On the flow of associative polymers past a sphere: Evaluation of negative wake criteria

Abstract

A study on falling spheres descending in associative polymers with sphere-container ratios of 0.05–0.15 for various polymer concentrations and Weissenberg numbers is presented. The fluid exhibits constant viscosity over a wide range of small to moderate shear rates, and shear thinning for large shear rates. The simple shear rheology and linear viscoelasticity of these polymers are modeled with the BMP equation of state [F. Bautista, J. M. de Santos, J. E. Puig, and O. Manero, J. Non-Newtonian Fluid Mech. 80, 93 (1999); O. Manero, F. Bautista, J. F. A. Soltero, and J. E. Puig, J. Non-Newtonian Fluid Mech. 106, 1 (2002)], which enables the prediction of the extensional viscosity as a function of the strain rate. The particle image velocimetry technique allows the measurement of the velocity field in the rear of the sphere. The container wall affects the formation of the negative wake at a critical Weissenberg number, which closely corresponds to the region around the peak of extension thickening of the Trouton ratio in the solution. A characteristic strain rate is estimated from the distance of the sphere surface to the stagnant point where the velocity changes direction. Using these data, various criteria for the appearance of the negative wake are discussed. Conclusions reached by Dou and Phan-Thien [Rheol. Acta 43, 203 (2004)] on the physical mechanisms for negative wake generation, are in agreement with the results exposed in this work.

Pressure-drop and kinematics of viscoelastic flow through an axisymmetric contraction–expansion geometry with various contraction-ratios

“…Predictions with the BMP model for simple shear and extensional flow are given in Mendoza-Fuentes et al [19]. In Fig.…”

Compact bubble clusters in Newtonian and non-Newtonian liquids

“…We conducted PIV measurements for the HASE fluid, whose extensional properties promote the formation of a negative wake behind particles or bubbles. 8,29 Differences in the negative wake structure or extensional properties between the HASE and Paam solutions are out of the scope of the present investigation; some information in this regard can be found in Refs. 29 and 30.…”

“…Consistent with the assumption that bubble clusters behave as rigid bodies and resist surface deformation, the appearance of the negative wake in this case is not related with a sudden change on the surface geometry of the bubble, as seen in single bubbles, 9 but it seems to depend just on the extensional properties of the fluid, as is in the case of settling particles. 29,31 The conjunction of all these observations leads us to consider a non-linear scenario, i.e., an information feedback between the liquid and the interface: the gradual increase of the extensional deformation affects the particle motion; in turn, the particle may adapt or not to such flow, affecting the fluid structure at the downstream flow. Hence, it seems reasonable to consider that deformable bodies can adapt to the extensional flow and promote an early formation of a negative wake near the particle.…”

Study on the pulsating flow of a worm-like micellar solution

“…The parameter (k) can be evaluated in stress relaxation experiments after steady shear flow [76,77]. The BMP model was selected for this study due to its ability to predict the thixotropic behavior of structured fluids (such as worm-like micellar solutions, dispersions of lamellar liquid crystals, bentonite suspensions and associative polymers) [72][73][74][75][76][77][78]. It reproduces the flow curve of shear-thinning fluids, i.e.…”

“…Notwithstanding, experiments are necessary to validate the predictions of negative flow enhancement in complex liquids such as worm-like micellar solutions, dispersions of lamellar liquid crystals, bentonite suspensions or associative polymers [72][73][74][75][76][77][78].…”