Session J07: Microscale Flows: Particles, Drops, Bubbles (8:00am - 8:45am CST)

Multi-scale dynamics of colloidal deposition and erosion in porous media

Diverse processes---e.g., environmental pollution, groundwater remediation, oil recovery, filtration, and drug delivery---involve the transport and deposition of colloidal particles in three-dimensional porous media. Using confocal microscopy, we directly visualize this process in situ and thereby identify the fundamental mechanisms by which particles are distributed throughout the pore space. At high injection pressures, hydrodynamic stresses cause particles to both deposit on and become eroded from the solid matrix continually--- strikingly, forcing them to be distributed throughout the entire medium. By contrast, at low injection pressures, the relative influence of erosion is suppressed, causing particles to be localized near the inlet of the medium. Unexpectedly, these macroscopic distribution behaviors are tuned by imposed pressure in similar ways for particles of different charges, even though the pore-scale distribution of deposited particles is sensitive to particle charge. Our results thus reveal how the multi-scale interactions between fluid, particles, and the solid matrix control how colloids are distributed in a porous medium.   

Shape of long gas bubbles propagating in square capillaries

We present the results of a systematic analysis of the shape of the thin lubrication film surrounding a long gas bubble transported by a liquid flow in a square capillary. Direct numerical simulations are performed for a range of capillary and Reynolds numbers Ca=0.002-0.5 and Re=1-2000, and very long bubbles, up to 20 times the channel hydraulic diameter. In agreement with previous studies, when Ca>0.05 the bubble exhibits an axisymmetric shape, whereas for Ca<0.05 the bubble flattens at the centre of the channel wall and thick liquid lobes are left at the corners. When Ca<0.01, the thin film at the centre of the wall assumes a saddle-like shape, which leads to the formation of two constrictions at the sides of the liquid film profile. The resulting cross-stream capillary pressure gradients drain liquid out of the thin-film, whose thickness decreases indefinitely as a power-law of the distance from the bubble nose. We report detailed values of the centreline and minimum film thickness along the bubble, bubble speed, and cross-sectional gas area fraction, at varying Ca and Re. Inertial effects retard the formation of the saddle-shaped film at the channel centre, which may never form if the bubble is not sufficiently long. However, the film thins at a faster rate as Re increases   

Acoustic Anti-Clogging Effect in Microfluidic Constrictions: Can Clogging Be Reduced by Simply Redistributing Particles?

Forcing stuff through narrow constrictions leads inevitably to clogging. Regardless the system we are dealing with: grains in silos, particles through funnels, crowds through narrow exits, or in our case, a suspension through a microfluidic constriction. Finding methods to influence and eliminate the clog formation is not only of crucial importance to improve the mass transfer in industrial systems, but also to save lives when dealing with crowds. In this work we study the effect of ultrasound actuation on a diluted suspension passing through a very narrow microfluidic constriction (from 1 up to 2 particle diameters). A standing acoustic wave with a central node in the middle of the channel induces acoustic radiation forces on the suspended particles, leading to particle migration towards the center of the channel. But, is this transversal particle redistribution -- caused by the acoustic radiation force-- enough to cause a substantial improvement of the mass transfer? We will present experimental and numerical results that confirm that, although ultrasound actuation indeed has a great influence on the performance of the microfluidic hourglass, the particle redistribution around the center of the channel plays only a minor role in the prevention of clogs.   

Using Hydrodynamic Forces to Tune the Particle Adhesion on Microchannel Walls

Hydrodynamic studies have made it possible to predict and quantify the rate of adhesion of molecules to a reactive surface located in a straight channel under flow [Squires et al, 2008]. However, many applications deal with the adhesion of much larger objects like particles. The behavior of these objects is not described by existing theories that focus on point objects. In our study, we seek to extend the molecular theories to the capture of solid particles. While few of our experimental results are well predicted by the pre-existing theory, most of them give much lower capture rates. However, numerous studies have shown that the liquid surrounding a particle exert an inertial lift force that pushes it away from the walls, which may be responsible for this adhesion rate drop. We show, through numerical simulations and modeling, that it is possible to quantitatively predict our experimental adhesion rate, without any fitting parameters, using a new dimensionless number, the lifto-diffusive number. This highlighted phenomenon is highly non-linear and abrupt: in a particular regime, doubling the flow rate leads to a decrease by a factor of 15000 in the rate of particle adhesion, thus allowing to trigger or to prevent the adhesion of particles by a pure hydrodynamic lever.   

Numerical Investigation of Paramagnetic Elliptical Microparticles in Curved Channels and Uniform Magnetic Fields

We present a numerical investigation on the dynamics of a paramagnetic elliptical particle traveling in a curved channel under a low Reynolds number Poiseuille flow and a uniform magnetic field. By applying a direct numerical simulation and using a finite element method, based on an arbitrary Lagrangian-Eulerian approach, we focus on the particle's rotation and radial migration. Our numerical results show that the particle's rotational and radial dynamics are affected by the channel geometry, the strength and direction of the magnetic field, and the particle shape. The migration of the particle was examined after executing a pi rotation and at the exit of the curved channel with and without a uniform magnetic field. In the absence of a uniform magnetic field, the net migration of the particle remains zero due to the symmetry of its rotation. On the other hand, in the presence of a uniform magnetic field, the symmetry is broken, and the net migration of the particle-wall distance increases along with the magnetic field strength. We determine that the particle's migration is due to its rotational dynamics altered by the magnetic torque that constantly changes direction during transportation.   

Hydrodynamic trapping of microrollers by cylindrical obstacles

Suspensions of microrollers show unique collective effects and emergent structure formation, such as clusters stabilized by hydrodynamics alone. Microrollers are rotating colloidal particles that become active close to a wall due to an asymmetric flow of the fluid around the particles. The flow field of the fluid around the microroller is distinctively different to the flow field of other commonly used swimmers such as pullers and pushers. Here, we study the interaction of microrollers with obstacles in their path. In contrast to many other active matter systems, the propagation direction in this system is prescribed, resulting in unique particle-obstacle interactions. Inspired by experiments, we study the interaction of the microrollers with cylindrical obstacles using high-resolution Brownian dynamics simulations, including long range hydrodynamics. Even in this basic model system for a complex environment, we find hydrodynamic trapping of the microroller in the wake of the obstacles for parameters readily accessible in the lab. We measure the trapping strength as a function of the size ratio of the microroller and obstacle, and the frequency of rotation of the microroller. Moreover, we find that Brownian motion is required for the microroller to both enter and leave the trap.   

Not Participating

EDGE microfluidic devices exploit a sudden expansion in channel depth -- and thus drop in Laplace pressure -- to drive formation of bubbles (or droplets). This geometry allows for the production of monodisperse, small bubbles over a wide range of air pressures, and independent of continuous phase shear. Here, we use arrays of extremely shallow rectangular pores (1 micrometer height) to study the formation of small bubbles (approx. 20 micrometer) and their stabilization with whey proteins commonly used in food foams. Protein adsorption to the air-water interface plays a crucial role in the bubble dynamics, giving rise to two distinct regimes of bubble creation that differ in frequency and size of bubbles formed at the pore, and the extent of coalescence. We calculate the pressure gradients driving the flows to provide further insights into the two regimes of bubble formation.   

Motion of Janus sphere in two-dimensional confinement

Janus particles propel themselves by generating concentration gradients along their surface. The corresponding concentration and hydrodynamic field decay as $ {O}(1/r) $ and $ {O}(1/r^{2}) $, respectively. Since these disturbances are long-ranged, even a remote interaction with confined geometry can have a profound effect on the self-propulsion. In this work, we theoretically study the motion of Janus sphere through a Hele-Shaw confinement; the particle is placed at an arbitrary location between walls which are bounded in $ y- $direction and infinite in $ x $ \& $ z- $directions. Using the method of reflections in conjunction with Faxen transformations, we study the competition between phoretic and hydrodynamic interactions. The presence of boundaries results in a modification of translation velocity and endows the Janus particle with a rotational velocity. Furthermore, we analyze the effects of mobility (i.e. solute-particle interaction) and surface activity coverage.   

Influence of interfacial tension on viscous multiphase flows in coaxial microchannels

The role of interfacial tension on liquid/liquid microfluidic flows is experimentally investigated for fluid pairs having similar viscosity contrasts. A coaxial microdevice is employed to examine the situation where a less viscous fluid is injected in a sheath of a more viscous fluid using both immiscible and miscible fluid pairs. Data obtained from high-speed imaging show a variety of regular flow patterns, including dripping, jetting, and core-annular flows, as well as less familiar flow regimes, such as wavy, mist, and inverted flows patterns. Flow maps are delineated over a wide range of injection flow rates to clarify the relationship between flow transition and fluid properties. In particular, interfacial tension is shown to affect the morphology and dynamics of flow patterns at different ranges of flow rates.   

Advection-diffusion coupling of nanoparticle ensembles from short to long times

Colloid transport in nanoscale flows is important in wide range of applications from chemical separation to drug delivery. In these flows, the coupling between advection and Brownian diffusion leads to an enhanced particle dispersion by orders of magnitude. Using evanescent wave microscopy in a microchannel, we observe nanoparticle motion in a near-surface zone where the velocity gradients, and thus the dispersion, are the largest. Supported by a theoretical model and simulations based on overdamped Langevin dynamics, our experimental results provide the full dynamics of the particle dispersion from short to long times. In particular, we highlight how the initial distribution of particles affects the time dependence of the transient regime. These results are crucial in controlling the nanoconfined chemical reactions or dynamical adsorption.   

Dynamics of deformable sheets in extensional flow: stretching, hysteresis, and folding

Applications of 2D materials such as graphene and boron nitride usually require a fluidic environment to achieve large-scale production. Those processes involve complicated fluid-structure interactions, such as stretching and folding, that have not been fully understood. We study here a continuum model of deformable sheets with disc, square or rectangular rest shapes, subjected to planar or uniaxial extensional flows. The model accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. In planar extensional flow, we observe for all shapes a hysteretic transition analogous to the coil-stretch transition of long flexible polymers in solution: an abrupt jump from a compact to the stretched state with a small increase in deformability. This discontinuity marks a bistable region where multiple stable steady states exist. In uniaxial extensional flow, besides a compact-stretched transition similar to that observed in planar extension, the radially compressive flow also induces interesting wrinkling and folding patterns depending on the deformability of the sheet; these affect the time dependence and final degree of stretching of the sheet, and further influence the hysteresis behavior.   

Cross-stream migration of non-spherical particles in a general second-order fluid flows

We have developed a theory to investigate the cross-stream migration of ellipsoids in a weakly viscoelastic fluid under various pressure-driven flow profiles (circular tube flows and slit flows). The viscoelastic fluid we investigate is a general second-order fluid characterized by Weissenberg number Wi$=\psi $1 $\gamma $/$\mu $ and constant $\alpha =\psi $2/$\psi $1, where the first and second normal stress coefficients are $\psi $1 and $\psi $2, $\gamma $ is the characteristic shear rate of the flow, and $\mu $ is the total viscosity. Considering the limit of weakly viscoelastic flow (Wi$\ll $1), we use perturbation theory and the reciprocal theorem to derive both the polymeric force and torque on a particle to O(Wi). Our theory is valid for an ellipsoid in any quadratic flow field, and have validated the theory for three cases: (a) sedimentation of a general ellipsoid in a second order fluid, (b) particle migration of a sphere in a pressure driven flow, and (c) particle migration of an ellipsoid in a pressure driven flow under the co-rotational limit ($\alpha =$ -1/2). After verification, we use our theory to compute how the first and second normal stresses affect the motion of a particle to towards the center of pressure driven flows, and discuss the orientation dynamics. Scaling results are presented for the particle migration speed.   

New repulsive lift force between objects due variations of wall slip

Surfaces in nature are rarely perfectly smooth but have physical, chemical and other defects. We present a new hydrodynamic repulsive lift force that arises when surfaces with chemical contrasts or with varying textures come near contact. This lift force modifies the mobility of cells, colloids, bubbles, grains, and fibers traveling near walls and interfaces. Specifically, we demonstrate the spontaneous emergence of oscillations, transverse migration, spiral-like propulsive motion of a cylinder as it moves near a wall; these motions would not occur if the surfaces of the wall and the particle were perfectly homogenous. The physical mechanism behind the lift force is the breaking of the fluid pressure symmetry in the thin gap between two surfaces induced by a change of wall slip. Our study has implications for understanding how inhomogeneous biological interfaces interact with their environment; it also reveals a new method of patterning surfaces to reduce friction/wear or to influence self-assembly processes. Our work provides scaling estimates of the lift force induced by a change of wall slip for different configurations. This enables biologists, engineers, and physicists to predict the order of magnitude of the lift force, prior to performing experiments.   

Inertial Focusing in High-Frequency Pulsatile Flows

Inertial focusing in microfluidic channels using oscillatory flows enable the manipulation of particles with considerably smaller particle Reynolds numbers as compared to steady unidirectional flow. We experimentally examine how this focusing performance varies with oscillation frequency by realizing pulsatile flows in a novel two-dimensional microchannel geometry. The particle focusing position, migration velocity, and focusing efficiency are found to depend on oscillation frequency, particle size, and steady transport velocity. A complementary asymptotic analysis was completed for comparison with experimental measurements, and an agreement to good accuracy is observed.   

Solution for time-dependent force on a sphere translating through a viscoelastic fluid

Understanding the time-dependent force exerted on a spherical particle translating through a viscoelastic fluid has the potential to aid in design of microrheology experiments. We present a method to calculate this force in a fluid described by the Johnson-Segalman constitutive model. The flow field is represented as a regular perturbation series for small values of the Weissenberg number ($U\lambda/a$), where $U$ is the maximum flow velocity, $\lambda$ is the characteristic relaxation time of the fluid, and $a$ is the particle radius. As the solution is valid for flows with arbitrary time courses, it is valid for arbitrary values of the Deborah number ($k\lambda$), where $k$ is the maximum rate at which the velocity changes. The governing equations for the flow field are solved analytically up to second order; these are then used to determine the force exerted on the particle at third order through application of the reciprocal theorem. Ultimately, the unsteady force is expressed as a Volterra series expansion, and material functions like those measured in MAPS rheology\footnote{K. R. Lennon, G. H. McKinley, J.W. Swan, J. Rheol., \textbf{64}, 551-579 (2020)} describing the first and third order relationships between the time course of the velocity and the force are computed.   

Under-Damped Active Matter via Levitation with Rotating Acoustics: Simulations

Many active model systems (flocks of birds, schools of fish) operate in under-damped inertial conditions. While colloidal systems provide models for over-damped active dynamics, there is a comparative lack of model systems for inertial active matter. Here, we investigate one such model system: sub-millimeter objects acoustically levitated in air. For unsteady acoustic fields with nontrivial mode shapes, levitated objects experience complex driving forces and torques. Furthermore, multiple levitated objects have secondary scattering interactions which drive aggregation. We apply the Lattice Boltzmann method (LBM) to conduct direct numerical simulations of objects levitated in a single-axis acoustic chamber. LBM simulation permits investigation of complex structure-fluid interactions including momentum transfer by acoustic wave scattering and viscous dissipation. We demonstrate how LBM simulation of levitated object-object interactions and trap-object interactions extends the range of investigation beyond that predicted by inviscid acoustic scattering from isotropic objects. Acoustic fields which carry angular momentum, as well as non-spherical levitated objects are investigated.   

Dynamics of an acoustically levitated granular fluid

Macroscopic particles in an acoustic trap can self-assemble into single layer close-packed granular rafts consisting of hundreds of particles. These rafts are formed and stabilised due to a sonic depletion force mediated by scattering, which establishes attractive forces between the constituent particles. We show that this cohesive, quasi-2D granular material displays fluid-like behaviour, forming circular “granular droplets” with an emergent surface tension and viscosity. Beyond cohesion, the acoustic field also induces forces and torques that drive the droplets to merge, deform, and break-up. We focus on a persistent acoustic torque that increases the angular momentum of objects in the acoustic field. As the angular momentum of a granular droplet is increased, it deforms from a circle to an ellipse, eventually pinching off into multiple separate droplets. We use hydrodynamic models for rotating liquid drops to describe the granular dynamics and extract the droplet surface tension.   

Nozzle flow characterization and motion of entrained bubble in industrial inkjet printer

Piezo-acoustic inkjet printing allows highly controlled deposition of droplets at picoliter volumes. However, sometimes jet stability is compromised by the entrainment of a bubble, which has been shown to occur in conjunction with dirt particle trapping in the printhead, in the vortex ring above the oscillating meniscus (Fraters et al. Phys. Rev. Appl. 12(6) 2019). In this experimental and numerical study, we explore the destabilizing conditions of the flow inside the ink channel that lead to the diffusive growth of the entrained bubble and thereby to complete nozzle failure. We model the unsteady flow inside the channel using a Helmholtz oscillator model for the driving channel acoustics coupled with Navier-Stokes equations for the flow which we validate through time-resolved fluorescent particle tracking velocimetry measurements. Furthermore, bubble dynamics and translation are modeled using the Rayleigh-Plesset equation coupled to a point-particle force balance. We study the flow, particle trapping, and bubble motion for different nozzle geometries and driving conditions, revealing pathways of bubble entrainment and growth, thereby enabling identification and quantification of parameters that ultimately influence the inherent stability of the jetting process.   

How is Surface Roughness Affecting the Supplementary Relationship of Dynamic Contact Angles Measured by the Sessile-Droplet and Captive-Bubble Methods?

The wettability of a solid surface is dictated by its chemical composition as well as its roughness. The wettability of the surface can primarily be characterized quantitatively by measuring the contact angles (CAs) of sessile droplets (SD) in air or captive bubbles (CB) in liquid. The intrinsic wetting characteristics of a substrate demarcate the application of the two techniques. For surfaces with extreme wetting properties (superhydrophilic or superhydrophobic) where one of the two methods cannot be successfully implemented, a relationship between the dynamic CAs measured using these two methods is required. We performed extensive CA experiments on solid Aluminum substrates with different degrees of surface roughness using the SD and CB methods. The sum of the dynamic CAs (advancing CA of SD and receding CA of CB) on a smooth surface was found to be 180\textdegree , in agreement with the known supplementary principle. However, this sum was found to deviate from 180\textdegree with increased surface roughness. We explain our experimental observations using a theoretical formulation based on well-known thermodynamic models of wetting and contact angle hysteresis on rough substrates.   

Elastohydrodynamics of Lubricated Viscoelastic Contacts

The deformability of a soft substrate breaks the reversibility of Stokes flow and produces a lift force on a nearby moving surface. Focusing on small deformations, we employ perturbation theory to find analytically the lift force on a surface translating relative to a nearby viscoelastic layer. This is achieved by using Lorentz's reciprocal theorem along with Parseval's integral identity, which circumvents the detailed calculations of pressure and displacement fields in previous works. The formulation is developed for an arbitrary Poisson's ratio, substrate thickness, and viscoelastic relaxation times and recovers known results in the appropriate limits. Our results show that the value of Poisson's ratio changes the scaling of the lift force with respect to the layer's depth. Additionally, we discuss the effect of viscoelastic loss on the lift force. Extendable to arbitrary linear (generally non-elastic) response, our approach provides a powerful tool to probe the mechanical properties of soft materials.