A model for ultrafine powder production in a plasma reactor

A model is proposed for the analysis of the production of ultrafine particles in thermal plasma reactors. The model initially solves the fluid flow, temperature, and concentration fields using a classical control volume approach. The nucleation and growth of ultra fine particles are then solved along each streamline. The evolution of the particle distribution is described by a statistical approach, using the first moments of the distribution as the dependent variables. Brownian coalescence is considered in the free molecular regime. In the discussion, the model is used to demonstrate the effects of some important parameters, such as the initial concentration of metal vapor, its radial distribution, and the radial injection of a cooling gas, on the particle size distribution.     

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self?" component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.     

Density-induced coupling effects on the dispersivity of a flexible chain particle

A model is introduced to investigate the transport properties of an inhomogeneously dense flexible chain particle. The specific model used is a sedimenting non-neutrally buoyant inhomogenously weighted flexible Brownian dumbbell, and it is shown that density inhomogeneity gives rise to a novel coupling effect between the "shape-fluctuation" and "size-fluctuation" dispersion mechanisms. The previously reported shape-fluctuation dispersion term stems from the dumbbell's nonspherical shape and the ensuing anisotropic mobility tensor, while the already investigated size fluctuation term is the result of the dependence of the overall dumbbell translational mobility on the separation distance between the constitutive spheres. Because the density of the constitutive spheres is unequal, the external force simultaneously reorients and deforms the flexible dumbbell, and it is this mutual dependence between dumbbell orientation and size that induces the coupling. Numerical results are presented for the case of a tethered dumbbell composed of two spheres, identical in size but differing in density. The "weak-field" limit is addressed, where the externally applied torque and particle deformation forces are dominated by the thermal fluctuations associated with rotational and deformation Brownian motion. This numerical solution, obtained by including a large number of higher order hydrodynamic interactions (120 terms), describes the Brownian particle's long-time transport without resorting to ad hoc approximations, such as preaveraging the hydrodynamic force or incorporating only first-order hydrodynamic interaction effects (such as employing the Burgers-Oseen tensor). Separate analytical solutions, based on these respective approximations, are also presented and it is concluded that in the limit of "long tethers," where the ratio of tether length to sphere size is greater than seven, no more than 15% error is introduced by neglecting higher-order hydrodynamic interactions. Similarly, the preaveraging approximation introduces no more than a few percent error in the limit of "almost-rigid" dumbbells, where the ratio of tether length to sphere size is less than three. For tethers of "intermediate" length, the full numerical solution must be employed.     

Effect of particle size distribution on the collection efficiency of Brownian particles

The main purpose of the present paper is to investigate the effect of the normal Gaussian size distribution on the deposition of Brownian particles onto a spherical collector, by applying the Brownian dynamic simulation method and the Kuwabara flow field model with different types of DLVO interaction energy curves and the shadow effect. The simulation results show that the collection efficiency of Brownian particles always increases with a wider particle size distribution region. The same increased tendencies are also observed for the case of increasing Reynolds number and for the case of increasing the particle size to the collector size ratio. When compared to the available experimental data, the present simulation method fits well with the experimental data when the specific deposit per collector is not large.     

Modeling of submicrometer aerosol penetration through sintered granular membrane filters

We present a deep-bed aerosol filtration model that can be used to estimate the efficiency of sintered granular membrane filters in the region of the most penetrating particle size. In this region the capture of submicrometer aerosols, much smaller than the filter pore size, takes place mainly via Brownian diffusion and direct interception acting in synergy. By modeling the disordered sintered grain packing of such filters as a simple cubic lattice, and mapping the corresponding 3D connected pore volume onto a discrete cylindrical pore network, the efficiency of a granular filter can be estimated, using new analytical results for the efficiency of cylindrical pores. This model for aerosol penetration in sintered granular filters includes flow slip and the kinetics of particle capture by the pore surface. With a unique choice for two parameters, namely the structural tortuosity and effective kinetic coefficient of particle adsorption, this semiempirical model can account for the experimental efficiency of a new class of "high-efficiency particulate air" ceramic membrane filters as a function of particle size over a wide range of filter thickness and texture (pore size and porosity) and operating conditions (face velocity).     

Estimating the viscoelastic moduli of complex fluids from observation of Brownian motion of a particle confined to a harmonic trap

A procedure is proposed to estimate the viscoelastic properties of a complex fluid from the behavior of the velocity autocorrelation function of a suspended Brownian particle, trapped in a harmonic potential. The procedure is tested for a model complex fluid with a given frequency-dependent shear viscosity. The analysis shows that the procedure can provide a rather accurate prediction of the viscoelastic properties of the fluid on the basis of experimental data on the velocity autocorrelation function of the trapped Brownian particle in a limited range of time.     

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.      

Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

Dynamics of shear-thinning suspensions of core-shell structured latex particles

The rheological behavior and microstructure of shear-thinning suspensions of core-shell structured carboxylated latex particles were examined. The steady shear viscosity of the suspension increased with increasing dissociation of the carboxyl groups or increasing particle concentration, however the critical shear stress sigma(c) and inter-particle distance xi of the microstructure did not change. With increasing particle diameter, sigma(c) increased and xi decreased. These results were consistent with a Brownian hard sphere model, in which competition exists between the bulk mass transfer due to the applied field and diffusion of the particles. We confirmed that sigma(c) depends on xi, as expressed by sigma(c) = 3kT/4pi xi3. This relationship is consistent with the dynamics of a Brownian hard sphere model with particle diameter xi. Thus the dynamics of shear-thinning suspensions of core-shell particles can be explained by a Brownian thermodynamic model.     

Optimal protocols for minimal work processes in underdamped stochastic thermodynamics

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects, the optimal protocol has been found to involve jumps of the control parameter at the beginning and end of the process. Including the inertia term, we show that this feature not only persists but that even delta-peak-like changes of the control parameter at both boundaries make the process optimal. These results are obtained by analyzing two simple paradigmatic cases: First, a Brownian particle dragged by a harmonic optical trap through a viscous fluid and, second, a Brownian particle subject to an optical trap with time-dependent stiffness. These insights could be used to improve free energy calculations via either thermodynamic integration or "fast growth" methods using Jarzynski's equality.     

A new semi-analytical model for effective thermal conductivity of nanofluids

A new theoretical model for thermal conductivity of nanofluids is developed incorporating effective medium theory, interfacial layer, particle aggregation and Brownian motion-induced convection from multiple nanoparticles/aggregates. The predicated result using aggregate size, which represents the particle size in the actual condition of nanofluids, fits well with the experimental data for water-, R113- and ethylene glycol (EG)-based nanofluids. The present model also gives much better predictions compared to the existing models. A parametric analysis, particularly particle aggregation, is conducted to investigate the dependence of effective thermal conductivity of nanofluids on the properties of nanoparticles and fluid. Aggregation is the main factor responsible for thermal conductivity enhancement. The dynamic contribution of Brownian motion on thermal conductivity enhancement is surpassed by that of static mechanisms, particularly at high volume fraction. Predication also indicated that the viscosity increases faster than the thermal conductivity, causing the highly aggregated nanofluids to become unfavourable, especially for d_f = 1.8.     

Elastic coefficient of a single polymer chain by using Brownian dynamics analysis

The elastic coefficient of a single polystyrene chain has been experimentally evaluated by using Brownian dynamics analysis. The Brownian motion of the chain is probed using a particle trapped by optical tweezers with a negligibly small spring constant. The displacement of the particle due to Brownian motion is measured by an interferometer assembled using the same laser beam as the optical tweezers. Two methods are employed for Brownian dynamics analysis: (1) the analysis of the time course of the displacement of the particle and (2) the fitting of the power spectrum of Brownian motion with a Lorentzian. The elastic constant of a polystyrene chain in dichloromethane at 21 degrees C is estimated to be 6.4 x 10(-6) and 1.1 x 10(-5) N/m when methods (1) and (2) are employed, respectively. The elastic constant obtained by approximating the polystyrene chain to a freely jointed chain is in agreement with the experimentally evaluated elastic constant.     

Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration

Particle deposition and fouling are critical factors governing the performance of microfiltration and ultrafiltration systems. Particle trajectories were evaluated by numerical integration of the Langevin equation, accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, and Brownian diffusion. In the absence of Brownian forces, particles are unable to enter the membrane pores unless the drag associated with the filtration velocity can overcome the electrostatic repulsion. Brownian forces significantly alter this behavior, allowing some particles to enter the pore even at low filtration velocities. The average particle transmission, evaluated from the probability of having a particle enter the pore, increases with increasing filtration velocity due to the greater hydrodynamic drag force on the particle. These results provide important insights into particle behavior in membrane systems.     

Brownian motion of a polymer-bound colloidal particle

A simple model of Brownian motion of a colloidal particle attached to the flat surface by a polymer thread is presented. The model results are discussed in terms of the measurability of the elastic properties of a linear polymer chain in the dispersion medium by observation of the motion of a colloidal particle connected to a fixed point by the polymer. Received: 11 November 1998 Accepted: 9 December 1998     

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

Scaling of the memory function and Brownian motion

It has been recently shown that the velocity autocorrelation function of a tracer particle immersed in a simple liquid scales approximately with the inverse of its mass. With increasing mass the amplitude is systematically reduced and the velocity autocorrelation function tends to a slowly decaying exponential, which is characteristic for Brownian motion. We give here an analytical proof for this behavior and comment on the usual explanation for Brownian dynamics which is based on the assumption that the memory function is proportional to a Dirac distribution. We also derive conditions for Brownian dynamics of a tracer particle which are entirely based on properties of its memory function.     

Friction and diffusion of a Brownian particle in a mesoscopic solvent

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.     

Particle laden fluid interfaces: Dynamics and interfacial rheology

We review the dynamics of particle laden interfaces, both particle monolayers and particle + surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle + surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.     

Diffusion coefficient of Brownian particle in rough micro-channel

This study examines the feasibility of using of the lattice Boltzmann method to determine how the surface roughness of a quadrate channel affects the diffusion coefficient of Brownian particle(s). The surface was represented by a regular array of spheres. Surface roughness reduced the diffusion coefficient of the Brownian particle(s) because of a change in the velocity autocorrelation function decay and in pressure. Additionally, the neighboring particles increased the diffusion coefficient of Brownian particle.