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

TL;DR

This paper investigates the complex flow behaviors of wormlike micellar solutions around microcylinders, revealing flow bifurcations, state transitions, and the influence of micelle dynamics on flow patterns in microchannels.

Contribution

It provides the first detailed numerical analysis of flow instabilities and bifurcations in wormlike micellar solutions past microcylinders considering micelle breakage and reformation.

Findings

Flow bifurcation observed with varying blockage ratio.

Three distinct flow states identified between two cylinders.

Flow state transitions depend on Weissenberg number and micelle breakage parameter.

Abstract

This study presents an extensive numerical investigation on the flow characteristics of wormlike micellar solutions past a single and vertically aligned two microcylinders placed in a microchannel in the creeping flow regime on the two-species Vasquez-Cook-McKinley (VCM) constitutive model, which takes into account both the breakage and reformation 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 flow transits from steady to unsteady state. 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 wormlike micellar 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 \xi, which basically indicates how easy or hard to break a micelle. Based on the results and discussion presented herein for the single and two microcylinders, we ultimately provide the explanation for 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.