Pressure drop enhancement in a concentrated suspension flowing through an abrupt axisymmetric contraction-expansion

Abstract

In this work, we investigate the pressure drop of concentrated suspensions flowing through a 4:1:4 axisymmetric contraction-expansion at low Reynolds number. Pressure drop measurements across the narrow tube show an enhanced pressure drop relative to a Newtonian fluid at the same flow rate. A linear increase in pressure drop as a function of flow rate is observed for the suspensions, with a steeper slope at higher particle volume fraction. However, due to shear-induced particle migration, the pressure drop at each concentration is lower than would be expected for a uniform Newtonian fluid of the same viscosity as the bulk suspension viscosity. The Krieger [I. M. Krieger, Adv. Colloid Interface Sci. 3, 111 (1972)] expression for the relative viscosity provides an accurate estimate of the dependence of the normalized suspension pressure drop on particle volume fraction, although the bulk suspension viscosity follows the more rapidly increasing curve of Zarraga [I. E. Zarraga, D. A. Hill, and D. T. Leighton, J. Rheol. 44, 185 (2000)]. As the particle volume fraction increases, the normalized pressure drop rises in a similar manner to the area of the recirculation regions in the corner of the expansion and also to the ratio of suspension viscosities in the tube center and recirculation regions. The pressure measurements, along with nuclear magnetic resonance imaging results, suggest that the viscosity ratio between the center and recirculation regions of the suspension, recirculation region size, and pressure drop are all related in contraction-expansion flows of suspensions.