Atypical non-Basset particle dynamics due to hydrodynamic slip

Surface slip does not simply reduce drag but strongly influences the behavior of unsteady particle motion. In this work, we revise the Maxey–Riley type equations in conjunction with the modified Faxen laws, showing that slip particles in unsteady motion, even if the amounts of slip are minuscule, can behave markedly different than no-slip particles due to the non-Basset history force and torque. The non-Basset memory kernels here are identified to be of Mittag–Leffler type but featured with the unique slip–stick transition that exists only for partial slip particles but not for full slip bubbles. The impacts especially manifest in the short time regime, illustrated with transient sedimentation, translational response to a suddenly applied stream, and angular response to a torque impulse. In these examples, the translational and angular velocities of a slip sphere are found to vary with time in different powers compared to those of single no-slip spheres. Dynamic distinctions to a spherical bubble can be best revealed by the asynchronous spinning of a slip sphere in an oscillatory vortical flow, showing that an additional inertia torque can arise from slip to give rise to a non-monotonic spinning response when the sphere is lighter than the surrounding fluid. As these non-Basset particle dynamics are rather atypically sensitive to the slip length, the impacts could be crucial to aerosol suspensions and inertial swimming of active hydrophobic particles where slip effects can no longer be negligible. The features might also have potential uses for achieving efficient hydrodynamic sorting of slip particles.