Particle manipulation by hydrodynamic effects in vortical stokes flow

Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices, particularly in the context of cell-sized objects in bioengineering and biomedical applications. Such particles tend to be nearly density-matched, and they have a strong tendency to follow the ambient flow passively. Particle manipulation necessitates pulling objects across streamlines; if they cannot be actuated by bulk forces (due to charges or significant gravitational forces), they must be moved by hydrodynamic forces. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles; however, a systematic quantification of the relevant hydrodynamic effects has been lacking. Here, we explore an alternate approach, elucidating manipulation strategies for particles in vortical internal Stokes flows given by Moffatt’s classical, analytically known solutions. We find that even force-free spherical particles can be moved across streamlines through the hydrodynamic particle-wall interaction. By rigorously modeling the wall interactions, we show that symmetry breaking of the vortex geometry is necessary for systematic and lasting deflection of particles, revealing a surprising variety of possible strategies. Depending on the flow geometry, particles can be made to accumulate at either fixed points or limit cycles. Moreover, particles can be forced onto trajectories approaching channel walls exponentially closely, making quantitative predictions of particle capture (sticking) by short-range forces possible. This rich, particle-size-dependent behavior suggests the versatile use of inertia-less flow in devices with a long particle residence time for concentration, sorting, or filtering. Generalizing from the case of single spherical particles, we also investigate the behavior of a rigid dumbbell particle in equivalent Moffatt eddy flows, adding a rotational degree of freedom to the dynamical system describing particle motion. Surprisingly, we find that even without the effect of particle-wall interaction, a rigid dumbbell can be forced onto a predetermined limit cycle. Again, this behavior is dependent on symmetry breaking of the vortex: without breaking the symmetry, we find dumbbell orbits to be quasi-periodic. We classify and quantify these effects relative to the impact of particle-wall interactions, further enriching the toolbox of particle manipulation strategies.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Liu, Xuchen

Contributors dc:contributor

• Hilgenfeldt, Sascha
• Chamorro, Leonardo
• Constante Amores, Cristian
• Feng, Jie

• Microfluidics
• Particle/fluid Flows

Statement dc:rights

• Copyright 2025 Xuchen Liu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129935

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129935