Bifurcation in flows of wormlike micellar solutions past three vertically aligned microcylinders in a channel

Abstract

This study presents a numerical investigation of path switching and selection phenomena in flows of wormlike micellar solutions (WLMs) past three vertically aligned microcylinders in a channel in the creeping flow regime. The flow characteristics of the wormlike micellar solution are examined with the help of a two-species Vasquez–Cook–McKinley constitutive model, which considers both the breakage and re-formation dynamics of wormlike micelles. At low Weissenberg numbers (ratio of the elastic to that of the viscous forces, Wi), the flow field in the present system is found to be steady and symmetric. Furthermore, the WLM solution passes through all the passages present between the microcylinders and channel walls. However, as the Weissenberg number reaches a critical value Wicri, a transition in the flow field from steady to unsteady occurs. Furthermore, the flow field is found to be bifurcated (a transition from symmetric to asymmetric flow field also occurs) as the Weissenberg number gradually increases. However, we observe that all these transitions are strongly dependent on the micelle breakage rate (i.e., how easy or hard to break a micelle) and the intercylinder gap. This study is an extension of our earlier studies on the flow of WLMs past a single and two vertically aligned microcylinders, which are often considered as model porous media for studying the flow dynamics of various complex fluids. The results presented in this work will be relevant for understanding the path switching phenomena of complex fluids during their flow through a porous media.