Particle Coherent Structures in Confined Oscillatory Switching Centrifugation

Abstract

A small spherical rigid particle in a cylindrical cavity is considered. The harmonic rotation of the cavity wall drives the background flow characterized by the Strouhal number Str, assumed as the first parameter of our investigation. The particle immersed in the flow (assumed Stokesian) has a Stokes number St=1 and a particle-to-fluid density ratio ϱ which is assumed as the second parameter of this study. Building on the theoretical understanding of the recently discovered oscillatory switching centrifugation for inertial particles in unbounded flows, we investigate the effect of a confinement. For the first time we study how the presence of a wall affects the particle trajectory in oscillatory switching centrifugation dynamics. The emergence of two qualitatively different particle attractors is characterized for particles centrifuged towards the cavity wall. The implication of two such classes of attractors is discussed focusing on the application to microfluidics. We propose some strategies for exploiting the confined oscillatory switching centrifugation for selective particle segregation and for the enhancement of particle interaction events.

Stokesian motion of a spherical particle near a right corner made by tangentially moving walls

“…(2017) and Romanò & Kuhlmann (2017). Similar non-trivial limit cycles have recently been reported by Romanò (2021), where inertial and Coriolis forces are balanced by particle–boundary interactions leading to particle limit cycles in a confined periodically rotating flow. The present study does complement the current literature by demonstrating that particle attractors/repellers exist in two-sided lid-driven cavities near two of the four corners as a result of a balance between gravitational settling and flow entrainment due to the finite particle size.…”

“…Since the Maxey-Riley approximation breaks down near the walls, we introduce extra forces in the Maxey-Riley equation such that the correct particle dynamics is recovered as a wall or a singular corner is approached. Similar approaches have widely been used in the literature to complement the Maxey-Riley equation by dedicated particle-boundary models (Kharlamov, Chára & Vlasák 2008;Yang 2010;Agarwal, Rallabandi & Hilgenfeldt 2018;Davies et al 2018;Romanò 2019;Romanò et al 2019a;Agarwal et al 2021;Magnaudet & Abbas 2021).…”

Reconstructing the neutrally-buoyant particle flow near a singular corner

“…The picture becomes even more complex when considering that a qualitatively novel dynamics can emerge when two or more of such effects gets combined. This is the case, for instance, of the non-trivial attactors reported for inertial particles in steady [37,38] or oscillatory [39][40][41] cavity flows. The prediction of the particle dynamics becomes even more challenging when the particles are immersed in a complex chaotic fluid flow [42,43], where non-dissipative forces, such as buoyancy, actively contribute to a symmetry breaking [44] or to the creation of attractors [45].…”