Slippage and migration in Taylor–Couette flow of a model for dilute wormlike micellar solutions

Abstract

We explore the rheological predictions of a constitutive model developed for dilute or semi-dilute wormlike micellar solutions in an axisymmetric Taylor-Couette flow. This study is a natural continuation of earlier work on rectilinear shear flows. The model, based on a bead-spring microstructure with nonaffine motion, reproduces the pronounced plateau in the stress strain-rate flow curve that is observed in laboratory measurements of steady shearing flows. We also carry out a linear stability analysis of the computed steady state solutions. The results show shear-banding in the form of sharp changes in velocity gradients, spatial variations in number density, and in alignment or stretching of the micelles. The velocity profiles obtained in numerical solutions show good qualitative agreement with those of laboratory experiments.

Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids

“…In the latter class of models it is necessary to solve the coupled differential equations for stress and conservation of momentum in order to determine the local velocity field and the resulting apparent flow curve. In the present paper we compare our results with those predicted by the Johnson-Segalman model [23], which has been extensively studied in inhomogeneous steady shear flows [22,[24][25][26][27]. Although motivated by physical processes such as non-affine chain deformation, the Johnson-Segalman (JS) class of models cannot be connected directly to microstructural features of the flow such as the breaking and reforming processes important in shear-banding transitions of wormlike micellar solutions.…”

“…In [34] Dirichlet conditions were imposed resulting in boundary layers at the walls. Alternate Neumann boundary conditions are considered in [24]. For further discussion on the variations in the rheological predications as the model parameters are varied see [30].…”

“…• PEC+M Model with Conformation-Dependent Diffusion: Circular Couette Equations In the PEC+M model, the contributions of the longer chain species are modeled by the PEC model and the stress components of species A are again given by Equations (24). These equations are coupled, through the momentum equations, with the equations for the contributions to the stress from the shorter chain species B obtained from Equation (16b),…”

“…There has been some discussion in the literature as to the appropriate boundary conditions to impose [37]. In the present computations, we use no flux of conformation as used by [22,24,34,38]. The Neumann boundary condition for the stress at the walls are then:…”

A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

“…The model is derived by starting with the basic equations in a solution of non-interacting dumbbells for the number density and polymeric stress, that are already available in the polymeric uids literature (Beris & Mavrantzas 1994;Bhave et al 1991;Cook & Rossi 2004;Rossi et al 2006). As a consequence, these basic equations are simply written down in Section 2.1.…”