Time reversibility and non-deterministic behaviour in oscillatorily sheared suspensions of non-interacting particles at high Reynolds numbers

Abstract

Collections of inertial particles suspended in a viscous fluid and subjected to oscillatory shear have recently attracted much attention due to their relevance to a number of industrial applications and natural phenomena. It is known that, even at very low values of the flow Reynolds number, particle-to-particle interactions can lead to complex chaotic displacements despite the reversibility of the overarching fluid-dynamics (Stokes) equations. For high-Re flows, the loss of predictability after a finite time horizon is generically ascribed to the non-linear nature of the Navier–Stokes equations. Where the sources of nonlinearity are located exactly and how they influence the motion of particles, however, has not been clarified yet. We show that assuming particle interactions to be negligible, surprisingly, at high values of the Reynolds number the major source of non-deterministic behaviour comes from effects of stationary nature in the carrier flow. We report numerical simulations showing precisely how for geometries of finite extent such stationary effects emerge as the time-averaged non-linear response of the Navier–Stokes equations to the applied oscillatory forcing. They cause small deviations of the inertial particle's trajectory from the streamlines of the instantaneous oscillatory flow, which accumulate in time until the system behaviour becomes essentially non reversible.