Session R8: Microscale Flows: Particles

Size-selective sorting in bubble streaming flows: Particle migration on fast time scales

Steady streaming from ultrasonically driven microbubbles is an increasingly popular technique in microfluidics because such devices are easily manufactured and generate powerful and highly controllable flows. Combining streaming and Poiseuille transport flows allows for passive size-sensitive sorting at particle sizes and selectivities much smaller than the bubble radius. The crucial particle deflection and separation takes place over very small times (milliseconds) and length scales (20-30 microns) and can be rationalized using a simplified geometric mechanism. A quantitative theoretical description is achieved through the application of recent results on three-dimensional streaming flow field contributions. To develop a more fundamental understanding of the particle dynamics, we use high-speed photography of trajectories in polydisperse particle suspensions, recording the particle motion on the time scale of the bubble oscillation. Our data reveal the dependence of particle displacement on driving phase, particle size, oscillatory flow speed, and streaming speed. With this information, the effective repulsive force exerted by the bubble on the particle can be quantified, showing for the first time how fast, selective particle migration is effected in a streaming flow.   

Forces on particles in microstreaming flows

In various microfluidic applications, vortical steady streaming from ultrasonically driven microbubbles is used in concert with a pressure-driven channel flow to manipulate objects. While a quantitative theory of this boundary-induced streaming is available, little work has been devoted to a fundamental understanding of the forces exerted on microparticles in boundary streaming flows, even though the differential action of such forces is central to applications like size-sensitive sorting. Contrary to other microfluidic sorting devices, the forces in bubble microstreaming act over millisecond times and micron length scales, without the need for accumulated deflections over long distances. Accordingly, we develop a theory of hydrodynamic forces on the fast time scale of bubble oscillation using the lubrication approximation, showing for the first time how particle displacements are rectified near moving boundaries over multiple oscillations in parallel with the generation of the steady streaming flow. The dependence of particle migration on particle size and the flow parameters is compared with experimental data. The theory is applicable to boundary streaming phenomena in general and demonstrates how particles can be sorted very quickly and without compromising device throughput.   

Drag and diffusion coefficient of a spherical particle attached to a fluid interface

We consider a spherical particle attached to the interface between two immiscible fluids of large viscosity contrast. The degree of immersion in the two fluids is determined by the contact angle. For small enough particles and significant contact-angle hysteresis, it can be assumed that the three-phase contact line is pinned at the particle surface. We study the movement of such particles along the fluid interface for the case of small Reynolds and capillary numbers. We solve the Stokes equation based on two geometric perturbation expansions around contact angles of 90 degrees and 180 degrees, the latter corresponding to a particle completely immersed in the less viscous phase. Based on the Lorentz Reciprocity Theorem we obtain expressions for the drag coefficient of an interfacial particle which are analogs of the well-known Stokes drag coefficient for a particle moving in an unbounded medium. Interpolation of the two results gives a relationship which approximates the drag coefficient quite accurately over the entire range of contact angles. A comparison with previously published numerical results for contact angles below 90 degrees shows good agreement. Using the fluctuation-dissipation theorem, we also obtain expressions for the diffusion constant of a small particle attached to a fluid interface.   

Size-sensitive particle trajectories in three-dimensional micro-bubble acoustic streaming flows

Oscillating microbubbles generate steady streaming flows with interesting features and promising applications for microparticle manipulation. The flow around oscillating semi-cylindrical bubbles has been typically assumed to be independent of the axial coordinate. However, it has been recently revealed that particle motion is strongly three-dimensional [A. Marin {\it et al.}, Phys. Rev. Appl. 3, 041001, (2015); Rallabandi {\it et al.}, J. Fluid Mech. 777, (2015)]: Small tracer particles follow vortical trajectories with pronounced axial displacements near the bubble, weaving a toroidal stream-surface. A well-known consequence of bubble streaming flows is size-dependent particle migration [C. Wang {\it et al.}, Biomicrofluidics (2012)], which can be exploited for sorting and trapping of microparticles in microfluidic devices. In this talk, we will show how the three-dimensional toroidal topology found for small tracer particles is modified as the particle size increases up to 1/3 of the bubble radius. Our results show size-sensitive particle positioning along the axis of the semi-cylindrical bubble. In order to analyze the three-dimensional sorting and trapping capabilities of the system, experiments with an imposed flow and polydisperse particle solutions are also shown.   

In-situ Microfluidic Measurement of the Dielectric Constant of Colloidal Particles

The ability to manipulate micron-sized colloidal particles or biological cells in a liquid medium in microfluidic geometries is necessary in lab on a chip devices for micro scale biological analysis and diagnostics for sorting and directing the trafficking of the particles. In dielectrophoresis, a nonuniform electric (E) field is applied to move the particles along the gradient of the field energy, and the velocity is a function of the particle's dielectric constant. Measurement of the dielectric constant is necessary in order to scale field strengths for applications, and it is important to undertake this measurement in-situ as the particle's dielectric content can be modified by the suspending medium (e.g. adsorption onto the particle surface). In this talk we measure directly the dielectric constant of colloids in a microfluidic channel by applying an electric field with ``V''-shaped and planar electrodes on opposite sides of the channel. The cusp of the ``V'' shape concentrates the field to provide a sufficient field intensity gradient which is designed to be uniform across the height of the channel and to vary only with its width. Optical measurements of the diffusiophoretic velocity of polymer colloids are compared to simulations based on numerical solution of the E-field and particle hydrodynamics to obtain the particle dielectric constant and investigate the effect of biomolecule adsorption on the particle surface.   

MicroPIV measurements of flows induced by rotating microparticles near a boundary

We report the hydrodynamics induced by single digit micron sized particles rotating in low Reynolds number environments and analysis of their flow fields using MicroPIV. Magnetic microparticles floating a few nanometers above a glass substrate, in an otherwise quiescent fluid, were actuated wirelessly using a rotating magnetic field controlled using two pairs of orthogonally positioned electromagnetic coils. A highspeed camera was used to sufficiently capture the motion of nanometer sized seeding particles at 500 frames per second as well as track the rotation of the microparticles. Analysis of microPIV data revealed good agreement with the analytical solution for flow generated by a sphere in an infinite fluid. Additionally, the sequential flow fields generated by two particles as they approach each other, to form dimers, was also analyzed. It was observed that as two synchronously rotating beads of equal diameter are placed closed together, their flow fields were offset, at their combined center of mass, and superimposed near their outer peripheries. These results suggest that colloidal magnetic particles can be pattered in a manner such that when rotated their generated flow is globally coordinated.   

Hydrodynamic repulsion of elastic dumbbells

Dynamics of two identical elastic dumbbells, settling under gravity in a viscous fluid at low Reynolds number are analyzed within the point-particle model. Initially, the dumbbells are vertical, their centers are aligned horizontally, and the springs which connect the dumbbell's beads are at the equilibrium. The motion of the beads is determined numerically with the use of the Runge-Kutta method. After an initial relaxation phase, the system converges to a universal time-dependent solution. The elastic dumbbells tumble while falling, but their relative motion is not periodic (as in case of rigid dumbbells or pairs of separated beads). The elastic constraints break the time-reversal symmetry of the motion. As the result, the horizontal distance between the dumbbells slowly increases - they are hydrodynamically repelled from each other. This effect can be very large even though the elastic forces are always much smaller than gravity. [For the details, see M. Bukowicki, M. Gruca, M. L. Ekiel-Jezewska, J. Fluid Mech. 767, p. 95 (2015).] The dynamics described above are equivalent to the motion of a single elastic dumbbell under a constant external force which is parallel to a flat free surface. The dumbbell migrates away from the interface and its tumbling time increases.   

Collective effects in the flotation of electrically charged particles at an interface

We study the flotation of electrically charged line particles at a liquid-gas interface. Motivated by recent experiments on the anomalous attraction of charged and magnetic particles at interfaces, we consider the equilibrium of the particles, accounting for the weight of each as well as the electrical and surface tension forces acting on them. Our numerical solution of the force balance equations shows that as the number of particles increases, the particles sink deeper into the liquid and ultimately sink. To understand whether the clumps of particles that are formed are stable, we use a free energy analysis; this shows that as the number of particles $N$ increases, the binding energy \textit{per particle} increases also. We compare our numerical results with scaling and experimental analyses.   

High-Throughput, Motility-Based Sorter for Microswimmers and Gene Discovery Platform

Animal motility varies with genotype, disease progression, aging, and environmental conditions. In many studies, it is desirable to carry out high throughput motility-based sorting to isolate rare animals for, among other things, forward genetic screens to identify genetic pathways that regulate phenotypes of interest. Many commonly used screening processes are labor-intensive, lack sensitivity, and require extensive investigator training. Here, we describe a sensitive, high throughput, automated, motility-based method for sorting nematodes. Our method was implemented in a simple microfluidic device capable of sorting many thousands of animals per hour per module, and is amenable to parallelism. The device successfully enriched for known \textit{C. elegans} motility mutants. Furthermore, using this device, we isolated low-abundance mutants capable of suppressing the somnogenic effects of the \textit{flp-13} gene, which regulates sleep-like quiescence in \textit{C. elegans}. Subsequent genomic sequencing led to the identification of a \textit{flp-13}-suppressor gene.   

Continuous size separation of micro/nano particles using ridged microchannel by controlling particle position in the z-direction

In the last meeting we presented results that demonstrated that the particle trajectories depend on their z-position inside a microchannel with diagonal ridges. The phenomenon arises due to vortices created by the diagonal ridges that transport the fluid at the channel center in the negative y-direction, whereas the fluid located near the bottom channel walls moves in the positive y-direction. This effect is harnessed to improve the separation of particles by size. We have incorporated a vertical sheath to improve the z focusing of particles in our device and operated the device at an optimized sample to vertical sheath flow rates. As the vertical sheath flow velocity increases, the sample flow streamlines are pushed towards the bottom channel wall. Due to vortices created by diagonal ridges the small particles are pushed towards the bottom channel and move with positive y-trajectories. Large particles also are pushed towards the bottom of the channel, yet due to their larger sizes and close to the gap size they experience a net negative y-trajectory. We are able to improve the purity of large particle enrichment by over 5 times as compare to our previous work.   

Control of Lateral Inertial Migration Rate of Particles in Microchannels

The net inertial lift force acting on particles results in lateral inertial migration across streams. The migration direction and magnitude is strongly dependent on channel geometry, size of the particle, Reynolds number and location of the particle within the channel cross-section. In many chemical and biological applications in which precise temporal control and solution exchange around particles is required, the initial variation in distribution of focusing positions of particles within the channel cross-section becomes a determining factor. This variation is shown to be a limiting factor in achieving precise control over the migration time in previous studies. In order to improve uniformity of the average migration rate, a microfluidic device is designed to aid particles in achieving a single stable equilibrium position by inducing a net helical flow. Using this inertial focusing platform, a comprehensive numerical and experimental study is performed to characterize the range of lateral migration rates for rigid spherical particles as a function of particle size, initial particle position, flow rates of each stream and Reynolds number for a given channel geometry. The tool developed in this study can be used to achieve precise migration characteristics for the microparticles crossing fluid streams in microchannels over millisecond time scales.