Session EK: Particle Laden Flows I: Structure and Coating

Modeling Particle Concentration In Slurry Flows Using Shear-Induced Migration: Theory vs. Experiments

Different flow regimes observed in our experimental study of particle-laden thin film flows are characterized by differing particle concentration profiles. We develop a theoretical model for particle concentration in order to capture our experimental observations. Our model is based on equilibrium assumption and it incorporates all relevant physical mechanisms, including shear-induced particle migration and settling due to gravity. It leads to a coupled system of ordinary differential equations for particle volume fraction and shear, which are solved numerically for various parameter sets. We find excellent agreement between our numerical results and experimental data. Our model is not only successful in reproducing the experimentally observed regimes, but also in capturing the connection between these regimes and the experimental parameters.   

Slurries: An Experimental Study Of Gravity-Driven Particle-Laden Thin Film Flows

An experimental study of gravity driven particle-laden thin film flows reveals several different regimes: particles either settle onto the solid substrate and out of the flow, they accumulate in the contact line region, or remain well mixed throughout the liquid layer. We carry out extensive experiments using liquids with varying viscosity, several different particle sizes and a wide range of particle concentrations and inclination angles, and accurately determine which regime characterizes each considered configuration. We compile our experimental observations and construct phase diagrams which clearly indicate the influence of the experimental parameters on the observed flow regime. In particular, our results reveal both an interesting influence of particle size on mixture dynamics as well as a connection between observed flow regime and the development of fingering instability at the contact line of a particle- laden thin film.   

An eXtended Finite Element Method (XFEM) for the simulation of the flow of viscoelastic fluids with suspended particles

We present an eXtended Finite Element Method (XFEM) combined with DEVSS-G/SUPG formulations for the direct numerical simulation of the flow of viscoelastic fluids with suspended rigid particles. In this method, the finite element shape functions are extended through the partition of unity method (PUM) by using virtual degrees of freedom as the enrichment for the description of discontinuities across interface. For the whole computational domain including both the fluid and particles, we use a regular mesh which is not boundary-fitted. Then, the fluid domain and the particle domain are fully decoupled by using the XFEM enrichment procedures. The no-slip boundary condition on the interface between fluid and rigid body is realized by using constraints implemented with Lagrange multipliers. For moving particle problems, we incorporate a temporal arbitrary Lagrangian-Eulerian (ALE) scheme without the need of any re-meshing. Furthermore, local mesh refinements around the interface are achieved using grid deformation methods, in which the number of elements is not increased. We show the motion of a freely moving particle suspended in a Giesekus fluid between two rotating cylinders. We investigate the effect of the Weissenberg number in this problem, and the effects of the mobility parameter and particle size on the migration of particles.   

The Structure of Nanoparticle Nucleation in Three-dimensional Wakes

Ultrafine, or nano-scale particles play an integral role in a wide variety of physical/chemical phenomena and processes and have application in microelectronics, chemical gas sensors, and atmospheric processes, to name a few. Accurate prediction of particle production rates and size distributions are of paramount importance in such processes. Physical measurement of particle nucleation and growth is difficult to observe in-situ and computation has the ability to shed light on the underlying physico-chemical dynamics. Direct numerical simulation of the homogeneous nucleation of dibutyl-pthalate (DBP) in turbulent, three-dimensional wakes is performed. The flows consistent of a ``hot'' mixture of DBP and nitrogen issuing into ``cool'' nitrogen. The effects of both large-scale and molecular mixing as well fluid turbulence on nano-sized nucleation are investigated under different flows. Additionally, the structure of nano-particle nucleation as well as the effect of the cooling rate on the size distribution of nucleating particles is investigated.   

Particle Focusing and Dispersion in Suspension Flow through a Corrugated Tube

A computational study is performed of the transport of a particulate suspension through a corrugated tube using a discrete-element method. The tube is axisymmetric with a radius that varies sinusoidally, which in the presence of a mean suspension flow leads to periodic inward and outward acceleration of the advected particles. The oscillations in radial acceleration and straining rate lead to a net radial drift, with mean acceleration measuring an order of magnitude smaller than the instantaneous radial acceleration, which over time focuses small particles within the tube. The foundations of particle focusing in this flow are examined analytically using lubrication theory together with a low Stokes-number approximation for the particle drift. Computations are then performed using a finite-volume method for fluid flow in the tube at higher Reynolds numbers over a range of amplitudes, wavelengths and Reynolds numbers, examining the effect of each of these variables on the averaged radial fluid acceleration. A discrete-element method (DEM) is used to simulate particle behavior at finite Stokes numbers.   

Particle focusing in Lagrangian Coherent Structures

We discuss the relation between finite sized, inertial particle dispersion and Lagrangian Coherent Structures identified with recent Lagrangian visualization techniques. We consider the flow over a rectangular cylinder that features a vortex-dominated wake. Fluid particle transport barriers that attract fluid particles are visualized through contours of the Finite Time Lyapunov Exponent (FTLE) that measures the stretching of the fluid. Combinations of the transport barriers form Lagrangian Coherent Structures that are typically visualized through dye in experiments. Inertial particles closely follow these attracting transport barriers, as visualized by maxima in the FTLE field determined in backward time, for Stokes numbers smaller than unity. With increasing Stokes number the particles increasingly align with the transport barriers. At unity Stokes number when particles are well-known to exhibit particle focusing, large parts of a sharp particle streak are exactly aligned with the transport barrier in the FTLE field. The attracting transport barriers in the wake are hence excellent predictors of the location where particles focus. The inertial particles are shown to depart from the fluid particle transport barrier when criteria based on the stress tensor are met.   

Axial and lateral particle ordering in finite Reynolds number channel flows

In pressure-driven channel flows at finite Reynolds number, suspended particles are known to undergo cross-streamline migration to a specific position off the centerline. We investigate the combined effects of channel geometry and particle concentration on the migration and ordering of particles in the channels with rectangular cross-sections using both experiments and numerical simulations. First we show that under confinement a single particle always migrates to the center of the longer dimension of the cross section for a range of cross-sectional aspect ratios. In case of a dilute suspension, the particles exhibit lateral and axial ordering owing to the hydrodynamic interactions of neighboring particles. Upon increasing the particle loading, a stepwise transition from one to two to many trains of particles in the lateral direction is observed. For a given channel cross-section, we present a criterion for this transition based on the number of particles per unit length.   

Hollow Vortices in Protoplanetary Disks Dynamically Stabilized by Trapped Dust Grains

We present 2D simulations of particle-laden vortices that dynamically maintain their hollow vorticity distribution (i.e., the vorticity is not a maximum at the vortex center). Vortices of this type may be the birthplaces of planets within in protoplanetary disks around newly formed stars. The vortices are embedded in a rotating, shearing Keplerian flow. Horizontally, the combination of the vortex flow and the Keplerian background flow drag dust grains, the building blocks of planets, to the center of the vortex. Vertically, grains may settle into the midplane of the disk, where the local gravity is zero, or they may be held aloft against gravity by an updraft within the vortex, just as hailstones are lofted in a thunderstorm. Our numerical simulations show that, as dust grains accumulate in the center of a vortex, the drag from the grains extracts angular momentum from the fluid flow, hollowing out the vortex. In the absence of dust grains, a hollow vorticity distribution is not stable; the vortex will readjust itself (sometimes violently) so that its vorticity decreases monotonically from the center. When dust is present, the vortex remains hollow in a dynamic equilibrium.   

Measurements of the Diameter and Velocity Distributions of Atomized Tablet-Coating Solutions for Pharmaceutical Applications

The atomization of colloidal suspensions is of particular interest to the manufacturing of tablets and pills used as drug delivery systems by the pharmaceutical industry. At various stages in the manufacturing process, the tablets are coated with a spray of droplets produced by co-axial atomizers. The mechanisms of droplet size and spray formation in these types of atomizers are dominated by Kelvin-Helmholtz and Raleigh-Taylor instabilities for both low[1] and high[2] Ohnesorge numbers. We present detailed phase Doppler measurements of the Sauter Mean Diameter of the droplets produced by co-axial spray atomizers using water-based colloidal suspensions with solid concentrations ranging from fifteen to twenty percent and acetone-based colloidal suspensions with solid concentrations ranging from five to ten percent. Our results compare favorably with predictions by Aliseda's model. This suggests that the final size distribution is mainly determined by the instabilities caused by the sudden acceleration of the liquid interface. [1]Varga, C. M., et al. (2003) J. Fluid Mech. 497:405-434 [2]Aliseda, A. et al. (2008). J. Int. J. Multiphase Flow, 34(2), 161-175.   

An evaporation model of colloidal suspension droplets

Colloidal suspensions of polymers in water or other solvents are widely used in the pharmaceutical industry to coat tablets with different agents. These allow controlling the rate at which the drug is delivered, taste or physical appearance. The coating is performed by simultaneously spraying and drying the tablets with the colloidal suspension at moderately high temperatures. The spreading of the coating on the pills surface depends on the droplet Webber and Reynolds numbers, angle of impact, but more importantly on the rheological properties of the drop. We present a model for the evaporation of a colloidal suspension droplet in a hot air environment with temperatures substantially lower than the boiling temperature of the carrier fluid. As the liquid vaporizes from the surface, a compacting front advances into the droplet faster than the liquid surface regresses, forming a shell of a porous medium where the particles reach their maximum packing density. While the surface regresses, the evaporation rate is determined by both the rate at which heat is transported to the droplet surface and the rate at which liquid vapor is diffused away from it. This regime continues until the compacting front reaches the center of the droplet, at which point the evaporation rate is drastically reduced.