The dynamics of a particle pair submerged in an oscillating flow

When two spherical particles of a constant diameter D are submerged in an oscillating, viscous fluid, they align themselves perpendicularly to the direction of the flow, leaving a small gap between them. The formation of this compact structure is attributed to a non-zero residual flow known as steady streaming.

We have performed direct numerical simulations of a fully-resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. Our simulations show that the particles oscillate both parallel and perpendicularly to the oscillating flow in elongated figure 8 trajectories.

In absence of bottom friction, the mean gap between the particles depends only on the normalized Stokes boundary layer thickness δ/D and on the streamwise excursion length of the particles relative to the fluid A_r/D.

For A_r/D < 1, viscous effects dominate and the mean particle separation only depends on δ/D. For larger values of A_r/D, advection becomes important and the gap widens. Additionally, the two regimes are observed in the magnitude of the oscillations of the gap perpendicular to the flow. Overall, we find that the mean gap scales as 3.0(δ/D)^1.5+0.03(A_r/D)³, which shows excellent agreement with previous experimental results.