Particle Size Distribution Model Research Articles

Fractal Dimensions of Suspended Particles in Seawater

Light scattering data measured in various sites ranging from open ocean to coastal and harbor waters have been analyzed. The dependence of scattered light intensity on scattering vector shows two distinctiveqregions. ThisI(q) behavior is consistent with the two component model of sea particle size distribution. The average particle fractal dimensions estimated from these data are 1.7 ± 0.1 for smallqvalues (q≤ 2.5 μm−1) and 2.7 ± 0.4 for largeqvalues. These fractal dimensions correspond to cluster–cluster aggregation of larger (B component) particles due to differential sedimentation and to shear induced particle–cluster aggregation of smaller (A component) particles. They also agree with the fractal properties of microaggregates obtained from the recent simula- tion of phytoplankton bloom in a mesocosm.

Modeling of particle size distribution and its influence on the radiative properties of mineral dust aerosol

The radiative parameters of mineral aerosols are strongly dependent on particle size. Therefore explicit modeling of particle size distribution is needed to calculate the radiative effects and the climate impact of mineral dust. We describe a parameterization of the global mineral aerosol size distribution in a transport model using eight size classes between 0.1 and 10 μm. The model prescribes the initial size distribution using soil texture data and aerosol size measurements close to the ground. During transport, the size distribution changes as larger particles settle out faster than smaller particles. Results of Mie scattering calculations of radiative parameters (extinction efficiency, single scattering albedo, asymmetry parameter) of mineral dust are shown at wavelengths between 0.3 and 30 μm for effective particle radii between 0.1 and 10 μm. Also included are radiative properties (reflection, absorption, transmission) calculated for a dust optical thickness of 0.1. Preliminary studies with the Goddard Institute for Space Studies (GISS) general circulation model (GCM), using two particle size modes, show regional changes in radiative flux at the top of the atmosphere as large as +15 W m−2 at solar and +5 W m−2 at thermal wavelengths in the annual mean, indicating that dust forcing is an important factor in the global radiation budget.

A model for particle size distribution and elutriation in fluidized beds

Knowledge of particle size distributions is crucial for establishing the utilization of solid carbonaceous and sorbents in fluidized bed combustors. Populational models should consider particle shrinking through disintegration and chemical reaction, and particle removal through elutriation and overflow. A modelling review is carried out and a populational model is constructed. Bed surface entrainment and elutriation models are used to deal with particle carryover. Entrainment is assumed to be accomplished through two different parallel mechanisms: the prompt entrainment of very fine particles, and the entrainment through bubble wake ejections. Attrition is identified as the main mechanism of particle disintegration. Concerning carbonaceous particles, attrition and chemical reaction are treated as parallel shrinking effects. Limestone sorbent particles are assumed to shrink only through attrition. The particle population model is solved simultaneously with the entrainment and the elutriation models. The predictions of the interlinked models are in good agreement with available experiment.

Modeling of Particle Size Evolution during Mechanical Milling

The process of mechanical alloying (MA) involves the repeated deformation, welding, and fracture of powder materials during grinding in high-energy mills. During MA, the size and size distribution of the particles change as a result of the particles’ different fracture and welding rates. The evolution of particle volume distributions during such a combined “fission-fusion” process can be describedvia a differential-integral equation. While analytical solutions are known for systems in which only fusion takes place, there is apparently no such solution for the fission-fusion problem. In this article, we describe a discretized form of the fission-fusion equation and apply it to modeling of particle size distributions during milling of elemental powders using previously determined fracture and welding rates appropriate to the global system of particles. Predicted particle size distributions mimic well those determined experimentally.

Two-component model of sea particle size distribution

A general two-component model of particle size distribution in sea water describes the components by a three parameter generalized gamma distribution. The values for two of these parameters, obtained from analysis of experimental data, prove to be constants, universal and valid for oligotrophic waters in all oceans. The third parameter is allowed to vary around a mean value characteristic for each component. In this way the component size distributions were reduced to a single parameter distribution. The model was successfully applied to various measured size distributions. This model predicts measured data with few errors and provides a better fit over a larger size range, 10 −2−10 2 μm, than commonly-used size distribution models. The model is useful for light scattering and radiative transfer calculations, especially in oligotrophic waters.

Formation of agglomerate particles by coagulation and sintering—Part II. The evolution of the morphology of aerosol-made titania, silica and silica-doped titania powders

A two-dimensional particle size distribution model is used to describe gas phase synthesis of titania and silica powders. By incorporating a coalescence term along with a particle sintering rate in the governing population balance equation, the model traces the evolution of both the volume and surface area of aerosol particles. The simultaneous calculation of particle volume and surface area distribution leads to a direct characterization of the primary particles (grains) as well as particle aggregates. The effects of residence time, temperature and particle material properties on powder morphology are investigated. Effective sintering rates for pure titania, silica and silica-doped titania are deduced by comparing grain sizes obtained by model simulations and those measured experimentally from specific surface area and microscopic analyses.

Formation of agglomerate particles by coagulation and sintering—Part I. A two-dimensional solution of the population balance equation

A two-dimensional particle size distribution model is presented, for the first time, describing the evolution of both particle size and shape during gas phase powder production. In addition to the coagulation term, the governing population balance equation includes a coalescence contribution based on the particle sintering rate. It is the finite coalescence rate that results in the formation of irregularly shaped aggregate particles. Using volume and surface area as the two particle size dimensions, the aerosol dynamic equations are solved by extending a one-dimensional sectional technique to the two-dimensional space. This model leads to a quantitative characterization of powder morphology as well as the average size and polydispersity of the powders. The volume and surface area of the particles can also lead to an estimation of the surface fractal dimension of these particles from first principles.

Dynamic modelling of particle size distribution and degree of agglomeration during precipitation

Dynamic modelling of particle size distribution and degree of agglomeration during precipitation

Soil spatial variability along transects

In this study, soil properties were measured along two parallel 100-m transects separated by 60 cm. Soil samples were taken at the 30 and 60 cm depths at 1 m intervals along each transect, for a total of 400 samples. Soil-water-characteristic curves, determined in the laboratory on these samples, were fitted to van Genuchten's five-parameter model which was simplified by assuming that the residual water content was negligible. Particle size measurements from each soil sample were fitted to a three-parameter model. In addition, saturated hydraulic conductivity K S and bulk density were measured. Several spatial correlations beyond lag 0 were found to be statistically significant for the van Genuchten model parameter n, for lnK s and for B 1, which is an empirical parameter in the particle size distribution model. The cross-correlation functions also contain significant values beyond lag 0 for n versus lnK s , n versus B 1 and lnK s versus B 1. The parameter B 1 was positively correlated with lnK s and n. Most of those properties, especially B 1 and n, revealed a strong periodic behaviour with a main cycle of 100 and 50 m at the 30-cm and 60-cm depths, respectively. Removing these cycles resulted in short lags with a spatial dependence of only 1 m. A state-space analysis was employed for predicting saturated hydraulic conductivity. The best result was obtained using a four-dimensional model containing Θ s, n, lnK s and bulk density.

Flocculation in Turbulent Flow: Measurement and Modeling of Particle Size Distributions

Fluid motion in an oscillating‐grid flocculator was investigated quantitatively with a laser Doppler velocimeter for two mixing conditions. Batch flocculation experiments were performed for monodisperse, bimodal, and trimodal latex suspensions. The effects of mixing intensity, particle charge, and suspension concentration on the rate of change in particle size distributions were studied. Experimental results indicated that large eddies are relatively unimportant for flocculation and that flocculation is induced by eddies of approximately the same size as the particles. A method for estimating the velocity gradients in eddies of different sizes in the flow was developed and incorporated into an existing mathematical model for flocculation. The predictions of the revised flocculation model were compared with the experimental results and indicated that the velocity gradients of the eddies adequately describe the interparticle contacts resulting from mixing during flocculation.

A mathematical model for particle size distribution in bell-type charging at blast furnace top.

A mathematical model for particle size distribution in bell-type charging at blast furnace top was developed, which is capable of estimating the radial average size distribution as well as the radial deposit distribution of each particle size for multiple size burden with a few fixed parameters.The following findings were considered in the construction of the model. The radial deposit distribution of particles in blast furnace was determined by both the sieving process and the deposit process on the slope. The elemental process in the sieving process is the percolation of small particles through voids between large particles acting as sieves. Principal factors affecting the percolation are the ratio of large particle size to small particle size and the particle velocity gradient in the flowing layer on the slope.The validity of the model was confirmed through actual filling tests at various blast furnaces with different throat diameters and charging conditions.The model was applied to the prediction of the change of particle size distribution caused by the decrease of large bell stroke at Wakayama #4 BF. The monitored results showed the decrease of gas flow resistance and the suppression of peripheral gas flow as were predicted by the model with help of a gas flow simulation model.

The effect of radical desorption on the particle size distribution in vinyl acetate emulsion polymerization

AbstractThe effect of free radical desorption is studied by using a mathematical model of particle size distribution in continuous emulsion polymerization. By comparing the theoretical prediction with experimental data, the value of Do for the vinyl acetate (VAc) system is best chosen as 0.19 × 10−7 cm2/h. The effect of radical desorption as well as mean residence time on the absolute particle size distribution, total concentration of polymer particles, conversion, and average number of radicals per polymer particle are analyzed by the model proposed.

PARTICLE SIZE DISTRIBUTION IN CONTINUOUS EMULSION POLYMERIZATION WITH FREE RADICAL DESORPTION

ABSTRACT A mathematical model of particle size distribution in continuous emulsion polymerization which accounts for the free radical desorption from polymer particles is presented. The desorption rate is based on the diffusion theories which suggest the rate coefficient should be inversely proportional to the surface area of the polymer particles. The number density and total particle number are estimated by our model. The average number of radicals per particle approaches Smith-Ewart case II In the range of large particle sizes. A means for predicting the nature of average desorption rate is proposed, and it seems to be influenced by concentrations of emulsifier and initiator, and residence times as well

FLOC SIZE REDUCTION IN THE TURBULENT ENVIRONMENT

ABSTRACT The dynamic behavior of the particle size distribution (PSD) in wastewater treatment processes results from the interaction of a random growth process with nonlinear, stochastic hydrodynamics. Successful modeling of the PSD response to high dissipation conditions depends upon accurate quantification of the breakage mode, the local dissipation rate, transition probability, and the daughter particle size distribution; the inferential determination of these quantities from PSD data is difficult, at best. Direct photographic observation of floc breakup in a turbulent jet apparatus and in the Impeller stream of a baffled, agitated tank has provided opportunities to measure both the breakage mode and the daughter particle size distribution for individual parent floes. These data have been used in successful PSD modeling in lean, batch systems characterized by irreversible breakage.

Mathematical model of particle size distribution of crystals taking into account the growth dispersion

AbstractThis paper presents a mathematical model to describe the effect which the growth dispersion has on the particle‐size distribution of crystals which are formed in a crystallizer with an ideally mixed suspension and ideal product discharge (MSMPR crystallizer). This model starts from a number density distribution of crystals, which shows dependence on the process duration, the rate of crystal growth and the crystal size. The model differs from the diffusion model. The distribution data calculated are in agreement with distribution data measured and published by a number of other authors. The influence of the two parameters b and rLH on the mathematically determined frequency distributions is being studied.

Distributed Parameter Modeling of Sediment Movement and Particle Size Distributions

ABSTRACT A spatially descriptive erosion submodel for estimating the particle size distribution of eroded sediment from disturbed upland watersheds and construction sites has been developed and incorporated into the ANSWERS watershed model. Model validation is accomplished using data from field plot studies. The model's usefulness as an erosion control planning tool is demonstrated on a construction site in central Indiana. The model divides the watershed into a uniform grid of square planar elements. Within each element, the model describes the processes of interception, infiltration, surface storage, surface flow, subsurface drainage, and sediment detachment, transport and deposition. The continuity equation is then used to integrate the individual elemental responses into a system response that describes the watershed as a whole. The erosion process is limited to the overland flow regime.

Survey for Model of Particle-size Distribution and Calculation of Packing Volume of Multi-component Particle-size System in Refractories Batches

To survey the author's method for calculating the packed volume of multi-component particle-size systems, the various equations for particle-size grading model for refractory batches were discussed and new model were derived.Employing the author's calculating method, the volumes of bodies packed by moulding method with stick penetration of magnesia clinker mixes, and the volume of bodies packed by press moulding of magnesia clinker mixes, were calculated.From the results, it was shown that the particle-size compositions or particle-size distributions of closest packing were in good agreement with tendency for those of observations, but the calculated values of packed volume were not agreed with observations.It was found that, however, the agreement could be achieved by the modification with values as function of number of components and the amount of finest-size component or grading systems coefficient.And the suitable grading model for refractory batches were discussed.

Models of tropospheric aerosol size distribution derived from measurements at three locations

A statistical technique for deriving size distribution models of tropospheric air-borne particles is described. The technique provides an estimate of the probable average size distribution for any total particle concentration between 0.1 and 10.0 cm−3 for three different geographical locations. The size distribution data obtained by Blifford and Ringer (1969), and Blifford (1970) are used to derive models of particle size distribution for three locations: Scottsbluff, Nebraska; Death Valley, California; and the Pacific Ocean, 250 km west of Santa Barbara, California. As a special application, these models are fitted by an optimization procedure to the modified Γ distribution function used by Deirmendjian. Some optical scattering properties of these particle models are estimated by use of Mie's solution, and the results are discussed.