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Non-inertial hydrodynamics of manipulating particle transport

Partha Kumar Das

Abstract

Inspired by numerous lab on a chip, biomedical and bioengineering applications such as cell sorting, focusing, trapping, and filtering of particles, manipulation of micron sized particle trajectories has been of significant interest in the context of microfluidics. Systematic deflection of microparticles away from their initial streamlines is a central objective in microfluidic particle manipulation. In many widely used microfluidic platforms including deterministic lateral displacement (DLD) devices, density matched, force free particles suspended in low Reynolds number flows encounter arrays of obstacles that potentially breaks the flow symmetry and alter their trajectories. Despite the prevalence of these devices, the physical mechanism responsible for particle deflection from encountering obstacle wall in strictly non inertial flows (Stokes flows) remains incompletely understood and is often attributed to short range contact interactions rather than hydrodynamic effects.

Non-inertial hydrodynamics of manipulating particle transport

Abstract

Inspired by numerous lab on a chip, biomedical and bioengineering applications such as cell sorting, focusing, trapping, and filtering of particles, manipulation of micron sized particle trajectories has been of significant interest in the context of microfluidics. Systematic deflection of microparticles away from their initial streamlines is a central objective in microfluidic particle manipulation. In many widely used microfluidic platforms including deterministic lateral displacement (DLD) devices, density matched, force free particles suspended in low Reynolds number flows encounter arrays of obstacles that potentially breaks the flow symmetry and alter their trajectories. Despite the prevalence of these devices, the physical mechanism responsible for particle deflection from encountering obstacle wall in strictly non inertial flows (Stokes flows) remains incompletely understood and is often attributed to short range contact interactions rather than hydrodynamic effects.
Paper Structure (73 sections, 102 equations, 45 figures)

This paper contains 73 sections, 102 equations, 45 figures.

Table of Contents

  1. Introduction
  2. Microfluidics for manipulating particles
  3. Particle manipulation leveraging Stokes flow hydrodynamics
  4. Review of previous related research
  5. Stokes flow driven by oscillatory boundary layers: Steady streaming flow
  6. Inertial force in steady streaming flow
  7. Manipulating particle motion for attachment and deposition
  8. Organization of the dissertation
  9. Key Accomplishments
  10. Hydrodynamic formalism of particle-wall interaction in arbitrary Stokes flow
  11. Introduction
  12. Particle velocity in the presence of a wall
  13. Wall-parallel corrections to the particle velocity
  14. Wall-normal corrections to the particle velocity
  15. Conclusion
  16. ...and 58 more sections

Figures (45)

  • Figure 1: (a) Streamlines through an array of pillars. Flow is from left to right kabacaouglu2019sorting. (b) Sketch of particles following different paths aghilinejad2019transport. Particles, depending on their size $D_p$, interact with pillars and then either follow the streamlines and “swap lanes” (blue) or stay in the same lane (red). (c) Fluorescent image of particle transport (blurry white strips) through porous media while showing the evidence of attachment of some of them around the obstacles (bright white spots) miele2025flow.
  • Figure 2: Stroboscopic images of complex streaming patterns. (a) droplet microstreaming, droplet is pinned in the microchannel and driven by the trapped bubble underneath das2020robustness. (b-d) in simple back and forth oscillation around (b) an equilateral triangle with sharp edges, vortex pairs form around the sharp corners (abrupt change in local curvature) tatsuno1975circulatory, (c) a square inducing multiple fountain and anti-fountain vortex pairs tatsuno1974circulatory, (d) a bullet shaped multi curvature obstacle, showing agreement in simulation (upper half) and experiment (lower half) bhosale2022multicurvature.
  • Figure 3: (a) Motion of a neutrally buoyant particle (red) in the vicinity of an oscillating bubble. (b) Close-up shows that particle trajectory (red) crosses streamlines (blue) while being transported over the bubble, indicating a net attraction towards bubble over fast time scales of a few ms agarwal2021unrecognized.
  • Figure 4: (a) Particle sticking and deposition induced by streaming vortices around the corner of a triangular obstacle (see appendix \ref{['appen sticking from streaming']} for more details). (b-d) particles trajectory exhibiting streamline crossing behavior (close loop (a), spiral in (b), and spiral out (c)) in simplified bubble microstreaming flows. liu2025particlethesis.
  • Figure 5: Schematic of a small spherical particle of radius $a_p$ located at $\boldsymbol{x}_p=(x_p,y_p)$ in the vicinity of an obstacle boundary of radius of curvature $R(\boldsymbol{x}$). The particle is immersed in a density-matched Stokes background flow $\boldsymbol{u}(\boldsymbol{x})$.
  • ...and 40 more figures