high weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. the flow is considered to be steady and two dimensional. flows of viscoelastic liquids at high weissenberg number exhibit stress boundary layers near walls. these boundary layers are caused by the memory of the fluid. upon proper scaling and by means of an exact similarity transformation, the n...

The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge, a phenomenon known as the High Weissenberg Number Problem. In this work we describe the application and implementation of continuation methods t...

A defect correction method for solving the time-dependent viscoelastic fluid flow, aiming at high Weissenberg numbers, is presented. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the residual is considered in the correction step. We show the convergence of the method and derive an error estimate. Numerical experi...

The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. In this paper a two-parameter defect-correction method for viscoelastic fluid flow is presented and analyzed. In the defect step the Weissenberg...

It is well known that the Poiseuille flow of a visco-elastic polymer fluid between plates or through a tube is linearly stable in the zero Reynolds number limit, although the stability is weak for large Weissenberg numbers (Wi). In this paper, we argue that recent experimental and theoretical work on the instability of visco-elastic fluids in Taylor–Couette cells and numerical work on channel f...

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation i...

In seeking to understand experiments on low-Reynolds-number mixing and flow transitions in viscoelastic fluids, we simulate the dynamics of the Oldroyd-B model, with a simple background force driving the flow. We find that at small Weissenberg number, flows are "slaved" to the extensional geometry imposed by forcing. For large Weissenberg number, such solutions become unstable and transit to a ...

In this work, we investigate the behavior of dilute and semidilute polymer solutions flowing in a microfluidic flow focusing device, in which an inlet stream is stretched by two balanced lateral streams. By varying the flow rates in the inlet and lateral channels and their ratio, several types of flow transitions are observed and the resulting velocity fields are analyzed both upstream and down...

We have analyzed the response of bead-spring chain models in strong elongational flow as the amount of polymer represented by a spring s changed. We examined the longest relaxation time of the chains which is used to quantify the strength of the flow in terms of a Weissenberg umber. A chain with linear springs can be used to predict the longest relaxation time of the nonlinear chains if the lin...