Pair-sphere trajectories in finite-Reynolds-number shear flow

Abstract

The pair trajectories of neutrally buoyant rigid spheres immersed in finite-inertia simple-shear flow are described. The trajectories are obtained using the lattice-Boltzmann method to solve the fluid motion, with Newtonian dynamics describing the sphere motions. The inertia is characterized by the shear-flow Reynolds number ${\it Re} \,{=}\,\rho\dot{\gamma}a^2/\mu$, where μ and ρ are the viscosity and density of the fluid respectively, $\dot{\gamma}$ is the shear rate and a is the radius of the larger of the pair of spheres in the case of unequal sizes; the majority of results presented are for pairs of equal radii. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O(0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiralling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O(0.1), the limits of the various regions in pair space yielding open, reversing and spiralling trajectories are roughly defined.

The effect of geometrical confinement on coalescence efficiency of droplet pairs in shear flow

“…As a consequence, for confined conditions there is not only an upper critical initial offset, above which the droplets do not coalesce, but there is also a lower critical initial offset, below which there is no coalescence. Reversing trajectories have been observed before in literature for a pair of equally charged droplets in shear flow [16] and for a pair of solid particles in shear flow that interact in the presence of inertia [44]. In this study the droplets are however not charged and effects of inertia can be excluded due to the low Re number.…”

Dynamic self-assembly and control of microfluidic particle crystals

“…Reversing streamlines accompanying rotating particles have been suggested as a unique and unexpected aspect of flow around a sphere in finite-Reynolds-number shear flow (26)(27)(28) and pressure-driven channel flow (16). However, recently it was shown theoretically that reversing streamlines and swapping trajectory particle motion do not necessarily require fluid inertia but can occur in Stokes flow in a confined channel geometry (29).…”

Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres

“…In addition, fluid inertia breaks the symmetry of the pairwise solid-solid and solid-tracer interactions allowing a net displacement of particles without requiring the influence of a third particle or bounding wall. 37,38 These effects may lead to an enhancement of the hydrodynamic diffusivity D H ‫ء‬ . On the other hand, it is known that a single neutrally buoyant particle in a sheared fluid tends to migrate away from the wall at finite Reynolds numbers, 39-42 whereas a zero Re particle would maintain a constant y position as a result of the linearity of the equations of motion.…”