Session E23: Microscale Flows: Particles, Drops, Bubbles II

A pairwise hydrodynamic theory for flow-induced structuring in dilute suspensions.

A modified diffusive flux model is presented for flow-induced particle structuring resulting from pair interactions in suspensions undergoing shear and pressure-driven flows. The analysis reveals the formation of an O(r_c) boundary layer in regions of vanishing shear rates (e.g., centerline of planar Poiseuille flow) where r_c is the radius of the upstream collision cross-section for pairwise particle interactions.  By contrast to the current theories for suspension microstructure, a non-singular spatial distribution of particles is predicted.  Particle segregation is predicted in bidisperse suspensions in regions of vanishing shear rate with enrichment and depletion depending principally on size ratio. Large particles are enriched in suspensions of rough particles; the opposite is true in emulsions.   

Drifting of an Asymmetric Bent Rod in Two-Dimensional Shear Flow

At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting overall dynamics of a suspension. While slender fibers may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibers have found Jeffery-like behavior along with chaotic orbits, decaying orbital constants, and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behavior of a composite asymmetric slender body made of two straight rods in a 2-D shear flow to understand the effects of shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines. This drift is of a similar magnitude to that in the literature but arises from a different mechanism. Such geometry-driven cross-streamline motion may be important in giving rise to Taylor dispersion for this class of particles, thereby potentially enhancing mixing.   

Synchronous Electrokinetic-Inertial Focusing in Microfluidic Devices

The application of electric fields to inertial focusing presents a rare interplay of electrokinetic and inertial phenomenon. It has also attracted considerable attention for its potential application for particle separation based on differences in electric properties at high throughput. A considerable challenge to its widespread practical implementation is the difficulty of maintaining large electric fields over long channel lengths, which are typically required for inertial focusing. Furthermore, the proposed mechanisms and scaling laws of electrokinetically enhanced migration are yet to be rigorously tested. Here, we present an experimental approach that attempts to address both of these challenges by synchronously applying oscillatory flow and an AC electric field in a microfluidic device. The dependence of particle migration on oscillation frequency and phase difference between the applied fields will be discussed.   

Magnetic manipulation of pairwise interactions between droplets in simple shear flows

Droplets dispersed in another immiscible liquid are frequently encountered in polymer blending process where the microscale structure of a polymer blend, developed during processing, is dependent on the droplet distribution. Here, using the level set method, we perform numerical investigations to explore the interaction behavior between a pair of equal-sized ferrofluid droplets in simple shear flows under uniform magnetic fields in the Stokes flow limit (Re ≤ 0.03). The results show that there exists a critical Capillary number Ca_cr, beyond which the droplets demonstrate separation through a sliding over motion, instead of coalescence. Application of a magnetic field along α = 0° (parallel to the flow) results in a faster coalescence phenomenon between droplets, whereas a magnetic field along α = 45° leads to separation followed by a reversal motion. However, at α = 90° (perpendicular to the flow), a critical magnetic field strength appears where the droplets show a reversing motion behavior, instead of passing over motion leading to coalescence. Moreover, the outcome of a collision event is found to be dependent on the initial vertical offset between the droplets.    

Surface discretization considerations for the boundary element method applied to 3D ellipsoidal particles in Stokes flow

The boundary element method has often been used for simulating particle motion in Stokes flow, yet there is a scarcity of quantitative studies examining local errors induced by meshing highly elongated particles. In this paper, we study the eigenvalues and eigenfunctions of the double-layer operator for an ellipsoid in an external linear or quadratic flow. We examine the local and global errors induced by changing the interpolation order of the geometry (flat or curved triangular elements) and the interpolation order of the double-layer density (piecewise-constant or piecewise-linear over each element). Interestingly, we find that increasing the interpolation orders for the geometry and the double layer density does not always guarantee smaller errors. Depending on the nature of the meshing near high curvature regions, the number of high aspect ratio elements, and the fitness of the particle geometry, a piecewise-constant density can exhibit lower errors than piecewise-linear density, and there can be little benefit for using curved triangular elements. Overall, this study provides practical insights on how to appropriately discretize and parameterize 3D boundary element simulations for elongated particles with prolate-like and oblate-like geometries.   

Wrinkling, multiplicity and hydrodynamic screening in the dynamics of elastic sheets in extensional flow

Thin-structured materials, from flexible graphene sheets to highly extensible polymer films, are often processed in a fluidic environment. We study the dynamics of elastic sheets in the canonical extensional flows with a continuum model that includes in-plane deformation and out-of-plane bending, and the fluid motion is computed by the method of regularized Stokeslets. In planar and biaxial extensional flow, all stable conformations stay flat. Sheets modeled by a strain-hardening model exhibit a discontinuity in stretched length within a small increase in flow strength, which marks a bistable regime where multiple stable steady states exist. The bistability is analogous to coil-stretch hysteresis in linear polymers in solution: it arises from the hydrodynamic interaction between different parts of the sheet. In uniaxial extensional flow, we explore stiff sheets that strongly resist bending deformation and flexible sheets that can wrinkle. For stiff sheets, a similar compact-stretched transition has been observed. For flexible sheets, the wrinkling strongly modifies the bistability by rendering a shift of bistable regime to higher flow strength regime. We also apply a linear stability analysis to predict and understand the nonlinear long-term dynamics for some parameter regimes.   

Sedimentation of chiral particles in viscous media

Sedimentation of particles is a classical problem of fluid mechanics. While it is well understood that the particle shape uniquely determines its dynamics, the precise trajectory and orientational dynamics are only known for a limited set of particle shapes. Here, we study theoretically sedimentation of chiral particles, focussing on rigid helical filaments and Moebius-strip ribbons. We combine the resistive-force theory, slender-ribbon theory, and numerical simulations to predict the details of particle trajectories. We demonstrate that the chirality of the particle leads to the chirality of its trajectory and discuss the physical origin of this phenomenon.   

Microfluidic mass transfer of CO2 at different phases

Quantifying the mass transport of CO₂ at pore-scales accurately is crucial but challenging for successful technological deployment of Carbon capture and sequestration (CCS) in a deep saline aquifer. We carry out high-pressure microfluidic experiments, mimicking reservoir conditions up to 9.5 MPa and 35 ^oC, to elucidate the microfluidic mass transfer process of CO₂ at different thermodynamic phases into water. We measure the size change of CO₂ micro-bubbles/droplets generated using a microfluidic T-junction to estimate the volumetric mass transfer coefficient (k_La), quantifying the rate change of CO₂ concentration under the driving force of concentration gradient. The results show that bubbles/droplets at high-pressure conditions reach a steady-state faster than those at low-pressure. The measured volumetric mass transfer coefficient shows an increase with the Reynolds number (based on the liquid slug) and is nearly independent of the injection pressure for both the gas and liquid phases. In addition, k_La, significantly enlarges with increasing high-pressure at the supercritical state.  Our microfluidic results with a small hydrodynamic diameter (of ≈ 50 μm) show a significantly increase in volumetric mass transfer of CO₂ into water by two to three order of magnitudes, O(10²-10³), compared with typical applications using millimeter-sized capillaries.    

Encapsulation by crossing of a liquid-liquid interface by a droplet at high inertia

Crossing of a liquid-liquid interface by particles has been essentially limited to solid particles so far. Here, we present an experimental investigation on the encapsulation of a droplet by crossing a liquid-liquid interface under centrifugal force using high-speed imaging. The aqueous droplets are injected into an oil phase through a capillary tube. The applied centrifugal force then drives the droplets towards the interface. Under adequate conditions, the droplets cross the interface, subsequently entraining a volume of the oil phase (liquid column) along with them, which ultimately pinches off leading to the coating of the droplet. We performed experiments for a wide range of process parameters and physical properties of the liquids, and obtained a "regime map" for the crossing conditions by plotting the density contrast ratio against the interfacial Bond number. We quantified the velocity and shape of the droplet as well as the coating volume, length and width of the entrained column as a function of relevant dimensionless numbers (We, Oh, Bo). In addition, we discuss the comparison with our recent numerical study as well as with previous studies on solid particles along with the role of surfactants.