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

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.