Second-order inertial forces and torques on a sphere in a viscous steady linear flow

We compute the full set of second-order inertial corrections to instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in general steady linear flow. This is achieved by using matched asymptotic expansions formulating problem coordinate system co-moving with background Effects unsteadiness fluid-velocity gradients are assumed be small, but dominate far field over those velocity difference between body fluid, making results essentially relevant weakly positively or negatively buoyant particles. The outer solution (which at first order responsible for Basset–Boussinesq history short time shear-induced forces such as Saffman lift long time) expressed via flow-dependent tensorial kernel. inner brings number different contributions torque. Some proportional relative translational angular acceleration while others take form products rotation/strain rate flow fluid. Adding contributions, known added-mass spin-induced recovered, new effects involving revealed. resulting equations provide rational extension classical Basset–Boussinesq–Oseen equation incorporating all first- fluid inertia from both carrying