Evolution Of Particle Size Distribution Research Articles

Miniemulsion copolymerization of styrene and butyl acrylate initiated by redox system at lower temperature: Reaction kinetics and evolution of particle-size distribution

The kinetics of the miniemulsion copolymerization of styrene (St) and butyl acrylate (BA) initiated by redox initiators, (NH4)2S2O8/NaHSO3, at lower temperature (45°C) was studied. The polymerization rate in miniemulsion copolymerization is lower than that of the corresponding conventional emulsion copolymerization. In regard to the rate of polymerization, the initiator concentration plays a more important role in miniemulsion copolymerization than in conventional emulsion polymerization, while the surfactant concentration has a more important role in conventional emulsion polymerization than in miniemulsion polymerization. These are attributed to their different nucleation mechanisms, which are the same as those found in the miniemul- sion polymerization carried out at higher temperatures. While by eliminating nucle- ation via micelle and ensuring against homogeneous nucleation, miniemulsion poly- merization can be carried out by the sole nucleation mechanism—monomer droplet nucleation—at lower temperature. Because of this, the particles become narrower during the polymerization and, finally, monodisperse polymer particles are obtained. The result of the particle numbers indicated that a continuous nucleation will cease at about 60% conversion. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 315-322, 1999

Shear-Induced Flocculation of Colloidal Particles in Stirred Tanks

Colloidal polystyrene and paramagnetic particles consisting of mixtures of polystyrene and magnetite are used to experimentally investigate flocculation kinetics in a stirred tank under turbulent shear flow. The effects of various parameters—agitation speed, solution pH, ionic strength, particle size, and particle concentration—on the flocculation rate are investigated. A trajectory model applicable for shear-flow systems is formulated to describe particle flocculation in stirred tanks. The collision efficiency of particles is obtained from the limiting trajectory of one particle moving toward another and is a function of interparticle forces and flow properties. The collision frequency is determined as a function of particle size and energy dissipation. The flocculation frequency is then determined by multiplying the collision frequency by the collision efficiency and is incorporated into a population balance model to predict the particle size evolution. Results suggest that the flocculation rate is enhanced by increasing the agitation speed, even though the collision efficiency is decreased at a higher agitation speed. It is also found that the collision rate increases and the collision efficiency decreases as the particle size ratio is increased. Results also suggest that the breakup rate of aggregates in a turbulent shear flow could be significant and may need to be included in the population balance modeling to correctly predict the evolution of particle size distribution.

Evolution of Particle Size Distribution During Suspension Polymerization: Theory and Experiments

An investigation has been undertaken in order to understand the evolution of particle size distributions during suspension polymerization. Experiments have shown that the interplay of breakage and coalescence phenomena with the change in viscosity and interfacial tension due to reaction may cause the appearance of both bimodal and unimodal distributions during the course of the reaction. A detailed model based on a population balance coupled with the polymerization kinetics has been developed in order to describe the experimental data.

Stochastic Simulation of Particulate Dynamic Breakup.

Based on the analysis of dynamic breakup process of particles in particulate systems, a direct stochastic simulation method is proposed in this paper, which is applicable for general population balances with particle breakup. The detailed algorithm is presented. There are two important steps in algorithm: 1. to determine whether a particle breaks up, using the breakup frequency function; 2. to determine the volume of daughter particles for one breakup, using the probability distribution function of daughter particles after the breakup of a mother particle. A calculation example of turbulent liquid-liquid dispersion is given to predict the development of particle size distribution. The calculation results are in very good agreement with the analytical solution from Das (1996).

Kinetics of Dispersion Polymerization of Styrene in Ethanol. 2. Model Validation

Predictions of monomer conversion, polymerization rate, and evolution of particle size distribution during seeded batch and continuous dispersion polymerization obtained from simulation are compared to experimental results. An understanding of the kinetic mechanisms governing the relative prevalence of solution and microbulk polymerization has been gained. Estimates of parameters in the radical transport rate coefficient models compare favorably with values reported in the literature.

A two dimensional analysis of the evolution of the particle size distribution in particle laden high temperature jet flows including the effects of coagulation and buoyancy

A numerical study has been done on the evolution of particle size distribution in particle laden high temperature jet flows undergoing convection, diffusion, thermophoresis and coagulation. The dynamic behavior of these particles have been modelled by approximating the particle size distribution by a lognormal function throughout the process and the moments of the particle size distribution have been used to solve the general dynamic equation. The size distributions of spherical particles in the radial and axial direction have been obtained including the effect of buoyancy. Of particular interests are the variations of geometric mean diameter, number concentration and polydispersity. Results show that buoyancy significantly alters the size distribution in both axial and radial direction. One dimensional analysis for non-spherical particles has also been done and the results have been compared with the existing experimental data.

Kinetics of phase coarsening in dense systems

Diffusion-limited coarsening is formulated as a statistical description of the evolving particle size distribution. Diffusional interactions among dispersed particles are accounted for using a statistical field cell associated with each particle size class. The field cells correlate particle volumes with an averaged growth rate and the corresponding volume of the matrix phase associated with a particle's transport field. The particle and matrix volumes obey a linear affine transformation, derived here from self-similar dynamics. The coarsening kinetics are determined by adding two global constraints on the distributional representation of the microstructure, which specify the volume fraction and critical (zero-growth) particle size in terms of explicit spatial and ensemble averages. Comparison of the theoretically predicted coarsening rates with those obtained from liquid-phase sintering experiments in binary alloys show agreement over a wide range of phase fractions.

Gas absorption in reactive slurries: Particle dissolution near gas-liquid interface

The rates of gas absorption into reactive slurries constituted by “fine” particles of a sparingly soluble reactant are known to be enhanced when the particle size is smaller than the characteristic diffusional lengths of the reactive species. This study examines the process of particle dissolution and the consequent change in particle size(s) near the gas-liquid interface, in the presence of diffusional gradients, using Higbie's extended theory of mass transfer with chemical (instantaneous) reaction. The effect of changing particle size (including complete dissolution of the particles in this “film” zone) on the mechanism and extent of enhancement in the specific rate of absorption has been assessed using a population balance approach to track the interaction of the dissolution process with the evolving particle size distributions. It has been shown that the rates predicted from the proposed theory differ considerably from those computed using models available in the literature, for particles which are “small” enough. A variety of initial particle size distributions of different spreads have been used to show that for a given mean particle size, wide distributions produce lower enhancements in the specific rate than narrow ones. The specific rate-batch time trajectories for a typical batch slurry reactor have been generated along with the evolution of the particle size distributions in the bulk slurry phase in order to track the solid conversion as a function of batch time. Such conversions computed from theories available in the literature are likely to be gross overestimates in relation to the actual scenario. Some of the reported experimental absorption data have been reinterpreted in the light of the models developed here.

Semicontinuous emulsion copolymerization of methyl methacrylate and n-butyl acrylate: 1. Effect of mixed emulsifiers in seeded polymerization

In the seeded semicontinuous emulsion copolymerization of methyl methacrylate and n-butyl acrylate, the use of mixed surfactant systems (anionic sodium lauryl sulfate and non-ionic Brij 35 and Glytanox 1001) leads to a decrease in the total particle number in the reactor during the reaction. Moreover, the decrease in the particle number is higher when the emulsifier used is non-ionic. The kinetic behaviour of the process is not influenced by the nature or amount of the emulsifier. The study of the evolution of particle size distribution shows that the distribution becomes broader during the reaction in all the cases studied. The total particle area decreases when the amount of non-ionic emulsifier in the recipe is increased.

From LDEF to EURECA: Orbital debris and meteoroids in low earth orbit

Many human operations have created a large population of small orbital debris in near Earth environment. The threat they represent for satellites is a major factor for the preparation of future space missions. Several experiments devoted to the study of this environment, as well as various materials exposed to space, have been retrieved in the past few years. The analysis of the results shows some differences with previous modeling. Comparison with data from LDEF and from EURECA give some insight in the long term evolution of particle size distribution. Chemical identification of particle remnants inside craters is difficult but provides valuable information on the origin of the impactors. Permanent monitoring of environment is obviously needed, especially for the type of orbits where data are presently scarce ie. heliosynchronous and geostationary orbits.

Dissolution and coarsening of large niobium carbonitrides in a microalloyed steel

Observations and measurements of the kinetics of coarsening and dissolution of large cuboidal niobium carbonitrides during solution treatments of a high nitrogen niobium microalloyed steel are reported. At temperatures between 1473 and 1573 K a competitive coarsening and dissolution process was established where the larger niobium carbonitrides grew at the expense of the smaller, or employing niobium and nitrogen which remained in solid solution. In this temperature range growth or dissolution rates and critical sizes could be determined from the analysis of the evolution of particle size distribution. At higher temperatures (1623–1723 K), only a dissolution process existed, where the dissolution rates as a function of particle size was found to increase with increasing temperature.

Influence of ash on particle size distribution evolution during coal combustion

In this work we describe a numerical model of the evolution of the particle size distribution (PSD) during coal combustion. The model includes burning and fragmentation. The model examines the sensitivity of PSD evolution to different modes of fragmentation by allowing the input of alternative fragmentation scenarios. A highlight of the model formulation is the incorporation of mineral matter as a distinct constituent of the coal. Evolution of the size distribution of mineral matter is modeled explicitly. We apply the model to two different initial size distributions, a monodispersion and a power-law distribution similar to that of pulverized coal, each with three alternative modes of fragmentation: no fragmentation, fragmentation into a few relatively large fragments, and fragmentation into a family of fragments covering a wide size range. The simulations suggest that the size distribution of ash particles obtained from an initially monodisperse feedstock is sensitive to the fragmentation scenario; in contrast the ash size distribution is not sensitive to the mode of fragmentation if the initial feedstock is power-law distributed.

Kinetic Model for Simulating the Evolution of Particle Size Distributions During Char Combustion

Abstract The details of a numerical simulation of particle size distribution evolution during ash-free char oxidation are presented. This work represents the first application of the population balance modeling approach to char combustion, and includes the effects of both oxidation and fragmentation. The simulation consists essentially of a transfer function 'hat determines the evolution of the entire char particle size distribution with lime. Determination of the input parameters to the model, and the sensitivity of the results to variations in these parameters are discussed.

Numerical simulation of particle size distribution evolution during pulverized coal combustion

Two numerical simulations of particle size distribution (PSD) evolution during ash-free char combustion are presented to help determine the sensitivity of measured coal PSD evolution to fragmentation. The first simulation is based on percolation theory, and it builds the PSD evolution from an ensemble of individual particle size time histories. The second simulation is population balance that operates on the entire distribution as a unit. Inputs to the simulations come from experimental data available in the literature, and results of the simulations are discussed in conjunction with these data.

Combustion of coal—water slurries: Evolution of particle size distribution for coals of different rank

The effect of coal rank on pulverized coal and coal—water slurry combustion was examined in a laboratory laminar flow reactor. Two coals were used: a low-rank lignite with high mineral matter content and a high-rank bituminous coal with low mineral matter content. The evolution of the particle size distribution of these two coals in both dry and slurry form during combustion was measured with an in situ optical particle counter. Samples were also collected after different combustion durations and were examined with a scanning electron microscope. The results indicate that the coal slurry atomization process affects the particle size distribution, but inherent coal properties associated with coal rank do not significantly affect the initial and early combustion behaviour of the pulverized coal or coal—water slurry. During char oxidation, the ash constituent of the coal dominates the small particle size distribution, while the behaviour of the large particle size distribution and agglomerates depends on the coal rank.

An observational study of the anvil of a winter maritime cumulonimbus cloud

AbstractThis paper reports on microphysical and dynamical measurements made from an aircraft in the anvil of a winter cumulonimbus cloud which grew in maritime air near the United Kingdom. The anvil had a well‐organized structure, with ice content in the central region exceeding 1 gm−3. The ice appeared to be distributed uniformly over the size range of crystals, with half the total mass contained in particles larger than 1 mm. The total particle concentration may have exceeded 1501−1 in places. A widespread supersaturation of typically 10% with respect to ice ensured that the ice crystals continued to grow by deposition. The microphysical and dynamical structures of the anvil are shown to be closely linked, and semi‐quantitative explanations are given for the evolution of particle size distributions in terms of deposition and gravitational settling.

A Simple Model of Particle Coalescence and Breakup

A simple model of the evolution of particle size distributions by coalescence and spontaneous and binary disintegrations is formulated. Spontaneous disintegration involves single particles, while coalescence and binary disintegrations involve pairs of particles. Analytical solutions for the mean mass of the distribution and the equilibrium size distribution are obtained for the case of constant collection kernel and disintegration parameters. At equilibrium, the forms of the size distributions are identical under the action of coalescence and either or both disintegration processes; the particle concentration is proportional to the total mass concentration (M) and the mean mass of the distribution is independent of M when only coalescence and binary disintegrations are operative. At small values of M, the effects of spontaneous disintegrations dominate over those of binary disintegrations while the reverse is the case at large values of M. Some of the findings of the present simple model are in qualitative agreement with the results of numerical calculations of the evolution of raindrop size spectra with realistic formulations of drop coalescence and breakup.

Continuity equation for evolving particle size distributions

Continuity equation for evolving particle size distributions

The analysis of the evolution of particle size distribution during microstructural change

The concept of the growth path envelope is introduced and combined with that of the rate of change of the number of particles to provide a detailed description of the dynamics of microstructural change in particulate systems. A graphical method is presented, which permits the determination of the nucleation rate and growth path envelope from quantitative measurements of the variation of the particle size distribution during the process. A straightforward mathematical relationship between the size distribution function at any time, nv(R,t), and the nucleation rate, N(Τ) and growth path envelope is derived: nv(R,t) = N(Τ)/G(R,Τ where Τ is the nucleation time for particles that grow to size R at time t, and G(R,Τ) is a properly evaluated growth rate for these particles. It is shown that this equation provides a basis for constructing models of the dynamics of microstructural change in geometrically complex systems.