Viscoelastic Hele-Shaw flow in a cross-slot geometry

In this paper a cross-slot geometry for which the height of the channel is small compared to the other channel dimensions is considered. The normal components of the viscoelastic stresses are found analytically for a second order fluid up to numerical inversion. The validity of the theoretical analysis was corroborated by comparison with numerical simulations based on a stabilized Galerkin least squares finite element method using an Oldroyd B fluid. Close agreement was found between numerical predictions and analytical results for Weissenberg numbers up to 0.2. An explicit expression is formulated for viscoelastic parameters in terms of the variation and strength of the first normal stress difference around the stagnation point. The analysis is generalized for the case where the inlet channel width is different from the outlet channel width. For such configurations it was found that uniformity of the elongation rate was reduced

Carreau fluid in a wall driven corner flow

Taylor’s classical paint scraping problem provides a framework for analyzing wall-driven corner flow induced by the movement of an oblique plane with a fixed velocity U. A study of the dynamics of the inertialess limit of a Carreau fluid in such a system is presented. New perturbation results are obtained both close to, and far from, the corner. When the distance from the corner r is much larger than UΓ , where Γ is the relaxation time, a loss of uniformity arises in the solution near the region, where the shear rate becomes zero due to the presence of the two walls. We derive a new boundary layer equation and find two regions of widths r−nr−n and r−2,r−2, where r is the distance from the corner and n is the power-law index, where a change in behavior occurs. The shear rate is found to be proportional to the perpendicular distance from the line of zero shear. The point of zero shear moves in the layer of size r−2r−2. We also find that Carreau effects in the far-field are important for corner angles less than 2.2 rad

Extensional flow affecting shear viscosity: experimental evidence and comparison to models

The effect of extensional flow on apparent shear viscosity has never previously been directly measured nor is it often considered. Here, for the first time, through using a novel flow configuration (two-phase shear response under extensional flow), we have directly measured the effect extensional flow has on the apparent shear viscosity of a viscoelastic polymer solution in a controlled and kinematically mixed manner. We show, via a control transient shear experiment, that the apparent shear viscosity of the solution under mixed deformation depends not only on the shear rate but also on the extension rate and their relative direction: shear thinning being enhanced by parallel and reduced by perpendicular extensional flow, respectively. A 62% reduction in apparent viscosity with parallel extension was seen in this work. We then test the ability of the commonly used Giesekus and Carreau–Yasuda (incorporating generalized shear rate) models to predict the effect of extension rate on apparent shear viscosity against our data. The Giesekus model was found to predict the correct qualitative behavior under both parallel and perpendicular extensional flow, and depending on the fitting parameters, also provided a loosely quantitative agreement. Conversely, the generalized shear rate description does not capture the qualitative behavior, with the most significant errors occurring for perpendicular extension (i.e., expansion) flows. This work emphasizes the rarely noted shortcomings of the latter approach when used for experimental analysis and engineering design when extensional flows are additionally present