Unsteady-State Permeate Flux of Crossflow Microfiltration

Abstract

In this study a membrane filtration cell was installed to investigate the variation of permeate flux with filtration time under various operating conditions including crossflow velocity, pressure drop, particle concentration, membrane pore size, particle size, pH, and electrolyte concentration. The dimensions of the filtration channel in the CFMF cell were 6 cm x 0.6 cm x 0.036 cm, and the flow of the suspension in the channel was controlled under the laminar flow region. Spherical polystyrene latex particles of 0.303, 0.606, and 1.020 μm were used as the suspension particles in the experiments. The density of the particles was 1.05 g/cm³. It was found that the unsteady-state permeate flux increased with an increase in particle size, membrane pore size, or crossflow velocity, but decreased with an increase in particle concentration or electrolyte concentration in the suspension. A mathematical model based on mass balance and hydrodynamic theory was developed in this study. In addition, the effect of cake growth and particle concentration decline during experiments on the permeate flux were also considered in this model. This model predicts satisfactorily the unsteady-state permeate flux of CFMF under various operating conditions.     

Experimental investigation of particle migration in suspension flow through bifurcating microchannels

Experimental measurements of velocity and concentration profiles were carried out to study transport of non‐colloidal suspension in bifurcating micro channels for both diverging and converging flow conditions using a combination of mirco‐particle image velocimetry and particle tracking velocimetry techniques. Migration of particles across the streamline was observed and symmetric velocity and concentration profile in the inlet branch becomes asymmetric in the daughter branches. Further migration of particles toward the center of the channel in the outlet branch make the profiles again symmetric. The evolution of velocity and concentration profiles was observed to be different in the symmetric and asymmetric bifurcation channels. The comparison of the streamlines for the fluid and the particles showed significant deviation near the bifurcation region. This may explain why there is unequal flow and particle partitioning during flow of suspension in asymmetric bifurcating channels as reported in many previous studies. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2293–2307, 2018     

Flow of concentrated suspension through oblique bifurcating channels

Suspensions of solid particles in viscous fluid flowing through bifurcating channels are encountered in various industrial processes and biological applications. This work reports the detailed numerical simulations of shear‐induced particle migration in oblique bifurcating channels. The effect of particle concentration, bifurcation angle, and flow rate on the partitioning of bulk flow and particles in the downstream branches is studied. It was observed that the particle distribution in the downstream branches does not follow the flow distribution due to shear‐induced particle migration. The velocity and concentration profile for suspension flow were observed to be symmetric in the inlet branch but asymmetric in the daughter branches. The degree of asymmetry and bluntness of velocity profile was observed to depend on the bulk particle concentration and bifurcation angle. The reported results could be useful in the design of flow devices handling suspension transport in bifurcating channels. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2692–2704, 2014     

In‐Line Monitoring of Crystallization Processes Using a Laser Reflection Sensor and a Neural Network Model

Laboratory‐scale experiments were carried out for measuring the chord length distribution of different particle systems using a laser reflection sensor. Samples consisted of monodisperse, polydisperse and bimodal FCC catalyst and PVC particles of different sizes, ranging from about 20 to 500 μm. The particles were dispersed in water, forming suspensions with solid‐phase mass fractions ranging from ca. 0.2 % until ca. 30 %. The experimental results, consisting of the particle number counting per chord length class, were used in fitting a neural network model for estimating the mass concentration of particles in the suspension and the volume‐based size distribution, eliminating the effects of suspension concentration and particle shape. The results indicate the feasibility of using such a model as a software sensor in crystallization processes monitoring.     

Analysis of dilute solid–liquid suspensions in turbulent stirred tanks

In this work, dilute suspensions of solid particles in stirred tanks are investigated by Particle Image Velocimetry measurements, which were specifically designed to determine the effects of the dispersed phase on mean velocity and turbulence levels of the continuous phase and the local solid–liquid slip velocity. In order to determine the effect of particle size and concentration, glass particles of narrow size distribution were selected; the particle content was increased stepwise up the maximum of 0.2 vol.%. Overall, moderate dampening of liquid turbulent fluctuations was found with the smaller particles, while turbulence enhancement was observed with the bigger ones. Continuous phase turbulence was found to affect the local map of the particle settling velocity, which was also discussed on the basis of a force balance analysis. The reduction of particle settling velocity due to free stream turbulence under specific conditions is confirmed.     

Spatial and temporal resolution of the particle image velocimetry technique in flame speed measurements

Limitations of the spatial and temporal resolution of the particle image velocimetry (PIV) technique in velocity field measurements in a laminar flame have been investigated. The limitations are due to the need to introduce a suspension of tracer particles into the flow. For a methane-air mixture with a stoichiometry coefficient of 0.9, it is determined that at a mass fraction of TiO₂ solid particles over 0.08%, the change in the flame propagation velocity by the particles exceeds 5%. The maximum spatial resolution of PIV for which the influence of the particles is insignificant corresponds to a concentration of 0.03%; in this case, the minimum resolvable scale is limited by a value 200 times larger than the size of tracer particles. Based on analytical estimates and a comparison of measured and numerically calculated particle velocities in the flame, it is concluded that particles smaller than 2 µm adequately track the flow velocity. Under these conditions, the error of the velocity measurement is mainly determined by the limited spatial resolution of PIV. The results of the work can be used to evaluate PIV measurement errors in other experimental studies of flames.     

PARTICLE FLOW PATTERNS IN THE RISER AND DOWNER OF CIRCULATING FLUIDIZED BED

This paper presents an experimental study on the flow patterns of FCC particles in a 140 mm ID Circulating Fluidized Bed with concurrent upflow and downflow gas-solid suspension. Based on the distribution of local particle velocity and particle concentration measured by a Fiber-Optical Probe Laser Doppler Velocimeter and a Fiber Optical Probe System respectively, the different flow patterns of local particls concentration, local particle velocity, local particle fluctuating velocity and sectionally average particle velocity in concurrent upflow and downflow gas-solid system have been investigated. It is found that the particle flow in the concurrent downflow is much more uniform radially than that in the concurrent upflow riser. The investigation of flow patterns in different flow systems is of significance to the development of a new gas-solid reactor.     

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.     

A theoretical and experimental study of the crossflow microfiltration process of silica particles in an aqueous suspension

This work presents a theoretical and experimental analysis of a crossflow microfiltration process of silica particles in suspension. The silica suspensions were 0.001 M of NaCl with a pH of 6 (to maintain a constant ionic force within the medium to produce a stable silica particle suspension) for three different concentrations of silica particles: 100, 300, and 500 mg L⁻¹. The membrane used in the crossflow microfiltration experiments was a commercial polymeric membrane, microporous, asymmetric with a nominal pore diameter of 0.2 µm, manufactured by OSMONICS (Minnetonka, MN). The experiments were performed in a bench scale crossflow microfiltration system with a flat rectangular membrane cell. The permeate flux was obtained as a function of the transmembrane pressure, the crossflow velocities, and the silica particles concentration. The mathematical model describing the process takes into account the variation of the physical properties of the suspension (dynamic viscosity and mass diffusivity) with the silica concentration. The experimental data are used to predict the maximum silica concentration at the membrane surface as a function of the operating conditions.     

提升管内气固两相双组分颗粒流动的离散颗粒硬球模型的模拟

基于离散颗粒(DPM)硬球模型,数值模拟提升管内双组分颗粒气固两相湍流流动行为。应用Vreman的亚格子尺度（SGS）模型模拟气体湍流,建立考虑不同颗粒加速度效应的两颗粒碰撞最小时间计算模型。数值模拟预测了大颗粒和小颗粒的速度和浓度分布。研究结果表明小颗粒具有高的轴向速度和脉动速度,而大颗粒具有低的轴向速度和脉动速度。在床中心区域,小颗粒轴向速度分布出现3个峰值,对于大颗粒轴向速度仅出现两个峰值。在壁面区域大颗粒和小颗粒速度均出现两个峰值。沿床径向方向呈现床中心颗粒浓度低、壁面区域颗粒浓度高的环核流动结果。随着表观气速的增大,颗粒浓度沿径向和床高分布趋于均匀。在床中心区域模拟计算轴向颗粒速度、颗粒浓度和RMS速度与文献实验结果相吻合。在提升管内气体湍流对小颗粒流动具有一定的影响,颗粒间碰撞作用对颗粒相流动的影响大于气相湍流的影响。     

Hydraulic transport of solids in horizontal pipelines - predictive methods for pressure gradients

The published methods for calculating pressure gradients for the flow of coarse particles in suspension in a horizontal pipeline have been criticlaly examined and have been found to show considerable inconsistencies. Experimental techniques have been developed for the measurement of two in-line parameters, particle concentration and liquid velocity, in order to obtain a better understanding of the transport mechanism.     

Separation performance of sub-micron silica particles by electrical hydrocyclone

Separation performance of sub-micron particles by use of a special electrical hydrocyclone was studied. The effects of feed suspension waiting time, applied electrostatic potentials, and the feed suspension concentration, on the separation performance of the electrical hydrocyclone were investigated. An aqueous suspension of sub-micron silica particles with median diameter of about 0.2 µm was used as the test powder. A 20 mm diameter of electrical hydrocyclone operated at 20% of the underflow ratio was used. A negative center wire electrode was inserted vertically inside the conical section, and electrostatic potentials up to 100 V were applied in this electrical hydrocyclone.It was found that the 50% cut size of the electrical hydrocyclone increased with the increase of the feed suspension waiting time after a particle dispersion process by the beads mill. The classification of the sub-micron particles occurred under applied electrostatic potentials greater than about 40 V, while better classification performance was obtained with the increase of the applied electrostatic potentials. The 50% cut size decreased with the increase of the feed suspension concentration up to 1.5 wt.%, and further increasing of the concentration led to the increase of 50% cut size.A simple model based on the time of flight model, was developed in order to predict the 50% cut size of the electrical hydrocyclone. The model results qualitatively agreed with the experimental results.It was found that classification the sub-micron particles is possible by use of the special electrical hydrocyclone proposed in this study.     

Motion of particles entrained in a plasma jet

The motion of small particles (glass microspheres, 30 to 140 microns in diameter) entrained in a free argon plasma jet was studied by means of high-speed cine streak photography. Radial temperature and velocity profiles as well as axial profiles of temperature, velocity, and argon concentration in the jet were experimentally determined by means of a plasma calorimetric probe. The system was found to be characterized by low relative Reynolds numbers (0.2 to 20) and extremely high deceleration rates (about –2,000 g). Under these conditions, an increase of drag coefficient over that predicted by the standard curve was experimentally observed. This increase was attributed to the nonsteady flow field around the particle (the so-called “history term” in the equation of motion). A general computer program has been proposed which predicts the particle velocity, acceleration and temperature along its trajectory.     

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.     

Migration and Deposition of Submicron Particles in Crossflow Microfiltration

Abstract

The migration and deposition of submicron particles in laminar crossflow microfiltration is simulated by integrating the Langevin equation. The effects of operating conditions on the particle trajectories are discussed. It is found that the Brownian motion of particles plays an important role in particle migration under a smaller crossflow velocity of suspension or a smaller filtration rate. Based on the simulated trajectories of particles, the transported flux of particles arriving at the membrane surface can be estimated. The particle flux increases with an increase of filtration rate and with a decrease of particle diameter; however, the effect of crossflow velocity on the particle flux is not obvious. The forces exerted on particles are analyzed to estimate the probability of particle deposition on the membrane surface. The probability of particle deposition increases with an increase of filtration rate, with a decrease of crossflow velocity, with a decrease of particle diameter, or with an increase of zeta potential on the particle surfaces. The simulated results of packing structures of particles on the membrane surface at the initial stage of filtration show that a looser packing can be found under a larger crossflow velocity, a smaller filtration rate, or a smaller diameter of filtered particles. Crossflow micro-filtration experiments are carried out to demonstrate the reliability of the proposed theory. The deviation between the predicted and experimental data of filtration rate at the initial period of filtration is less than 10% when the Reynolds number of the suspension flow ranges from 100 to 500.     

Penetration of Particles into Buildings and Associated Physical Factors. Part I: Model Development and Computer Simulations

The PM_2.5 standard proposed by the U.S. Environmental Protection Agency (EPA) has stimulated research on the relationships between particulate matter concentrations and the exposures and subsequent health responses of sensitive subpopulations, such as the elderly. Since individuals in these subpopulations may spend more than 90% of their time indoors, understanding the relationship between outdoor particle concentrations and those found in indoor microenvironments is critical. This research resulted in a time-dependent indoor air quality model incorporating all potential particle sources and loss mechanisms. Monte Carlo simulations of the model identified the mechanisms, such as particle loss during penetration through the building envelope, that modify the outdoor particle size distribution during transport into the interior of a building, calculated indoor-to-outdoor (I/O) concentration ratios, and estimated penetration factors as a function of particle size. Indoor particle generation and transport of outdoor particles through the HVAC system were the most important contributors to the indoor concentration in residential and commercial buildings, respectively. The most significant removal mechanisms included ventilation through and particle removal by the HVAC filter if an HVAC system was present, or particle deposition on indoor surfaces if an HVAC system was not present. The modeled I/O concentration ratios varied between 0.05 and 0.5, depending on particle size and type of ventilation system, and agreed well with published experimental results. Penetration factors less than unity were calculated for particles with aerodynamic diameters larger than 0.2 θ m if the air exchange rate and steady-state I/O concentration ratio were correlated during the simulations. An additional correlation between the air exchange rate and particle deposition velocity is required if penetration factors less than unity are to be modeled for particles with aerodynamic diameters smaller than 0.2 θ m. These results     

搅拌釜内固-液悬浮体系的CFD-DEM模拟(英文)

Computational fluid dynamics-discrete element method （CFD-DEM） coupled approach was employed to simulate the solid suspension behavior in a Rushton stirred tank with consideration of transitional and rotational motions of millions of particles with complex interactions with liquid and the rotating impeller. The simulations were satisfactorily validated with experimental data in literature in terms of measured particle velocities in the tank. Influences of operating conditions and physical properties of particles （i.e., particle diameter and density） on the two-phase flow field in the stirred tank involving particle distribution, particle velocity and vortex were studied. The wide distribution of particle angular velocity ranging from 0 to 105 r·min-1 is revealed. The Magnus force is comparable to the drag force during the particle movement in the tank. The strong particle rotation will generate extra shear force on the particles so that the particle morphology may be affected, especially in the bio-/polymer-product related processes. It can be concluded that the CFD-DEM coupled approach provides a theoretical way to under-stand the physics of particle movement in micro-to macro-scales in the solid suspension of a stirred tank.     

Dense non-Newtonian suspension flow: Effect of solids properties and pipe size

High concentration tailings transport is a promising approach for improving the safety and environmental impact of mining tailings disposal. High concentration suspensions exhibit complex non-Newtonian behavior. The interaction between the non-Newtonian carrier and the coarse particles is still poorly understood, particularly in the turbulent regime. This article considers the effect of solids concentration, particle and pipe size on transport characteristics in a weakly turbulent non-Newtonian suspension using a DNS-DEM methodology. Heterogeneous flow and a sliding bed are presented in the turbulent regime, with particles being more suspended in a small pipe. Although stratification is observed, there is no “packed” bed predicted for these cases. The presence of the viscous core region contributes to the dominance of the drag force in the central region in a non-Newtonian suspension. Non-Newtonian suspensions can also be transported at a much lower velocity and display a comparable specific energy consumption to a conventional dilute suspension.     

Flow of particles suspended in a sheared viscous fluid: Effects of finite inertia and inelastic collisions

We investigate in this article the macroscopic behavior of sheared suspensions of spherical particles. The effects of the fluid inertia, the Brownian diffusion, and the gravity are neglected. We highlight the influence of the solid‐phase inertia on the macroscopic behavior of the suspension, considering moderate to high Stokes numbers. Typically, this study is concerned with solid particles O (100 μm) suspended in a gas with a concentration varying from 5% to 30%. A hard‐sphere collision model (with elastic or inelasic rebounds) coupled with the particle Lagrangian tracking is used to simulate the suspension dynamics in an unbounded periodic domain. We first consider the behavior of the suspension with perfect elastic collisions. The suspension properties reveal a strong dependence on the particle inertia and concentration. Increasing the Stokes number from 1 to 10 induces an enhancement of the particle agitation by three orders of magnitude and an evolution of the probability density function of the fluctuating velocity from a highly peaked (close to the Dirac function) to a Maxwellian shape. This sharp transition in the velocity distribution function is related to the time scale which controls the overall dynamics of the suspension flow. The particle relaxation (resp. collision) time scale dominates the particulate phase behavior in the weakly (resp. highly) agitated suspensions. The numerical results are compared with the prediction of two statistical models based on the kinetic theory for granular flows adapted to moderately inertial regimes. The suspensions have a Newtonian behavior when they are highly agitated similarly to rapid granular flows. However, the stress tensors are highly anisotropic in weakly agitated suspensions as a difference of normal stresses arises. Finally, we discuss the effect of energy dissipation due to inelastic collisions on the statistical quantities. We also tested the influence of a simple modeling of local hydrodynamic interactions during the collision by using a restitution coefficient which depends on the local impact velocities. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Influence of particle concentration on initial collection efficiency and surface coverage in porous media filtration

Four sizes (0.095, 0.53, 1.0 and 2.01 μm) of polystyrene latex particles were used to prepare monodispersed suspensions at three different ionic strengths (10³,10^-2.5 and 10^-2 M KCl). Filtration experiments were conducted using those suspensions in a filter column with glass beads as porous medium. The filter bed depth and the filtration velocity were kept at 5 cm and 1 m/h, respectively. When suspensions with equal mass concentrations (0.2 mg/L) or equal surface area concentrations (0.12 cm²/mL) were filtered through the system, the largest particles exhibited higher initial single collector efficiency, ⪯. The difference between the ? of largest particles and the smaller particles was prominent for suspensions with equal surface area concentrations at higher ionic strengths. The collision efficiency,α of those particles exhibits higher values at higher ionic strengths. Both at equal mass concentration and equal surface area concentration,α is only slightly dependent on particle sizes when compared to its dependence on ionic strength. Further, it was found that the specific surface coverage was similar for 0.095 μm, 0.53 μm and 1.0 μm particles during the transient stage of filtration at any ionic strength when the surface area concentrations of those suspension were equal.