Numerical investigation of the effect of viscoelasticity on the dynamics of a solid sphere in a shear flow via VOF

Abstract

We used the volume-of-fluid (VOF) method to predict the effect of viscoelasticity on the rotational speed of a solid sphere immersed in the shear flow between two parallel plates. We modeled the non-Newtonian fluid with the Oldroyd-B constitutive equation, letting the Weissenberg number ($\text{Wi}$) vary between 0 and 3. As expected, the sphere rotational period increased with the viscoelasticity of the flow, being strongly influenced by the buildup of normal stresses. Moreover, the analysis of the streamlines around the sphere revealed that, at large $\text{Wi}$, the values of the blockage ratio suggested in the literature are insufficient to eliminate the effect of the boundary conditions on the flow field around the sphere. Finally, our values of the sphere rotational velocity agree with the numerical data reported in the literature up to $\text{Wi}=1$. Above this value, our results deviate from those of other works but match well the experimental data.