Is the Choice of Flow Curve Fitting Equation Crucial for the Estimation of Pumping Characteristics?

Abstract

The answer to this provocative question is “no”! This is demonstrated by experiment and analysis for two very different materials – a highly concentrated emulsion and an 8%v/v Kaolin clay suspension. The flow curves of both materials clearly showed a low shear Newtonian asymptote and a pseudoplastic domain. The difference in the accuracy of the fitting equations relates mainly to the low shear rate domain. While the Cross equation is adequate over the full flow curve, the power law and the Herschel-Bulkley equations are clearly inadequate for the low shear rate range. These equations as well as the direct numerical method (using the Rabinowitsch-Weissenberg integral) were used for the calculation of the laminar pipe flow transport characteristics and the results were compared with experimental pipe flow data. It was shown that in all cases the maximum error did not exceed 5%, which is quite acceptable for engineering design, indicating that the choice of the flow curve fitting equation was unimportant.

Keywords

• emulsion
• kaolin
• flow curves
• cross equation
• power law
• herschel-bulkley equation
• rabinowitsch-weissenberg equation
• laminar pipe flow