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The flow of viscoelastic wormlike micellar solutions (WLMs) in porous media is encountered in many practical applications like enhanced oil recovery or groundwater remediation. To understand the flow dynamics of these complex fluids in porous media, a model porous media consisting of a straight microchannel with micropore throats present in it, is very often used. In this study, we perform an extensive numerical investigation to understand the flow dynamics of wormlike micellar solutions based on the two-species Vasquez-Cook-McKinley (VCM) model for micelles through such model porous media. We find the existence of an elastic instability once the Weissenberg number exceeds a critical value; likewise, it was seen in many prior experimental and numerical studies dealing with polymer solutions. However, for the present case of a WLM solution, we observe that this elastic instability is greatly influenced by the breakage and reformation mechanisms of the wormlike micelles. In particular, we notice that the intensity of this instability (characterized by the fluctuating flow fields) increases as the Weissenberg number increases; however, beyond a critical value of it, this elastic instability and/or the flow field fluctuation is suppressed because of the breakage of long micelles. This is in contrast to the polymer solutions for which the flow field gradually transits to a more chaotic and turbulent-like state (or the so-called elastic turbulence state) as the Weissenberg number gradually increases. Additionally, we observe that the flow dynamics of these WLM solutions are strongly dependent on the type of micropore throat, the number of pore throats, and the spacing between two consecutive pore throats. An extensive discussion on the pressure drop and apparent viscosity is also presented in the present study., Comment: arXiv admin note: text overlap with arXiv:2101.06367

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.