Elastic instabilities and bifurcations in flows of wormlike micellar solutions past single and two vertically aligned microcylinders: Effect of blockage and gap ratios

Abstract

This study presents an extensive numerical investigation on the flow characteristics of wormlike micellar (WLM) solutions past a single and vertically aligned two microcylinders placed in a microchannel in the creeping flow regime. The rheological behavior of the micellar solution is realized based on the two-species Vasquez–Cook–McKinley (VCM) constitutive model, which takes into account both the breakage and re-formation dynamics of micelles. For the case of single microcylinder, as the blockage ratio (ratio of the cylinder diameter to that of the channel height) is gradually varied, we find the existence of a flow bifurcation in the system, and also a gradual transition for a range of flow states, for instance, steady and symmetric or Newtonian like, steady and asymmetric, unsteady periodic and asymmetric, unsteady quasiperiodic and asymmetric, and, finally, unsteady quasi-periodic and symmetric. For the case of two microcylinders, we observe the presence of three distinct flow states in the system, namely diverging (D), asymmetric-diverging (AD), and converging (C) states as the intercylinder spacing in between the two cylinders is varied. Similar types of flow states are also observed in the recent experiments dealing with WLM solutions. However, we show that either this transition from one flow state to another in the case of a single microcylinder or the occurrence of any flow state in the case of two microcylinders is strongly dependent upon the values of the Weissenberg number and the nonlinear VCM model parameter n, which basically indicates how easy or hard it is to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we hope this study will facilitate the understanding behind the formation of preferential paths or lanes during the flow of viscoelastic fluids through a porous media, which was seen in many prior experiments in the creeping flow regime.