Flow of wormlike micelle solutions through a periodic array of cylinders

Abstract

Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellar dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. In this paper, we present the results of our investigation into the flow fields generated by a controllable and idealized porous media: a periodic array of cylinders. Our test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. A combination of particle image velocimetry in conjunction with flush mount pressure transducers were used to characterize the flow, while flow induced birefringence measurements were used to determine micelle deformation and alignment. The pressure drop was found to decrease initially due to the shear thinning of the test fluid, and then exhibit a dramatic upturn as other elastic effects begin to dominate. We present evidence of the onset of an elastic instability in one of the test fluids above a critical Deborah number manifest in fluctuating transient pressure drop measurements and asymmetric streamlines. We argue that this disparity in the two test fluids can be attributed to the measurable differences in their extensional rheology.