Power law fluid flow over a sphere: average shear rate and drag coefficient

Abstract

Based on the consideration of the rate of mechanical energy dissipation, an expression for the average shear rate for a sphere falling in a power-law fluid in the creeping flow regime has been deduced. The average shear rate in a power-law fluid (n<1) appears to be higher than that in an equivalent Newtonian fluid. This in turn has been combined with the numerical predictions of drag coefficient (up to Reynolds number of 100) of a sphere to develop a generalized drag correlation for power-law liquids encompassing both n > 1 and n < 1 which appears to apply up to much higher values of the Reynolds number. The available experimental data have been used to demonstrate the reliability and accuracy of the new correlation for shearthinning liquids. Also, in the limit of n = 1, this expression reproduces the standard drag curve with a very high accuracy.