Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part I: Simulation results

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.