The effect of the Stokes boundary layer on the dynamics of particle pairs in an oscillatory flow

TL;DR

This study investigates how the Stokes boundary layer influences particle pair dynamics in oscillatory flows, revealing fundamental differences between oscillating box and channel systems through direct numerical simulations.

Contribution

It demonstrates that particle dynamics differ significantly between the two systems due to the Stokes boundary layer, highlighting the importance of boundary layer effects in such flows.

Findings

Particle pair dynamics differ between box and channel flows.

The two systems are only equivalent under limited conditions.

An additional parameter governs particle behavior in channel flow.

Abstract

The alignment of a pair of spherical particles perpendicular to a horizontally oscillating flow is attributed to a non-zero residual flow, known as steady streaming. This phenomenon is the basis of complex patterns in denser systems, such as particle chains and the initial stages of rolling-grain ripples. Previous studies on such self-organization processes used two distinct systems: an oscillating box filled with viscous fluid and an oscillating channel flow, where the fluid oscillates relative to the bottom boundary. In this paper, we show that particle pair dynamics in these two systems are fundamentally different, due to the presence of a Stokes boundary layer above the bottom in the oscillating channel flow. The results are obtained from direct numerical simulations in which the dynamics of a pair of particles are simulated using an immersed boundary method. The oscillating box and the oscillating channel flow are only equivalent in a limited region of the parameter space, where both the normalized Stokes boundary layer thickness and the normalized relative particle excursion length are small. Overall, the particle dynamics in the oscillating channel flow, compared to the oscillating box, are governed by an additional dimensionless parameter.