  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.
