Sphere rotation in a uniformly rotating or shearing flow

It is known that, in a linear shear flow, inertia causes a particle to rotate more slowly than the surrounding fluid. Experiments performed with a sphere fixed, but free to rotate, in a fluid undergoing solid body rotation indicate that the angular velocity of the sphere can be larger than that of the flow. Numerical simulations at moderate Re confirm this observation. To gain a better understanding of the phenomenon, the flow is decomposed into a stream-wise and a cross-stream shear component. The individual effects of these flow components on the sphere rotation rate are investigated numerically. It is found that the cross-stream shear has a much stronger effect on the particle rotation rate than the stream-wise shear. For Re = 20 and 50 a linear addition of the effects on particle rotation of the stream-wise and cross-stream shears yields the rotation rate of the particle in a solid body rotation flow and when the effects of the two shear types are subtracted, the particle rotation rate for a strain is found. In the experiments a particle is inserted in a horizontally rotating cylinder. If the particle density is smaller than the fluid density, the particle will find an equilibrium position away from the cylinder center where all forces balance (Lohse & Prosperetti (2003)). By marking the particle the particle rotation rate can be measured. When the particle is more than about 1 particle radius away from the cylinder center, it will rotate faster than the surrounding flow. The numerical results are obtained by using the Physalis method (Zhang & Prosperetti (2005)). Here the flow near the particle in the reference frame of the particle is approximated by the Stokes equations and the solution is matched to a finite difference solution on the rest of the grid. The particle is fixed to a position, but allowed to rotate. The situation is tested for several types of flow, amongst which a linear shear flow, a cross stream shear, a straining flow and a solid body rotation. For the last also the effect of rotation on the lift coefficient is investigated. For a linear shear flow several other results are known, for example Lin et al. (1970); Bagchi & Balachandar (2002). To the best of the authors knowledge there are no other results that show the rotation of a sphere to increase with inertial effects for a sphere in solid body rotation.