Flow properties of surfactant solutions of rod-like micelles passing through a small slit

Abstract

Pressure drops in flows through a small slit were experimentally measured at constant flow rates to investigate flows with an abrupt contraction and expansion. The flow properties of water, 50 wt% glycerol solution, and two types of surfactant solutions (Lipoquad and Lipothoquad) with a counterion (NaSal) were examined. The slit heights used were 480 µm, 222 µm, and 129 µm, with estimated hydraulic diameters of 938 µm, 439 µm, and 256 µm, respectively. Viscosity was measured using a capillary-type viscosity meter. Water and the 50 wt% glycerol solution exhibited Newtonian viscosity, with the viscosity of the glycerol solution being 10 times that of water. By contrast, the surfactant solutions, which contained rod-like micelles, exhibited non-Newtonian viscosity. A power law model was therefore applied for the relationship between shear viscosity and shear rate on the wall. The observed flow properties of water (and the 50 wt% glycerol solution) and the numerical predictions of the Navier–Stokes equations were found to agree to within the experimental errors. In plots of the dimensionless pressure drop against the generalized Reynolds number, however, anomalous flow properties of the surfactant solutions were observed. The pressure drops of Lipoquad/NaSal agreed with those of water (and the 50 wt% glycerol solution) at low apparent strain rate (Reynolds number) but were larger at high apparent strain rate (Reynolds number). Furthermore, the pressure drops of Lipothoquad/NaSal were greater than those of water in the investigated range of the generalized Reynolds number. To examine these experimental results further, flows in a planar channel with an abrupt contraction and expansion were observed using a polarization measurement system based on a high-speed polarization camera. In contrast to polymer solutions (in which polymer chains were oriented along the flow direction), the phase difference for Lipoquad/NaSal before and in the slit region was high in regions with a strong elongational component. In addition, it was high along the centerline after the slit region. These results also differ from those of simple shear flows. Furthermore, the phase difference of Lipothoquad/NaSal was very unstable. In addition, the relationship between the resultant pressure drop and the measured phase differences was investigated, and a dependence was found on the apparent strain rate (Weissenberg number).