has been developed in detail only for the case of pseudo-plastic flow, but the principle can be applied to other types of flow.