Flow of wormlike micellar solutions through a long micropore with step expansion and contraction

Abstract

In this study, an extensive numerical investigation has been carried out in order to understand the flow characteristics of a wormlike micellar (WLM) solution through a long micropore with step expansion and contraction. The VCM (Vasquez-Cook-McKinley) [P. A. Vasquez, G. H. McKinley, and P. L. Cook, “A network scission model for wormlike micellar solutions: I. Model formulation and viscometric flow predictions,” J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)] constitutive model has been used for the present WLM solution for predicting its rheological behavior and the governing equations, namely, mass and momentum equations along with the VCM constitutive model equations have been solved using the finite-volume method based open source code OpenFOAM. Within the range of conditions encompassed in this study, different flow regimes have been observed in the pore geometry, for instance, Newtonian like regime, lip vortex formation regime, unsteady and vortex merging regime, etc. In particular, an elastic instability regime has been observed in the pore geometry, and the onset of this regime is accentuated with the increasing values of the Weissenberg number and decreasing values of the nonlinear VCM model parameter ξ. Apart from the flow pattern, a detailed discussion on the distribution of the wormlike micellar concentration, principal stress difference, apparent relative viscosity, etc., is also presented. Finally, a good qualitative agreement (in terms of the flow pattern) has been found between the present simulations and the corresponding experiments.