Particle manipulation by hydrodynamic effects in vortical Stokes flow

Abstract

The main motivation of this work is the quantitative prediction and description of particle manipulation (displacement across streamlines) in microfluidic flow. Much attention has been paid recently to placing particles in fast oscillatory flow fields, usually driven by microbubbles actuated by low-frequency ultrasound, where particle inertia leads to deterministic displacements. However, such devices invariably set up simultaneous streaming flows that are interpretable as driven Stokes flows. The potential role of these flows in not just passively transporting but likewise manipulating the particles has not been appreciated. Therefore, we investigate whether a Stokes flow by itself can meaningfully affect the displacement of a single particle or a rigid dumbbell, given the properties and symmetries of the flow. To manipulate a single particle, its hydrodynamic interaction with a nearby boundary is crucial for obtaining non-trivial results. To irreversibly displace a particle using this effect, we find that the flow symmetry must be broken in specified ways. Controlling the flow geometry, one can drive particles to fixed points, cycles, or towards boundaries, with the possibility of controlling eventual attachment (sticking) of the particle. For rigid dumbbell particles, we show that such controlled displacement in Stokes flow is possible even without the presence of nearby boundaries, but again with requirements on the broken symmetry of the chosen flow. In practical microfluidic devices, these effects could be set up in manifold ways, by themselves or in combination with inertial forces for more versatile particle manipulation.

Figures (40)

• Figure 1: (a) A vibrating bubble located at a side channel opening in a microfluidic channel with tracer particles present in the fluid. (b) Characteristic vortex pair streaming flow around a bubble, visualized by streaks of passive tracers rallabandi2014two.
• Figure 2: Schematic and nomenclature for a quantitative description of the particle trajectory $\vb{r}_{p}(t)$ under the action of the bubble-driven oscillatory flow thameem2017fast.
• Figure 3: Particle trajectories ($a_p =7\mu m$) in different Stokes flows near a wall. (a) Particles move in closed loops, $\Psi_a(r,\theta)=-(\frac{1}{r^2}-\frac{1}{r^4})(\sin2\theta-\sin4\theta)$. (b) Particles show spiral-in behavior, $\Psi_b(r,\theta)=-(\frac{1}{r^2}-\frac{1}{r^4})\sin2\theta+(\frac{1}{r^4}-\frac{1}{r^6})\sin4\theta$. (c) Particles show spiral-out behavior, $\Psi_c(r,\theta)=-(\frac{1}{r^2}-\frac{1}{r^4})\sin2\theta-(\frac{1}{r^4}-\frac{1}{r^6})\sin4\theta$.
• Figure 4: Schematic of a particle at $(x_p,y_p)$ near a flat wall submerged in an arbitrary background flow ${\bf u}$, with further geometric parameters defined.
• Figure 5: (a) Schematic of Stokes flow in a wedge between rigid boundaries. (b) Schematic of Stokes flow between parallel plates; the source of the fluid motion can be visualized as a rotating cylinder at a large negative $x$ coordinate between the plates. Modified from the original sketches in moffatt1964viscous.