Suspension Of Spherical Particles Research Articles

The coherent shear wave in suspensions

We consider a disordered suspension of spherical silica particles in water. For a particle size of a few hundred nanometres and concentration (volume fraction) around 0.15 to 0.2, experiments conducted in the MHz range have shown that the non ideal nature of water must be taken into account for the "longitudinal" coherent wave attenuation to be understood, because of wave conversions, from longitudinal to shear and then back to longitudinal, occurring at each pair of scattering events. We are interested here in the properties of the "shear" coherent wave that are given by the expansion of its squared wavenumber, around that in the absence of particles, in powers of the concentration. At 1 MHz and a particle radius of 0.05 μm, we show that convergence of the modal series involved in that expansion may be reached after three terms: we use ten terms subsequently. We study the evolution of both the effective shear velocity and attenuation with concentration, as well as that of the effective shear viscosity deduced therefrom.

Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow

Non-Brownian suspension of monodisperse spherical particles, with volume fractions ranging between ϕ = 0.05 and 0.38 and particle Reynolds numbers ranging between Rep = 0.002 and 20, in plane Couette shear flows is investigated using three-dimensional particle-resolved numerical simulations. We examine the effects of volume fraction and particle Reynolds number on the macroscopic and microscopic stresses in the fluid phase. The effective viscosity of the suspension is in a good agreement with the previous empirical and experimental studies. At Rep = 20, however, the effective viscosity increases significantly compared to the lower particle Reynolds number simulations in the Stokes flow regime. Examining the stresses over the depth of the Couette gap reveals that this increase in wall shear stresses at high particle Reynolds numbers is mainly due to the significantly higher particle phase stress contributions. Next, we examine the momentum balance in the fluid and particle phase for different regimes to assess the significance of particle/particle interaction and fluid and particle inertia. At the highest particle Reynolds number and volume fraction, the particle inertia plays a dominant role in the momentum balance and the fluid inertia is non-negligible, while the short-lived contact forces are negligible compared to these effects. For all other regimes, the fluid inertia is negligible, but the particle inertia and contact forces are important in the momentum balance. Reynolds stresses originated from velocity fluctuations do not contribute significantly to the suspension stresses in any of the regimes we have studied, while the reduction in the shear-induced particle rotation can be a reason for higher wall shear stress at Rep = 20. Finally, we study the kinematics of particles, including their velocity fluctuations, rotation, and diffusion over the depth of the Couette gap. The particle diffusion coefficients in the cross flow direction exhibit an abrupt increase at Rep = 20.

Combined Lattice–Boltzmann and rigid-body method for simulations of shear-thickening dense suspensions of hard particles

We present a high-fidelity simulation model for dense suspensions of spherical and non-spherical particles suspended in a Lattice–Boltzmann Method (LBM) based fluid. The non-spherical particles are composed of an arbitrary number of overlapping spheres of different sizes and arbitrary relative positions in the particle reference frame which stay fixed during the simulation. This approach allows to approximate a wide range of rigid particle shapes. Fluid Structure Interactions (FSI) are realized using a hybrid of immersed-boundary methods and bounce-back schemes, that employs coupling coefficients dependent upon particle overlap with the fluid lattice, resulting in smooth hydrodynamic interactions when particles move over the lattice. Numerical lubrication breakdown is overcome by applying appropriate corrections for small inter-particle gaps and hydrodynamic interactions are resolved down to scales much smaller than the LBM lattice spacing. For improved numerical stability in the limit of stiff particle-particle interactions, a generalized-α method together with a dynamically refined time-step is used for rigid body dynamics. An unbounded shear flow with large shear rates is realized by splitting the computational domain into multiple co-moving reference frames coupled through Galilean transformations of both fluid and particle phase. For fast simulations of hundreds of particles over physical times-spans of seconds, the LBM sub-model and FSI computations are accelerated on GPUs and MPI/OpenMP are used to parallelize the computation over networked/shared-memory resources. All these innovations together lead to a very powerful simulation environment for sheared dense suspensions, facilitating study of rheology close to the jamming limit. In this paper we present benchmark results and simulations of continuous and discontinuous shear-thickening of dense polydisperse frictional suspensions, demonstrating the accuracy and predictive power of the model over a large range of volume fractions of suspended particles and a large range of shear rates.

Lattice Boltzmann simulation of dense rigid spherical particle suspensions using immersed boundary method

We present a lattice Boltzmann model designed for the simulation of dilute and dense finite-sized rigid particle suspensions under applied shear.We use a bottom-up approach and fully resolve the mechanical interaction between fluid and particles. Our model consists in coupling a lattice Boltzmann scheme for Newtonian and incompressible fluid flows with an immersed boundary scheme to simulate two-ways fluid-particles interaction. We introduce a simple yet robust contact model that includes repulsive elastic collision between particles, and neglects lubrication corrections. We apply this model to simple sheared flow with rigid spherical particles and we provide results for the relative apparent viscosity of the particle suspension as a function of the particle volume fraction and strain rate of the flow.We show that, using the proposed approach, there is no need for a lubrication model in the Newtonian regime, provided that an elastic contact model is included. Our algorithm, therefore, can be based only on physically sound and simple rules, a feature that we think to be fundamental for aiming at resolving polydispersed and arbitrarily shaped particle suspensions.Comparing our results with Krieger–Dougherty semi-empirical law, we confirm that the simulations are not sensitive to the particle Reynolds number for Rep ≪ 1 in the Newtonian regime. We show that the proposed model is sufficient to obtain a correct description of the rheology of particle suspension up to volume fraction equal to 0.55 (approaching the critical random packing fraction for monodispersed spheres), which goes beyond the state of the art.

Rheology of fiber suspensions using MRI

The suspensions of non-Brownian fibers are of interest for many applications. Although many studies concerning suspensions are available in the literature, most of them concern suspensions of spherical particles. In this paper, global and local rheology of fiber suspensions are explored near the jamming transition. A critical volume fraction is extracted from the experimental data. The value of this critical volume fraction is in agreement with the expected value of the concentration of rigid rods above which the isotropic phase becomes unstable. Moreover, non-reversible effects of the shearing are observed in flow curves because of the non-Brownian behavior of the studied fibers.

Effects of polydispersity on the glass transition dynamics of aqueous suspensions of soft spherical colloidal particles

Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) particles of a nearly constant swelling ratio and with polydispersity indices (PDIs) varying over a wide range (7.4% - 48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The PNIPAM particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The zero shear viscosity ($\eta_{0}$) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction $\phi_{eff}$ of the suspensions, increases with increase in $\phi_{eff}$ and shows a dramatic increase at $\phi_{eff}=\phi_{0}$. The data for $\eta_{0}$ as a function of $\phi_{eff}$ fits well to the Vogel-Fulcher-Tammann (VFT) equation. It is observed that increasing PDIs results in increasingly fragile supercooled liquid-like behavior, with the parameter $\phi_{0}$, extracted from the fits to the VFT equation, shifting towards higher $\phi_{eff}$. The observed increase in fragility is attributed to the prevalence of dynamical heterogeneities (DHs) in these polydisperse suspensions, while the simultaneous shift in $\phi_{0}$ is ascribed to the decoupling of the dynamics of the smallest and largest particles. Finally, it is observed that the intrinsic nonlinearity of these suspensions, estimated at the third harmonic near $\phi_{0}$ in Fourier transform oscillatory rheological experiments, increases with increase in PDIs. Our results are in agreement with theoretical predictions and simulation results for polydisperse hard sphere colloidal glasses and clearly demonstrate that jammed suspensions of polydisperse colloidal particles can be effectively fluidized with increasing PDIs.

Tree-ansatz percolation of hard spheres.

Suspensions of hard core spherical particles of diameter D with inter-core connectivity range δ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two particles separated by a distance smaller than δ. By exploiting the property that closed loops of connected spheres become increasingly rare as the connectivity range diminishes, we study continuum percolation of hard spheres by treating the network of connected particles as having a tree-like structure for small δ/D. We derive an analytic expression of the percolation threshold which becomes increasingly accurate as δ/D diminishes and whose validity can be extended to a broader range of connectivity distances by a simple rescaling.

Electrospray as a Sample Preparation Tool for Electron Microscopic Investigations: Toward Quantitative Evaluation of Nanoparticles

The potential of electrospray deposition, for the controlled preparation of particles for imaging in electron microscopes, is evaluated on various materials: from mono-modal suspensions of spherical particles to multimodal suspensions and to real-world industrial materials. It is shown that agglomeration is reduced substantially on the sample carrier, compared with conventional sample preparation techniques. For the first time, it is possible to assess the number concentration of a tri-modal polystyrene suspension by electron microscopy, due to the high deposition efficiency of the electrospray. We discovered that some suspension stabilizing surfactants form artifact particles during electrospraying. These can be avoided by optimizing the sprayed suspension.

Tunable acoustic attenuation in dilute suspensions of subwavelength, non-spherical magnetic particles

The microstructure (e.g., particle orientation and chaining) of suspensions of non-spherical ferromagnetic particles can be controlled by an external field, potentially making it possible to tune the acoustic properties of the suspension. Here, we experimentally demonstrate that dilute suspensions of subwavelength-sized oblate-spheroidal nickel particles exhibit up to a 35% change in attenuation coefficient at MHz frequencies upon changing the direction of an external magnetic field, for particle volume fractions of only 0.5%. Comparison is made to suspensions of spherical particles, in which the attenuation is smaller and nearly isotropic. Optical transmission measurements and analysis of the characteristic timescales of particle alignment and chaining are also performed to investigate the reasons for this acoustic anisotropy. The alignment of the oblate-spheroidal particles is found to be the dominant mechanism for the anisotropic and tunable acoustic attenuation of these suspensions.

Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence

We have performed interface-resolved direct numerical simulations of forced homogeneous-isotropic turbulence in a dilute suspension of spherical particles in the Reynolds number range $Re_{\unicode[STIX]{x1D706}}=115{-}140$. The solid–fluid density ratio was set to $1.5$, gravity was set to zero and two particle diameters were investigated corresponding to approximately $5$ and $11$ Kolmogorov lengths. Note that these particle sizes are clearly outside the range of validity of the point-particle approximation, as has been shown by Homann & Bec (J. Fluid Mech., vol. 651, 2010, pp. 81–91). At the present parameter points the global effect of the particles upon the fluid flow is weak. We observe that the dispersed phase exhibits clustering with moderate intensity. The tendency to cluster, which was quantified in terms of the standard deviation of Voronoï cell volumes, decreases with the particle diameter. We have analysed the relation between particle locations and the location of intense vortical flow structures. The results do not reveal any significant statistical correlation. Contrarily, we have detected a small but statistically significant preferential location of particles with respect to the ‘sticky points’ proposed by Goto & Vassilicos (Phys. Rev. Lett., vol. 100 (5), 2008, 054503), i.e. points where the fluid acceleration field is acting such as to increase the local particle concentration in one-way coupled point-particle models under Stokes drag. The presently found statistical correlation between the ‘sticky points’ and the particle locations further increases when focusing on regions with high local concentration. Our results suggest that small finite-size particles can be brought together along the expansive directions of the fluid acceleration field, as previously observed only for the simplest model for sub-Kolmogorov particles. We further discuss the effect of density ratio and collective particle motion upon the basic Eulerian and Lagrangian statistics.

Evaluation of Electrospray as a Sample Preparation Tool for Electron Microscopic Investigations: Toward Quantitative Evaluation of Nanoparticles.

The potential of electrospray deposition, for the controlled preparation of particles for imaging in electron microscopes, is evaluated on various materials: from mono-modal suspensions of spherical particles to multimodal suspensions and to real-world industrial materials. It is shown that agglomeration is reduced substantially on the sample carrier, compared with conventional sample preparation techniques. For the first time, it is possible to assess the number concentration of a tri-modal polystyrene suspension by electron microscopy, due to the high deposition efficiency of the electrospray. We discovered that some suspension stabilizing surfactants form artifact particles during electrospraying. These can be avoided by optimizing the sprayed suspension.

Multiple scattering in random dispersions of spherical scatterers: Effects of shear-acoustic interactions.

The propagation of acoustic waves through a suspension of spherical particles in a viscous liquid is investigated, through application of a multiple scattering model. The model is based on the multiple scattering formulation of Luppé, Conoir, and Norris [J. Acoust. Soc. Am. 131, 1113-1120 (2012)] which incorporated the effects of thermal and shear wave modes on propagation of the acoustic wave mode. Here, the model is simplified for the case of solid particles in a liquid, in which shear waves make a significant contribution to the effective properties. The relevant scattering coefficients and effective wavenumber are derived in analytical form. The results of calculations are presented for a system of silica particles in water, illustrating the dependence of the scattering coefficients, effective wavenumber, speed, attenuation on particle size and frequency. The results demonstrate what has already been shown experimentally; that the shear-mediated processes have a very significant effect on the effective attenuation of acoustic waves, especially as the concentration of particles increases.

Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions.

In order to assess the effect of hydrodynamics in the assembly of active attractive spheres, we simulate a semi-dilute suspension of attractive self-propelled spherical particles in a quasi-two dimensional geometry comparing the case with and without hydrodynamics interactions. To start with, independent of the presence of hydrodynamics, we observe that depending on the ratio between attraction and propulsion, particles either coarsen or aggregate forming finite-size clusters. Focusing on the clustering regime, we characterize two different cluster parameters, i.e. their morphology and orientational order, and compare the case when active particles behave either as pushers or pullers (always in the regime where inter-particle attractions compete with self-propulsion). Studying cluster phases for squirmers with respect to those obtained for active Brownian disks (indicated as ABPs), we have shown that hydrodynamics alone can sustain a cluster phase of active swimmers (pullers), while ABPs form cluster phases due to the competition between attraction and self-propulsion. The structural properties of the cluster phases of squirmers and ABPs are similar, although squirmers show sensitivity to active stresses. Active Brownian disks resemble weakly pusher squirmer suspensions in terms of cluster size distribution, structure of the radius of gyration on the cluster size and degree of cluster polarity.

Conductive polymer-based nanoparticles for laser-mediated photothermal ablation of cancer: synthesis, characterization, and in vitro evaluation.

Laser-mediated photothermal ablation of cancer cells aided by photothermal agents is a promising strategy for localized, externally controlled cancer treatment. We report the synthesis, characterization, and in vitro evaluation of conductive polymeric nanoparticles (CPNPs) of poly(diethyl-4,4′-{[2,5-bis(2,3-dihydrothieno[3,4-b][1,4]dioxin-5-yl)-1,4-phenylene] bis(oxy)}dibutanoate) (P1) and poly(3,4-ethylenedioxythiophene) (PEDOT) stabilized with 4-dodecylbenzenesulfonic acid and poly(4-styrenesulfonic acid-co-maleic acid) as photothermal ablation agents. The nanoparticles were prepared by oxidative-emulsion polymerization, yielding stable aqueous suspensions of spherical particles of <100 nm diameter as determined by dynamic light scattering and electron microscopy. Both types of nanoparticles show strong absorption of light in the near infrared region, with absorption peaks at 780 nm for P1 and 750 nm for PEDOT, as well as high photothermal conversion efficiencies (~50%), that is higher than commercially available gold-based photothermal ablation agents. The nanoparticles show significant photostability as determined by their ability to achieve consistent temperatures and to maintain their morphology upon repeated cycles of laser irradiation. In vitro studies in MDA-MB-231 breast cancer cells demonstrate the cytocompatibility of the CPNPs and their ability to mediate complete cancer cell ablation upon irradiation with an 808-nm laser, thereby establishing the potential of these systems as agents for laser-induced photothermal therapy.

Rheology of dense suspensions of non colloidal particles

Dense suspensions are materials with broad applications both in industrial processes (e.g. waste disposal, concrete, drilling muds, metalworking chip transport, and food processing) and in natural phenomena (e.g. flows of slurries, debris, and lava). Despite its long research history and its practical relevance, the mechanics of dense suspensions remain poorly understood. The major difficulty is that the grains interact both by hydrodynamic interactions through the liquid and by mechanical contact. These systems thus belong to an intermediate regime between pure suspensions and granular flows. We show that we can unify suspension and granular rheology under a common framework by transferring the frictional approach of dry granular media to wet suspensions of spherical particles. We also discuss non-Newtonian behavior such as normal-stress differences and shear-induced migration. Beyond the classical problem of dense suspension of hard spheres which is far from being completely resolved, there are also entirely novel avenues of study concerning more complex mixtures of particles and fluids such as those involving other types of particles (e.g. fibers) or non-Newtonian fluids that we will also address.

Shear-induced particles migration in a Bingham fluid

Shear-induced particle migration in monodisperse and bi-disperse suspension of spherical particles in a Bingham fluid is considered. Previous models of particle migration in Newtonian suspensions are extended to account for the existence of un-yielded regions in the visco-plastic domain when forced to flow in a tube and in a concentric Couette device. In suspension with a monodisperse particle phase, it is shown that particle concentration is continuously augmented in low shear rate regions. The yield boundary is monotonically shifting, affecting the velocity profiles, and the power to maintain the flow is monotonically reduced. When the suspension size distribution is bi-modal, the migration, eventually, results in a separation of the species. Larger particles migrate to the low shear rate zones and the smaller phase is pushed away from there. The velocity profiles, yield boundary and power do not change monotonically, and several stages in this dynamics can be identified.

Measurements and Comparison to Predictions of Viscosity of Heavily Filled HDPE with Natural Fibers

AbstractComposites of rice hulls at various levels of loadings in recycled HDPE were characterized rheologically using a conical extrusion die and small amplitude oscillatory shear (SAOS) measurements. Although the results do not match, due to the invalidity of the Cox–Merz rule for such composites, both types of measurements indicate that increasing the filler concentration results in significantly higher viscosities and increased shear thinning. The errors associated with the use of a conical die due to viscous dissipation are assessed through computer simulations. They are small for relatively small throughputs (small pressure drops). The experimental results for viscosity are compared to predictions of the Einstein–Batchelor equation for suspensions of spherical particles, the Guth–Simha equation, and the empirical Krieger–Dougherty correlation, for filler loadings of up to 70% by weight. The comparison indicates that reasonable approximations of the consistency index of the power law viscosity model are possible through using the above expressions for loadings up to perhaps 40–50% by weight.

Effective viscosity of two-dimensional suspensions: Confinement effects

Confined 3D suspensions of spherical and non-Brownian particles show a remarkable rheological property: hydrodynamic interactions between spheres negatively contribute to the effective viscosity. This effect survives in 2D, and simulations help explain this surprising effect

Settling behavior of particles in fiber-containing Herschel Bulkley fluid

Fiber-containing, or fibrous, fluids are used in the petroleum industry to improve well-bore cleaning. Field studies indicate that fiber-containing sweep fluids can clean horizontal and highly inclined wells of drill cuttings very effectively. Fibrous fluids are also utilized in fracturing operations to place proppant particles within induced fractures. Efficiency of solid particle transport by these fluids depends on their ability to hinder settling of the dispersed particles.This article presents results of experimental and theoretical investigations conducted on settling behavior of spherical particles in Herschel-Bulkley fluids containing chemically inert monofilament fibers 10mm in length and 0.1mm diameter at concentrations ranging up to 0.08% by weight. A model has been developed to predict particle settling velocity under transient and steady state settling conditions. Experiments were carried out with spherical glass particles 2 to 8mm in diameter in a 100-mm fully transparent cylinder of sufficient length (2m) to establish terminal settling conditions. Wall effects were minimized by maintaining a ratio of particle diameter to cylinder internal diameter (dp/dcyl) no greater than 0.08. To vary the rheological properties of the fluid, xanthan gum suspensions with three different polymer concentrations were used as base fluids. A moving digital video camera was used to track settling particles. The camera records were used to determine instantaneous settling velocity of each particle as a function of time.In fibrous suspensions, resistance to settling is provided by both the base fluid (viscous drag) and the fibers (fiber drag). Fiber drag arises from mechanical and hydrodynamic interferences. Measurements of the terminal velocity of particles in the base fluids were used to compute viscous drag, while the terminal velocity data in the fibrous fluids was utilized to determine total drag (i.e. fiber drag plus viscous drag). Analysis of the data resulted in the development of an empirical correlation for the “fiber drag coefficient,” which varies with particle Reynolds number, fiber concentration and fluid behavior index. With this information, a model has been developed that can be used to predict settling velocity of spherical particles in suspensions of the prescribed fiber in Herschel-Bulkley fluids.

Particle transport in laboratory models of bifurcating fractures

This article provides experimental analysis as well as numerical simulation of flow of liquids and suspensions through laboratory models of basic bifurcating channel geometries. Numerical results of single phase Newtonian and non-Newtonian (power law) fluid flow in 3-dimensional square channels show good agreement with experimental data. The particle-laden experiments are carried out with neutrally buoyant suspension of spherical particles for different inlet solid volume fraction and different D∥/D⊥ where D∥ is the width of the straight branch and D⊥ is the width of side branch of the channel for a range of Reynolds numbers, 0 < Re < 800; D∥ = D0, with D0 the width of the inlet branch. The focus of the multiphase flow study is on the role of the size ratio of the side channel to the primary or straight channel, and the relative size of the particle to the channel widths. The Reynolds number is defined as Re = ρD0U/η, where U is the average velocity at inlet, while ρ and η are density and viscosity of the fluid, respectively.