A study of pressure-driven flow of wormlike micellar solutions through a converging/diverging channel

The pressure-driven flow of a macroscale network model, which was derived from mescoscale network considerations and was developed to describe wormlike micellar mixtures, the Vasquez, Cook, McKinley (VCM) model [Vasquez et al., J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)], is investigated in a periodically varying, converging/diverging channel. The VCM model consists of a coupled system of nonlinear partial differential equations describing two elastically active breaking and reforming micellar species. Previous analysis of the VCM model has shown that it captures both purely shear and purely extensional flow behaviors of wormlike micellar solutions. In this paper, the combined effects of shear and extension are probed by simulating the flow in a converging/diverging channel. Using domain perturbation analysis, the model equations are perturbed about the straight channel geometry thereby describing the flow through the perturbed, wavy wall geometry. The resulting first order perturbed system of (linear) partial differential equations is solved numerically using the overlapping Schwarz alternating domain decomposition method. The analysis shows that even in this simple perturbation, the VCM model is capable of capturing signatures of experimental flow behaviors of wormlike micelles through converging geometries. These signatures include the deviation from Newtonian fore-aft symmetry as well as a nonmonotonic relationship between the first normal stress difference and the extension rate along the centerline.