A new method for the control of dilute suspension sedimentation by horizontal movement

This research addresses some factors that control the stability of dilute suspensions in sedimentation processes under a dynamic environment. Experimental and numerical studies were conducted about the sedimentation velocity control of dilute suspensions by horizontal movement for particle concentrations up to 8 wt.%. Nearly monodispersed particles were used as test particles. The effects of horizontal movement speed and amplitude on particle sedimentation process were investigated. Under stationary conditions, particles settle in only one vertical direction because of gravitational force. However, complicated particle motions arise under moving conditions due to circulation flow in horizontal moving conditions. The results show that horizontal movement can reduce the particle settling velocity or maintain the stability of the suspension.     

Hydrodynamics of a rheologically complicated liquid in a self-cleaning filter

A mathematical model has been developed for non-Newtonian flow in a hydrodynamic self-cleaning filter. The system of rheodynamic equations describing the flow of a rheologically complicated medium in the filter has been solved by a numerical method. The velocity and effective viscosity fields for the non-Newtonian liquid have been determined. The effect of the rheological properties of the liquid on the hydrodynamic characteristics of the flow has been investigated. The liquid stream lines, the trajectories of the solid particles, and the efficiency of the hydrodynamic separation of particles have been calculated. The deviation of the experimental particle separation data from the corresponding calculated data does not exceed 15%, indicating the validity of the mathematical model and computational method and demonstrating their applicability to design of hydrodynamic and separation processes.     

Particle shape and suspension rheology of short-fiber systems

The effective viscosity of short-fiber suspensions is studied from a theoretical and experimental point of view. The theory of dilute suspensions with elongated particles is briefly summarized and explicit formulae for the dependence of the intrinsic viscosity on the particle shape (aspect ratio) are given in a form that should be useful for practical purposes. Concentration regimes, the influence of Brownian motion and sedimentation kinetics are mentioned. The effective viscosity of suspensions of two polydisperse wollastonites with significantly different average aspect ratios (approximately 5 and 16, respectively) is measured in dependence of the solids volume fraction and fitted with power-law models (Krieger and Maron–Pierce relations). It is shown that the intrinsic viscosity determined is higher than theoretically predicted via the Brenner formula, while the critical volume fraction is lower than predicted by the empirical Kitano relation. Possible reasons for these discrepancies, common to most real polydisperse systems, are discussed.     

Simulation of sedimentation and fluidization of polydisperse suspensions via a Markov model

The particle-based approach to sedimentation is extended to include velocity fluctuations that result in hydrodynamic diffusion. The vector process describing the joint values of position and velocity is Markov. Thus, no integration of velocity is required. Height-velocity “skeletons” for each particle are generated from a bivariate-normal distribution with means, variances, and covariance that depend on three parameters. For each particle, there is a unique region in which the vector of species concentrations determines that particle's parameters and hence its Markov process, but the concentrations in that region depend on the Markov processes of neighboring particles. Though only discrete values of height and velocity are generated, the model ensures that sample paths and particle velocities are continuous. Furthermore, steady-state velocities are normally distributed and velocity autocorrelations decay exponentially. Published experimental results indicate that both are excellent approximations. For polydisperse suspensions, the Markov model is much simpler than the standard hydrodynamic-diffusion model and represents the actual process much better. We simulate the sedimentation and fluidization of polydisperse suspensions and study the effects of two additional parameters: variance and autocorrelation decay rate of particle velocities.     

Characterization of rheological properties of colloidal zirconia

Dynamic viscosity of aqueous suspensions of nanosized zirconia (ZrO₂) have been studied for the low volume fraction range. The specific surface area of dry powder was determined from the BET method. The zeta potential of zirconia particles as a function of pH was measured by the microelectrophoretic method. The isoelectric point found in this way was 4.7. The particle density in aqueous suspensions was found by the dilution method. The dynamic viscosity of suspensions was measured by using a capillary viscometer that eliminated the sedimentation effects. Experimental data showed that for dilute zirconia suspension, the relative viscosity increased more rapidly with the volume fraction than that the Einstein formula predicts. This allowed one to calculate the specific hydrodynamic volume of particles in the suspensions and their apparent density. It was found that particles forming zirconia suspensions were composed of aggregates having porosity of 40–50%. The size of the primary particles forming these aggregates was 0.2 μm that agrees well with the BET specific surface data. The influence of an anionic polyelectrolyte:polysodium 4-styrenesulfonate (PSS) on zirconia suspension viscosity also was studied. First the PSS viscosity alone was measured as a function of its volume fraction for various ionic strength of the solutions. The data were interpreted in terms of the flexible rod model of the polyelectrolyte. Then, the viscosity of ZrO₂ in PSS solutions of fixed concentration was measured as a function of the concentration of zirconia. It was revealed that the viscosity of the mixtures was proportional to the product of the zirconia and polyelectrolyte viscosities taken separately.     

MEASUREMENT OF AEROSOL EFFECTIVE TRANSPORT COEFFICIENTS IN CYLINDRICAL TUBES

Transport of submicrometer aerosols in flows in tubes can be described by an effective one-dimensional axial convection–diffusion equation with apparent aerosol transport properties: mean aerosol velocity, mean aerosol diffusion coefficient (dispersivity) and mean aerosol deposition coefficient. These quantities are investigated experimentally by shape analyses of boluses of submicrometer Latex aerosol particles injected in the clean air flow through long tubes and a diffusion battery of capillary tubes. It is shown that the aerosol effective dispersivity and volumetric deposition coefficient significantly depend on the particle transit (residence) time within the tubes. For sufficiently long residence times these quantities are found to approach their asymptotic limiting values, predicted by the existing theories of the hydrodynamic dispersion. On the other hand, the mean aerosol velocity only weakly differs from the mean air velocity, and is almost independent of the aerosol residence time. The results obtained are important in several applications, including particle sampling using long tubes or lines.     

Colloidal Filtration and (Simultaneous) Sedimentation of Alumina and Silica Suspensions: Influence of Aggregates

Colloidal filtration and (simultaneous) sedimentation is studied for suspensions of alumina particles and monodisperse silica spheres. A comparison is made between stable suspensions and systems which are aggregated due to salt addition (silica) or absence of a deflocculant (alumina). From separate sedimentation experiments we conclude that the stable silica settles as an ordered particle array, that the unstable silica sediments as separate aggregates, and that aggregated aluina behaves as a densifying network. The filtration results show that settling of aggregates during filtration changes the filtration kinetics in accordance with our model for simultaneous filtration and sedimentation. Further, aggregates in suspension are shown to have little influence on the silica compact microstructure, whereas they clearly increase porosity and permeability of the alumina compact. We also find that for all suspensions porosities of compacts prepared by sedimentation are clearly larger then porosities of filter compacts.     

运用稠密气体理论建立气粒两相流流动模型

循环流化床内的复杂流动特征使其工业放大较困难,迄今对其流动特征尚缺乏充足的理论解释。本文从流体力学及稠密气体分子运动的相关理论出发,定义了“颗粒温度”;对双颗粒碰撞分布函数建立了Ｂｏｌｔｚｍ ａｎ Ｉｎｔｅｇｒａｌ－ｄｉｆｆｅｒｅｎｔｉａｌ方程,简单介绍了该方程的求解方法,从而进一步推导出颗粒相的连续方程、动量方程、拟热能（颗粒温度）方程,给出了颗粒相的压力、粘度和关于颗粒温度传递系数的表达式,建立了完整的颗粒相湍流动力学模型,并把模拟结果与实验结果相比较,进一步验证了模型的科学合理性。     

Rheology and sedimentation velocity of alkaline suspensions of hematite particles at elevated temperature

This study aims to characterize the sedimentation velocity and the rheology of suspensions of hematite particles suspended in strongly alkaline media at 100 and 110 °C, as done for an alternative electrochemical process in development for iron production by direct electrode reduction of hematite. Considering the medium used in the process, i.e. 12% (v/v) suspension of hematite particles in 50% sodium hydroxide aqueous, the sedimentation velocity of hematite particle at 110 °C is 0.010 mm/s, which is very slow because the average size of the solid particles is around 10 μm and the significant collisions and interactions occuring between the particles in the concentrated suspension. Two geometries were used to characterize the rheological behavior of the apparent viscosity of the suspension of 12% (v/v) (i.e. 33 wt%) at 100 °C: a conventional Couette geometry and a helical ribbon mixer. The suspension was found shear thinning in the range of shear rate studied. The rheological behavior of the suspension can be described by a power-law model. The apparent viscosity of the hematite suspension estimated at a shear rate between 0.5 and 10 s⁻¹ is between 100 and 20 mPa s for the two geometries. The apparent viscosity calculated from the terminal velocity of 10 μm particles is of the same order of magnitude of the results obtained with the two rheometer configurations. The effect of the particle concentration on the sedimentation velocity and viscosity of the hematite suspensions was also studied.     

Role of Bound Water on the Viscosity of Nanometric Alumina Suspensions

Rheological properties of aqueous nanometric alumina suspensions with fructose as dispersant were investigated. Differential scanning calorimetry and thermogravimetry indicated that a significant fraction of the water is immobilized by the nanometric particles in the suspension. This in turn increased the viscosity of the suspensions. It was also shown that the addition of monosaccharides, fructose in particular, reduced the viscosity of the suspensions dramatically. Nuclear magnetic resonance experiments indicated that a monolayer of fructose was adsorbed on the particle surfaces. The reduction in viscosity could be attributed to release of water imposed by fructose adsorption on the alumina particles present.     

Clusters Formation during Sedimentation of Dilute Suspensions

Abstract

Particle interactions in dilute monodispersed sedimenting suspensions of spherical particles are studied as a function of solid concentration. It is shown that in suspensions with solid concentrations below 0.83%, the interactions are too insignificant to effect the use of Stokes' law in sedimentation results. Beyond this concentration, however, a definite change in suspension behavior occurs, as particles come close enough to form clusters of varying sizes causing faster settling rates. Optimum clustering takes place around 4.5%-solid concentration, corresponding to mean interspacing of 2.2 particle diameter within suspension and giving settling rates 1.58 times faster than the Stokes' velocity for a mean particle. Clusters start breaking beyond this concentration as the sedimentation becomes more hindered and the return upward flow of liquid becomes increasingly tortuous. The probability of clusters formation and their stability as a function of particle size, concentration, and the Reynolds number of suspensions are also investigated. The studies are further extended to demonstrate the effect of “immobile” liquid within the clusters in interpreting the sedimentation results.     

The flow of suspensions through tubes: V. Inertial effects

The behavior of particles undergoing Couette and Poiseuille flows at rates when inertial effects become significant was investigated. The rotation of rigid particles was similar to that in the Stokes flow regime, except for a drift of cylinders to limiting rotational orbits corresponding to the maximum energy dissipation. In Poiseuille flow, rigid particles migrated to an equilibrium radial position which depended on the density difference of two phases, the directions of sedimentation velocity and flow, and the ratio of particle to tube radius. Neutrally buoyant deformable particles always migrated to the tube axis. In concentrated suspensions a plasmatic layer developed near the tube wall as a consequence of radial migration. The formation of this layer modified the velocity profile and caused a reduction in the apparent viscosity coefficient.     

Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005     

EFFECTS OF INTERPARTICLE INTERACTIONS ON STABILITY, AGGREGATION AND SEDIMENTATION IN COLLOIDAL SUSPENSIONS

Relations between interparticle effective interactions, structure formation, stability and sedimentation for a colloidal system are presented in this paper. For a binary mixture of large and small particles, the potential of the mean forces between large particles is obtained from the Ornstein-Zernike equation. We incorporated the small particles in our numerical simulations by using this potential of the mean force as the interparticle effective interaction. Our numerical results reveal the phenomenon of strong particle aggregation due to the attractive depletion force exerted by small particles. In the absence of the effect of gravity, this aggregation can result in flocculation and the formation of particle clusters thereby forming “void” structures, while under the influence of gravity, the aggregation can greatly affect the sedimentation rates. An analytical expression relating the aggregation number to the sedimentation velocity is presented. Our sedimentation experiments with a bidisperse latex suspension as well as clay particle dispersions show both the destabilizing and stabilizing effects of small particles, which are in qualitative agreement with our theoretical predictions.     

Direct numerical simulation of gas-solid suspensions at moderate Reynolds number: Quantifying the coupling between hydrodynamic forces and particle velocity fluctuations

Predictive device-level computational fluid dynamics (CFD) simulation of gas-solid flow is dependent on accurate models for unclosed terms that appear in the averaged equations for mass, momentum and energy conservation. In the multifluid theory, the second moment of particle velocity represents the strength of particle velocity fluctuations and is known to play an important role in the prediction of core-annular flow structure in risers (Hrenya and Sinclair, AIChEJ, 43 (4) (1994) [5]). In homogeneous suspensions the evolution of the second velocity moment is governed by the particle acceleration-velocity covariance. Therefore, fluctuations in the hydrodynamic force experienced by particles in a gas-solid flow affect the evolution of particle velocity fluctuations, which in turn can affect the mean and variance of the hydrodynamic force. This coupling has been studied in the limit of Stokes flow by Koch and co-workers using a combination of kinetic theory and multipole expansion simulations. For Reynolds numbers beyond the Stokes limit, direct numerical simulation is a promising approach to quantify this coupling. Here we present direct numerical simulation (DNS) results for the evolution of particle granular temperature and particle acceleration variance in freely evolving homogeneous gas-solid suspensions. It is found that simple extension of a class of mean particle acceleration models to their corresponding instantaneous versions does not recover the correlation of particle acceleration with particle velocity. This study motivates the development of better instantaneous particle acceleration models that are able to accurately capture the coupling between particle acceleration and velocity.     

Physicochemical Factors Influencing Colloidal Particle Transport in Porous Media

Abstract

The mobilization/immobilization of colloidal-sized particles which have high surface areas per unit mass is an important process occurring in groundwater flow systems. Association of contaminants with mobile colloidal particles may enhance the transport of adsorbed pollutants, or deposition of colloidal particles in porous media may decrease permeability and reduce contaminant transport. The general objective of this work was to elucidate physical and chemical factors affecting colloidal particle (Brownian and non-Brownian) transport in porous media under typical groundwater flow velocities. The most critical chemical factor influencing Brownian particle (0.1 and 1.0 μm) transport in a packed column was found to be pH. The next most critical factor was electrolyte concentration (calcium ion and sodium ion concentration). Gravitational force was found to be an important factor for non-Brownian particle (10 μm) transport. The non-Brownian particle transport was observed to be independent of solution chemistry. Increases in superficial velocity (from 0.9 to 2.7 m/day) resulted in different types of behavior for Brownian and non-Brownian particle transport under different conditions. The Brownian particle throughputs at a superficial velocity of 0.9 m/day were mainly controlled by the surface interaction forces, that is, hydrodynamic action was not important. The difference in Brownian diffusivity between 0.1 and 1.0 μm particles caused opposite results in particle throughputs in all experimental columns regardless of solution chemistries. Particles of 0.1 μm produced the maximum transport in the column filled with the smallest glass beads, while 1.0 μm particles produced the maximum transport in the column packed with the largest glass beads.     

Synthesis and application of an anionic water‐soluble copolymer as a dispersant for barium titanate slurries

An anionic water‐soluble copolymer, poly(acrylamide/4‐carboxylamino‐4‐oxo‐2‐butenate) (PAAM/COB), was synthesized and used as a dispersion agent for BaTiO₃ particles. PAAM/COB was prepared from acrylamide and 4‐carboxylamino‐4‐oxo‐2‐butenate in basic conditions through free‐radical polymerization. The structure of this copolymer was verified by IR and ¹H‐NMR spectra. We examined the dispersion effects of PAAM/COB by measuring the viscosity and sedimentation of BaTiO₃ suspensions and by analyzing the particle sizes. The results indicate that this copolymer was indeed effective in dispersing the particles, for the resulting suspensions were less viscous, more stabilized, and contained powder with smaller particle sizes. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 109–115, 2005     

Linking particle properties to dense suspension extrusion flow characteristics using discrete element simulations

Extrusion is a widely used process for forming suspensions and pastes into designed shapes, and is central to the manufacture of many products. In this article, the extrusion through a square‐entry die of non‐Brownian spheres suspended in Newtonian fluid is investigated using discrete element simulations, capturing individual particle‐particle contacts and hydrodynamic interactions. The simulations reveal inhomogeneous velocity and stress distributions, originating in the inherent microstructure formed by the constituent particles. Such features are shown to be relevant to generic paste extrusion behavior, such as extrudate swell. The pressure drop across the extruder is correlated with the extrudate flow rate, with the empirical fitting parameters being linked directly to particle properties such as surface friction, and processing conditions such as extruder wall roughness. Our model and results bring recent advances in suspension rheology into an industrial setting, laying foundations for future model development, predictive paste formulation and extrusion design. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3069–3082, 2017