Particle deposition and layer formation at the crossflow microfiltration

A microscopic model of the layer formation and the cake growth at the crossflow microfiltration will be introduced. The model considers the hydrodynamic, adhesive and friction forces acting on a single particle during the filtration process. It can be shown that mainly the balance between the lift force and the drag force of the filtrate flow determines the layer formation at the membrane. Particle attachment to the layer is mostly an irreversible process. This is due to the large influence of the adhesive forces. The irreversibility of particle attachment was proved by experiments with monodisperse particles. The introduced model allows the prediction of the instationary crossflow filtration processes. The filtration rate and structure of the formed layer can be calculated. In the case of a filtration at constant transmembrane pressure the model calculation shows a good correspondence to the experimental results.     

Dielectrophoresis of nanoparticles

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of nano-sized particles of dielectric suspensions subjected to uniform and nonuniform electric fields. Particles are subjected to both electrostatic and hydrodynamic forces, as well as Brownian motion. The results of the simulations presented in this paper show that uniform electric fields the evolution of the particle structures depends on the ratio of electrostatic particle-particle interactions and Brownian forces. When this ratio is of the order of 100 or greater, particles form stable chains and columns, whereas when it is of the order of 10 or smaller the particle distribution is random. For the nonuniform electric field cases considered in this paper, the relative magnitude of Brownian forces is in the range such that it does not influence the eventual collection of particles by dielectrophoresis and the particular locations where the particles are collected. However, Brownian motion is observed to influence the transient particle trajectories. The deviation of the particle trajectories compared to those determined by the electrostatic and hydrodynamic forces alone is characterized by the ratio of Brownian and dielectrophoretic forces.     

Effects of pre-oxidation temperature on coal secondary spontaneous combustion

The hydrodynamic force (drag) on spherical and irregularly shaped particles significantly increases when the particles move close to solid and permeable boundaries. The overall effect of the increased hydrodynamic drag is to hinder the particle movement in the vicinity of boundaries and this includes the Brownian movement and electrophoresis. The Monte Carlo simulation method is used to model the Brownian movement, the resulting diffusion, and the electrophoresis of spherical particles in narrow, cylindrical pores, filled with Newtonian fluids. It is observed that the effect of the pore walls is a significant reduction of the space-averaged electrophoretic velocity of the particles, which implies reduced particle flux through the pores. The hindered electrophoresis is primarily a geometric phenomenon, caused by the increased drag and depends on the size of the particles and the pore-to-particle diameter ratio. The temperature of the fluid slightly affects the hindered electrophoresis through its effect on the viscosity, which is a determinant of the Brownian force, the diffusivity and the electrophoretic velocity. The hindered electrophoresis is almost independent of the other fluid and particle properties, such as density. Based on the simulation results a non-linear correlation for the flux of particles is derived, valid in the ranges 5?<?R/α?<?120, 5 nm?<?α?<?100 nm and 273 K?<?T?<?355 K.

     

Dynamic drag force based on iterative density mapping: A new numerical tool for three‐dimensional analysis of particle trajectories in a dielectrophoretic system

Dielectrophoresis is a widely used means of manipulating suspended particles within microfluidic systems. In order to efficiently design such systems for a desired application, various numerical methods exist that enable particle trajectory plotting in two or three dimensions based on the interplay of hydrodynamic and dielectrophoretic forces. While various models are described in the literature, few are capable of modeling interactions between particles as well as their surrounding environment as these interactions are complex, multifaceted, and computationally expensive to the point of being prohibitive when considering a large number of particles. In this paper, we present a numerical model designed to enable spatial analysis of the physical effects exerted upon particles within microfluidic systems employing dielectrophoresis. The model presents a means of approximating the effects of the presence of large numbers of particles through dynamically adjusting hydrodynamic drag force based on particle density, thereby introducing a measure of emulated particle–particle and particle–liquid interactions. This model is referred to as “dynamic drag force based on iterative density mapping.” The resultant numerical model is used to simulate and predict particle trajectory and velocity profiles within a microfluidic system incorporating curved dielectrophoretic microelectrodes. The simulated data are compared favorably with experimental data gathered using microparticle image velocimetry, and is contrasted against simulated data generated using traditional “effective moment Stokes‐drag method,” showing more accurate particle velocity profiles for areas of high particle density.     

Influence of particle-particle interactions and particles rotational motion in traveling wave dielectrophoresis

Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.     

Investigation of the Velocity Field and Nanoparticle Concentration Distribution of Nanofluid Using Lagrangian-Eulerian Approach

In this study, we use the Lagrangian-Eulerian approach to determine the concentration distribution and velocity of nanoparticles are investigated in nanofluid. Furthermore, the velocity of the fluid phase affected by the particle movement is examined. Moreover, the effects of Brownian, thermophoretic, gravitational,, and drag forces on particles and fluid velocity and nanoparticle distribution are studied, as are the effects of Reynolds number on the concentration distribution.According to the results of this study, particles are not uniformly distributed, rather, they areconcentrated more in the vicinity of the centerline of the pipe than the wall; the cause of this lack of uniform distribution is due to Brownian and thermophoretic forces. In addition, the results of this study show that the effects of Brownian forces on nanoparticle distribution and velocity field is stronger than that of other forces including thermophoretic ones.     

A Brownian dynamics study on the self-diffusion of charged tracers in dilute polyelectrolyte solutions

Brownian dynamics simulations with hydrodynamic interactions are conducted to investigate the self-diffusion of charged tracer particles in a dilute solution of charged polymers, which are modeled by bead-spring chains. The Debye-Hückel approximation is used for the electrostatic interactions. The hydrodynamic interactions are implemented by the Ewald summation of the Rotne-Prager tensor. Our simulations find that the difference in short- and long-time diffusivities is very slight in uncharged short-chain solutions. For charged systems, to the contrary, the difference becomes considerable. The short-time diffusivity is found to increase with increasing chain length, while an opposite behavior is obtained for the long-time diffusivity. The former is attributed to the hydrodynamic screening among beads in a same chain due to the bead connectivity. The latter is explained by the memory effect arising from the electrostatic repulsion and chain length. The incorporation of hydrodynamic interactions improves the agreement between the simulation prediction and the experimental result.     

Modeling Elastic Pore Sensors for Quantitative Single Particle Sizing

An empirically derived model of how the dimensions of an elastic size-tunable pore sensor change with applied membrane stretch is presented. Quantitative modeling of the pore dimensions, in conjugation with a simplified pore resistance model, enabled particle size and translocation velocity profiles to be calculated from the individual particle 'pulse' events, at any membrane stretch. Size analysis of a trimodal suspension, composed of monodisperse 220, 330 and 410 nm particles, gave rise to 3 distinguishable particle peaks with coefficient of variances below 8.2% and average size values within 2.5% of single modal dynamic light scattering measurements. Particle translocation velocity profiles, over the approximate 12 μm pore sensing zone, showed that particles entering the small pore were initially accelerated to velocities approaching 5,000 to 6,000 μm/s. They then rapidly decelerated due to the pore geometry affects on the forces driving particle translocation, being the electric field strength and fluid flow.     

Effects of Various Forces on Particle Distribution and Thermal Features of Suspensions Containing Alumina Nanoparticles

The two-phase Euler-Lagrange method has been used in order to investigate the effects of various forces on particle distribution and thermal characteristics of the water-based Al₂O₃ nanofluid flow inside a pipe under uniform wall heat flux. In the Euler-Lagrange approach, the particles are individually tracked in Lagrangian frame, while the fluid is evaluated in Eulerian frame. Brownian, thermophoretic, drag, lift, and virtual mass forces have been considered. Moreover, experimental data from various researchers were used to analyze the results. Concentration distribution is nonuniform at cross section of the pipe which increasing each parameters of Reynolds number, mean concentration and particles size will intensify its nonuniformity. This nonuniformity will make velocity profile flatter. The Brownian force makes the particle distribution more uniform, whereas the thermophoretic force enhances nonuniformity of the particle distribution. The effects of not considering the Brownian and thermophoretic forces on heat transfer are more significant for finer particles and higher concentrations. Furthermore, at lower Reynolds number, the Brownian force incorporates a more significant role especially in farther distances from entrance.      

Effect of particle shape on crossflow filtration flux

In an effort to further increase the understanding of crossflow filtration, experiments were performed on the influence of particle shape on permeation flux. Five particles of similar density and size distribution but of different shapes were used to test the influence of particle shape, while varying experimental parameters such as crossflow velocity, filtration pressure, solids concentration, membrane morphology and pore size. Particle shape was found to influence the equilibrium flux by the structure of the cake layer formed. Irregularly shaped particles such as branched carbon particles provided higher fluxes due to the high voidage cakes. More regularly shaped particles such as glass spheres resulted in lower fluxes. Platelet aluminium particles had relatively high filtration rates due to the gaps between the plates. The effects of the other experimental parameters typically showed results consistent with previous publications. Using the measured cake mass, a theoretical model based on D'Arcy and Kozeny gave reliable filtration flux compared to the experimental results.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.     

Hydrodynamic permeability of a membrane composed of porous spherical particles in the presence of uniform magnetic field

This work concerns the flow of an incompressible viscous fluid past a porous sphere in presence of transverse applied uniform magnetic field, using particle-in-cell method. The Brinkman equations are used in porous region and the Stokes equations for non-porous region. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). The hydrodynamic drag force experienced by a porous spherical particle in a cell and hydrodynamic permeability of membrane built up by porous spherical particles are evaluated. The patterns of streamlines are also obtained and discussed. The effect of stress jump coefficient, Hartmann number, dimensionless specific permeability of the porous particle and particle volume fraction on the hydrodynamic permeability and streamlines are discussed. Some previous results for hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified.     

Magnetic Hetero-flocculation of Paramagnetic Colloidal Particles

The feasibility of a high-gradient magnetic separation process, utilizing magnetite as the energizable element in lieu of stainless steel wool, is evaluated by means of an equilibrium, two-particle, magnetic hetero-flocculation model. The model calculates the net force, defined as the sum of the magnetic, electrostatic, and van der Waals forces, exerted on a paramagnetic nanoparticle that is in the proximity of a fixed magnetite particle. Since the nanoparticle-magnetite system is assumed to be in direct contact with the moving fluid, the influence of the hydrodynamic force on the magnetic attractive force between the two particles is also explored. This model clearly reveals the ranges and conditions over which each of these various forces contributes to the net force relative to Brownian (thermal) motion. The model also reveals the feasibility of using magnetite particles instead of stainless steel as the energizable element for high-gradient magnetic separation. Important variables investigated include the size and surface charge of the particles, the magnetic field, the flow velocity, the electrolyte concentration, and the magnetic susceptibility of the nanoparticle. Copyright 2000 Academic Press.     

Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.     

Coupled Influence of Colloidal and Hydrodynamic Interactions on the RSA Dynamic Blocking Function for Particle Deposition onto Packed Spherical Collectors

The influence of electrostatic double-layer and hydrodynamic interactions on random sequential adsorption (RSA) of colloidal particles onto packed spherical collectors was investigated using inverse analysis of colloid breakthrough data obtained from well-controlled particle deposition experiments. Deposition experiments were carried out using monodisperse aqueous suspensions of positively charged latex colloids and packed columns of negatively charged uniform glass beads for different combinations of ionic strength, particle size, and approach velocity. From the experimental particle breakthrough data, the initial particle deposition rates and the virial coefficients of the dynamic blocking function based on RSA mechanics were determined. The magnitudes of the virial coefficients were observed to increase from the hard sphere values with increasing flow rates and decreasing ionic strengths of the background electrolyte. Particle size also plays a significant role in governing the deposition dynamics. The deviation from the hard sphere RSA behavior becomes more prominent for larger particles. Copyright 2000 Academic Press.     

Regularities of latex filtration through microfiltration membranes

Filtration of suspensions of emulsifier-free monodisperse polystyrene latexes with particle sizes of 0.25, 0.3, and 0.4 μm through acetylcellulose microfilters is studied as depending on the composition of liquid phases, the rate and time of filtration, and the particle-to-pore size ratios. The effect of particle-membrane interactions, which are governed by the electrostatic repulsion and molecular attraction forces, on particle rejection by membranes is considered. It is shown that, when analyzing the mechanism for the rejection, it is necessary to take into account the electrophoretic motion of particles in the field of the streaming potential arising in the course of suspension filtration.     

Surface Potential of Coal Particles in Coal-Oil Mixture and Control of Settling Stability Under Gravity

This work deals with the problem of settling under gravity for coal-oil mixtures when the concentration of particles is large. The repulsive force necessary to ensure stability of coal particle is vital. The net forces acting on the particle include gravity, buoyancy, viscous drag force, and electrostatic repulsive force. Accordingly, the equation at the terminal velocity at settling is obtained along with a critical surface potential to prevent settling under gravity.     

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.     

The effect of bulk motion on coagulation rates of colloidal dispersions

Following the work in 1917 of Smoluchowski, the theory of coagulation of micronsized particles progressed very little until quantitative estimates were possible for induced-dipole attraction and electrostatic double-layer repulsion. A second increase in our understanding of coagulation of colloids has been achieved through application of recent results in fluid mechanics concerning the viscous forces operative between two particles in relative motion.In this survey the essential features of recent theories and experiments of the behavior of spherical of hydrophobic colloids in aqueous suspensions are outlined. Departures from earlier theories are reviewed, and attempts to incorporate simultaneously the effects of bulk flow and of Brownian motion are described.     

Communication: Generalizing Rosenfeld's excess-entropy scaling to predict long-time diffusivity in dense fluids of Brownian particles: from hard to ultrasoft interactions

Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, Gaussian-core, and Hertzian pair interactions are considered. Within the generalized Rosenfeld scaling method, long-time diffusivities of ultrasoft Gaussian-core and Hertzian particle fluids, which display anomalous trends with increasing density, are predicted (to within 20%) based on knowledge of interparticle interactions, excess entropy, and scaling behavior of simpler inverse-power-law fluids.