Session ZC18: Microscale and Nanoscale Flows: Particles, Drops, Bubbles II

Permanent displacement and particle capture in vortical Stokes flow

Density-matched, force-free particles in Stokes flow are typically assumed to passively follow streamlines. When encountering a boundary, steric requirements forbidding penetration enforce deviations from the initial streamline, leading to well-defined changes in normal and tangential velocity components. We show that, if the geometry of the boundary or the geometry of the flow field break multiple symmetries, such deviations result in net displacement, and thus meaningful manipulation of particle transport, is possible. Internal vortical Stokes flows are well-suited for related applications, as the small displacement effects of wall encounters accumulate. In a class of symmetry-broken vortex and cavity flows, derived from Moffatt eddy solutions of the Stokes equations, significant displacements both away from and towards the wall become possible. In certain flows of this type, particles thus converge to predictable fixed points or limit-cycle trajectories. In others, they approach a wall or boundary ever more closely while contact remains impossible; in realistic situations, small-scale forces then lead to sticking in predictable positions. Exploiting such effects of particle displacement at zero Reynolds number together with those using finite particle inertia will lead to new protocols of particle manipulation generally and particle capture in filters specifically.   

High-Speed Droplet Generation in 3D Gas-Liquid Droplet Microfluidic Systems

Generation of liquid droplets within a confined gaseous microflow is a relatively unexplored approach to that of conventional liquid-liquid droplet systems. The creation of uniform particles purely in air (monodisperse aerosols), avoiding cross-contamination of the droplets’ contents by the presence of a secondary liquid is the main advantage. Earlier work has shown that the production of extremely small droplets (15 μm, perhaps submicron) at >100 kHz frequencies, an order of magnitude higher than those of liquid-liquid droplet systems, is possible. The flow regime of gas-liquid droplet microfluidic devices was also characterized to find the conditions necessary for droplet generation in quasi two-dimensional (where all flow channels have the same height), flow-focusing geometries.

Here, we explore and characterize non-planar, ‘three-dimensional’ gas-liquid droplet microfluidic devices to overcome some of the problems that quasi two-dimensional structures have. By ensuring that the carrier phase (liquid) is enveloped by the continuous phase (gas), additional contact of the carrier phase with the flow channel walls is avoided, enhancing throughput performance and system robustness. We use standard 2D planar soft lithography techniques to create 3D architectures instead of custom assemblies needed for each 3D microfluidic device using concentric capillaries. This allows for easier customizability of the flow-focusing geometries to determine optimal architectures.

We have experimentally visualized and comprehensively mapped the flow regime of various 3D gas-liquid droplet microfluidic chip designs via a high-speed camera. We compare the results of the work on quasi-2D chips and discuss how 3D gas-liquid droplet microfluidic systems obtain a higher droplet generation throughput; via a faster transition to the jetting regime by avoiding liquid-wall collisions that delay said transition. Finally, we test the effects of geometry on the flow regime and discuss further optimization to maximize droplet generation.   

Eccentric equilibration of buoyant, deformable drops in a channel

The motion of droplets and bubbles under gravity is fundamental to several multiphase processes, including liquid-liquid extraction and emulsion stability and separation. We use a boundary-integral method to simulate the motion of non-neutrally buoyant, deformable droplets between two horizontal, flat plates in a pressure-driven Poiseuille flow at low Reynolds number. Unlike neutrally buoyant drops that always migrate cross-stream to reach a steady state at the channel centerplane when released off-center, the equilibrium position of non-neutrally buoyant drops is determined by a balance between the buoyancy force and the deformation-induced hydrodynamic drift. We study the effect of variation in Bond number, capillary number, drop size, and initial lateral position of a buoyant drop on its lateral migration and the steady-state position. With increasing Bond number, the drop equilibrates closer to one of the walls, drop velocity decreases, and drop deformation increases. We predict a critical Bond number, above which the deformation-induced drift is overpowered by gravity and drops cease to reach a steady state. With increasing capillary number, drops equilibrate closer to the channel centerplane. Above a critical capillary number, however, drops experience large deformation and may not reach a steady state. Drops starting from different initial positions under identical conditions equilibrate at the same lateral position.   

Estimating the Rate of Nanopartice Aggregation in Porous Media

The diffusivity of nanoparticles (NPs) in porous media is strongly affected by aggregation among particles, a poorly understood phenomenon due to the challenges of conducting experiments in complex porous media and simulating interaction forces responsible for agglomeration. Our aim was to build a Lagrangian particle tracking method based on the force balance approach to simulate the movement, interaction, and aggregation of cerium dioxide (CeO₂) NPs suspended in 0.2 M potassium chloride (KCl) when they moved through randomly packed spheres.¹ The movement of each particle at each timestep was generated by six major forces including gravity, buoyance, random, drag, Van der Walls, and electrostatic forces. The distances among particles were calculated at each step, and two particles would be in the same cluster if the separation distance between them was less than the primary minimum. Thus, the number of aggregates and their sizes were tracked in time and space. We also set up a model to examine the effects of fluid velocity, particle size, and particle concentration on the aggregation rate of CeO₂.² Different simulations of NPs with different particle sizes and concentrations moving through porous media at different velocities were performed. The aggregation rate of CeO₂ NPs in the diffusion-limited aggregation was found to be linearly dependent on time (in pore volume units), and the slope of the line was a power function of Reynolds number, Schmidt number, and particle concentration.³ Moreover, the exponent of the Sc number is three times larger than that of the Re number, suggesting that the dominance of random particle movement surpasses convection.

REFERENCES

Purely Geometrical Effects in Self-locomotion of Microswimmers

Within the geometrical kernel framework, we provide a unified approach for studying the self-locomotion of microswimmers by surface distortion or self-phoresis. We provide geometrical kernels and discuss the effect of surface concavity or convexity on microswimmer dynamics. The geometrical kernel is constructed from the surface traction of an auxiliary problem of Stokes flow past the same geometry.   

Drift of elastic hinges in oscillating shear flows

Elastic filaments are prevalent in many natural and industrial systems, including bacterial flagella, polymer chains, and natural and synthetic fibers advected in flows. Due to their elastic nature, they deform under the influence of hydrodynamic stresses as they are advected by flows. This deformation leads to more complex dynamics than that of a rigid particle. We are particularly interested in cases of drift, where passive particles by virtue of their shape and deformation self-propel in directions perpendicular to the mean flow direction. We use an elastic hinge, consisting of two rigid rods joined by an elastic torsional spring, as an analog for an elastic fiber. Similar rigid hinge shapes have been shown to drift in steady shear flows when they are very asymmetric. However, no such rigid particles drift in flows with a shear rate that is a sinusoidal function of time. Here, we demonstrate that symmetric hinges can drift in oscillating shear flows and that the magnitude and direction of drift can be selected by choosing the hinge material properties, geometry, and frequency of oscillation. This opens the possibility of tuning both particles and flows to control particle motion, leading to enhanced particle separation, mixing, or self-assembly of more complex structures.   

Dynamics of a deformable droplet inside a microfluidic chamber under gravity

Biomicrofluidics research like cell-perfusion, cell-sorting, and droplet-based microchemical reactors often involves isolating a single cell or drop in a bioreactor chamber and exposing it to controlled flow of nutrient-rich solution. This chamber enables hydrodynamic trapping of the small cell or drop in microwell. We use a moving-frame boundary-integral simulation to study the motion of a three-dimensional deformable droplet under gravity in a chamber with nearly sharp corners in the Stokes flow regime. The dynamics of the droplet is influenced by the drop-to-bulk fluid viscosity ratio, capillary number, Bond number, chamber size, and the smoothing radii of the arced corner. Increasing the Bond number causes the drop to settle towards the bottom of the chamber, while a smaller Bond number allows the drop to escape without any hook or tail. A moderate Bond number may result in droplet breakup with thin neck formation near the corner. Under the same flow conditions, a smaller chamber size results in droplet trapping, while a larger chamber size facilitates droplet escape. Higher capillary numbers lead to large drop deformation, with the tail becoming trapped and the head elongating out of the channel.   

Scalable production of functional Janus particles in 3D printed microfluidic device for heavy oil removal

Microfluidic droplet generators can produce droplets and particles of uniform size and varying morphologies. However, due to the low throughput, production scale-up through device parallelization is essential to apply them practically. While high-level microfabrication techniques have been required to fabricate parallelized devices, the advent of 3D printing has enabled the fabrication of devices with complex 3D channel structures at a low cost and with minimal effort. In this study, we designed and fabricated a parallelized and multiplexed droplet generator that can produce amphiphilic magnetic Janus particles (AMJPs) at a rate 40 times faster than a single device while maintaining monodispersity and uniformity. In this device, each droplet generator is connected via flow distributors, which achieve uniform flow distribution and minimizes device volume. The resulting AMJPs can be irreversibly adsorbed at the interface, effectively Pickering emulsifying oil contaminants in water and preventing further contamination. The effects of oil viscosity, water pH, and salinity on the size and removal rate of AMJPs-covered Pickering emulsion were experimentally investigated. Furthermore, the effectiveness and reusability of AMJPs in removing heavy crude oil were demonstrated.   

Dynamics of spherical squirmers under gravity near a no-slip planar wall

The hydrodynamic interactions between a microswimmer and a wall have ubiquitous biological and technological applications. A plethora of gravity-induced dynamics of a squirming microswimmer near a planar no-slip wall provides a platform for designing artificial microswimmers that can generate directed propulsion through their translation-rotation coupling near a wall. In this work, we provide exact solutions for a squirmer facing perpendicularly towards or away from the planar wall. We use these solutions to validate numerical code based on a boundary integral method for arbitrary squirmer-to-wall distances down to 0.1% of the squirmer radius. We then use this boundary integral code to investigate the rich gravity-induced dynamics of a squirmer near a wall with and without repulsion, mapping out the detailed bifurcation structures of a squirmer in terms of its orientation and distance to the wall. Simulation results show a squirmer may transverse along the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion.