History force on a sphere in a weak linear shear flow

A numerical study of history forces acting on a spherical particle in a linear shear flow, over a range of finite Re, is presented. In each of the cases considered, the particle undergoes rapid acceleration from Re₁ to Re₂ over a short-time period. After acceleration, the particle is maintained at Re₂ in order to allow for clean extraction of drag and lift kernels. Good agreement is observed between current drag kernel results and previous investigations. Furthermore, ambient shear is found to have little influence on the drag kernel. The lift kernel is observed to be oscillatory, which translates to a non-monotonic change in lift force to the final steady state. In addition, strong dependence on the start and end conditions of acceleration is observed. Unlike drag, the lift history kernel scales linearly with Reynolds number and shear rate. This behavior is consistent with a short-time inviscid evolution. A simple expression for the lift history kernel is presented.