Particle Size Distribution Function Research Articles

Unsteady-state particle-size distributions at the coagulation stage of phase transformations

In this paper, a new analytical solution of nonstationary integro-differential coagulation equation, which describes the concluding stage of a phase transformation process in metastable liquids, is deduced. This solution takes into account the initial distribution function, which is found on the basis of previously developed theory for the intermediate stage. It is demonstrated that the derived particle-size distribution function representing a bell-shaped curve decreases with time and describes the long-term experimental data. The developed theoretical approach describes the transition of a phase transformation process from its intermediate stage to the stage of particle coagulation.

Size Distribution of Nascent Soot in Premixed n-Hexane, Cyclohexane, and Methylcyclohexane Flames

The evolution of particle size distribution function (PSDF) of nascent soot in premixed flames of n-hexane, cyclohexane, and methylcyclohexane was studied on the burner-stabilized stagnation flame platform. The cold gas velocities were changed to keep the maximum flame temperatures of different flames approximately constant. The PSDFs of all fuels tested transited from the unimodal (nucleation mode only) to the bimodal (both nucleation and accumulation modes) distribution with increased particle residence time. Soot nucleation and growth in the n-hexane flame were found to appear later than those in the cyclohexane and methylcyclohexane flames. In addition, the methylcyclohexane flame exhibited the highest nucleation and accumulation rate at the early stage of soot formation. However, the particle nucleation strength and the soot mass growth rate of the cyclohexane flame exceeded those of the methylcyclohexane flame at long particle residence times.

Effect of Dimethyl Ether Addition on Soot Formation Dynamics of Ethylene Opposed-Flow Diffusion Flames

Soot formation dynamics in C2H4/dimethyl ether (DME) opposed-flow diffusion flames was numerically studied in this paper, employing detailed gas-phase and dispersed-phase chemistries and transport models. A wide range of DME additions from pure C2H4 to pure DME was involved to systematically examine its impact on the soot formation process. It was found that the flow field had an important impact on the soot structure inside the flame. The soot volume fraction reached a maximum at the stagnation plane due to the infinite residence time, and then vanished abruptly on the fuel side of the stagnation plane. In the opposed-flow diffusion flames, enhancements of nucleation, H-abstraction–C2H2-addition (HACA) reaction, and polycyclic aromatic hydrocarbon (PAH) condensation rates in the near-stagnation region disappeared, such that the local particle size distribution function (PSDF) curve became unimodal, which was rather different from the burner-stabilized stagnation premixed flame. A synergistic effect of DM...

On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization.

A generalized theory of nucleation and growth of crystals in a metastable (supercooled or supersaturated) liquid is developed taking into account two principal effects: the diffusion mechanism of the particle-size distribution function in the space of particle radii and the unsteady-state growth rates of individual crystals induced by fluctuations in external temperature or concentration field. A system of the Fokker-Planck and balance integro-differential equations is formulated and analytically solved in a parametric form for arbitrary nucleation kinetics and arbitrary growth rates of individual crystals. The particle-size distribution function and system metastability are found in an explicit form. The Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetic mechanisms, as well as the unsteady-state growth rates of nuclei (Alexandrov & Alexandrova 2019 Phil. Trans. R. Soc. A 377, 20180209 ( doi:10.1098/rsta.2018.0209 )), are considered as special cases. Some potential biomedical applications of the present theory for crystal growth from supersaturated solutions are discussed. The theory is compared with experimental data on protein and insulin crystallization (growth dynamics of the proteins lysozyme and canavalin as well as of bovine and porcine insulin is considered). The hat-shaped particle-size distribution functions for lysozyme and canavalin crystals as well as for bovine and porcine insulin are found. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function.

In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Phase transformations in metastable liquids combined with polymerization.

This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space-time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

Influence of ethanol blended and dual fueled with gasoline on soot formation and particulate matter emissions in a small displacement spark ignition engine

The implementation of environmentally friendly internal combustion engines (ICEs) has become an urgent need in recent years due to the strict current legislation. The high pollutant emissions such as particulate matter (PM) exhausted from ICE has driven many researchers to explore the possible advantages of alternative fuels. Ethanol is one of the most suitable alternative fuel for spark-ignition (SI) engines due to its higher heat of evaporation, octane number and larger oxygen content that allow to obtain positive effects on engine performance and particle formation and emissions. The main goal of the experimental research is the study of the effect of the different methods of ethanol fueling on particulate matter by means of the correlation between the in-cylinder soot formation and the exhaust particle emissions. The experimental investigation was carried out in a 4-stroke small displacement optical spark ignition engine operated at 2000 and 4000 rpm under full load conditions. The engine was fueled with gasoline and ethanol pure, blended (E30) and dual fueled (EDF). For both E30 and EDF configurations, 30 vol% of ethanol in gasoline was supplied. An optical technique based on 2D-digital imaging was used. Two-color pyrometry theory was applied to assess the in-cylinder soot formation. Particle emissions were measured at the exhaust by means of a smoke meter. The particle size distribution function (PSDF) was measured in the range from 5.6 to 560 nm with an Engine Exhaust Particle Sizer (EEPS). The research has shown that the effect of ethanol on soot formation and particle emission depends not only on ethanol fuel properties, but also on engine configuration and engine operating conditions.

HDL modification: recent developments and their relevance to atherosclerotic cardiovascular disease.

In the last 2 years, significant advances in the understanding of HDL particle structure and the associations between particle structure, function, and atherosclerosis have been made. We will review and provide clinical and epidemiological context to these recent advances. Several recent studies have analyzed the associations between HDL particle size distribution, number, and particle function and specific environmental, behavioral, and pharmacologic exposures. Detailed phenotyping of HDL-associated protein complements, particularly apolipoproteins, strongly suggests structural subspecies of HDL exist with differential associations with HDL function and ASCVD risk. The recent data on biological and structural variation in HDL suggests the existence of relatively discrete particle species, which share a similar structure and function. We propose that the classical taxonomy that clusters HDL particles by cholesterol content is incomplete. Detailed phenotyping of HDL subspecies in clinical and epidemiological research may yield insights into new risk markers and biochemical pathways that could provide targets for atherosclerotic cardiovascular disease (ASCVD) therapy and prevention in the future.

Simultaneous reconstruction of the complex refractive index and the particle size distribution function from the lidar data: examination of the algorithms

Simultaneous reconstruction of the complex refractive index and the particle size distribution function from the lidar data: examination of the algorithms

Combustion of Spherical Agglomerates of Titanium in Air. III. Motion of Agglomerates and the Effect of Blowing Velocity on Nanosized Combustion Products and Burning Time

The combustion of monodisperse titanium particles with a characteristic size of 38 and 320 μm moving in air was studied. Pyrotechnic samples generating monodisperse particles were burned in a chamber with a nozzle to impart an initial velocity to the burning particles. The particles were accelerated by the jet of gaseous combustion products discharged from the nozzle. The maximum path-averaged particle velocity relative to the ambient air was 7.9 m/s. Combustion of moving particles was carried out in a quartz tube 2 m long. At the end of the combustion, combustion products (oxide aerosol) were sampled from the tube using a thermophoretic precipitator. Size distribution functions of nanometer-sized spherule particles were determined by processing electron micrographs of samples. The velocity and burning time of burning particles were determined by video recording at a speed of 300 fps. It was found that increasing the velocity of motion of agglomerate particles with a diameter of 320 μm relative to the gas from 0.9 to 7.9 m/s leads to a decrease in the size of the spherules from 28 to 19 nm and to a decrease in the burning time from 0.45 to 0.26 s.

Analysis of Recrystallization of Fine-Crystalline Corundum in a Supercritical Water Medium Using the Lognormal Particle Size Distribution Function

The mechanism of synthesis of fine-crystalline corundum from aluminum hydroxide under induced nucleation conditions in a supercritical water fluid at 400°C and initial pressure of 26.4 MPa followed by exposure in the synthesis medium was studied. The crystal size distribution was analyzed by electron microscopy. The use of the lognormal function to describe the crystal size distribution of the synthesized corundum particles was substantiated. The possibility of using the lognormal particle size distribution function and the time dependence of its parameters to reveal the routes of product formation was analyzed. The dimensional spectrum of microcrystals has four components, whose appearance is associated with different routes of product formation. The number of distribution components remains unchanged during prolonged exposure, but their average characteristics have different time dependences. The mass redistribution during recrystallization, generally leading to a decrease in the average crystal size, is explained by differences in the crystal structure mobility of different components. It was concluded that the states of corundum in the newly formed crystals and in the overgrown layer on the particles of the inducing additive are different.

The influence of Brownian coagulation on the particle-size distribution function in supercooled melts and supersaturated solutions

A theoretical description for particle coagulation due to Brownian motion combined with coalescence is presented and experimentally verified. The present theory confirms that the particle-size distribution function possesses a universal state, which is described by the self-similar kinetic equation. A complete analytical solution of this integro-differential equation is found in the case of Brownian coagulation mechanism. An explicit analytical particle-size distribution function, , which approximately satisfies the coagulation equation is derived too. It is shown that a universal particle-size distribution is broader, more flat and bell-shaped than the classical Lifshitz and Slyozov distribution function.

On the Effective Density of Soot Particles in Premixed Ethylene Flames

In this work, the effective density of soot particles was studied in burner-stabilized-stagnation premixed ethylene flames, at an equivalent ratio of 2.0 and over the maximum flame temperature of 1747 K < Tmax < 1837 K, using micro-orifice probe sampling in tandem with a centrifugal particle mass analyzer, a differential mobility analyzer (DMA) and a condensation particle counter. For a better understanding of the variation of effective density with mobility diameter, monodisperse soot particles between 10 and 50 nm were classified via the DMA and imaged by transmission electron microscopy (TEM). The particle size distribution functions and the C/H ratio of the particles were measured by a scanning mobility particle sizer and an elemental analyzer, separately. The results show that for all these flames, effective density first increases and then decreases with increasing mobility diameter, and the maximum occurs at the mobility diameter of ∼20 nm, which is consistent with the size for soot morphology changing from spherical-like to non-spherical shapes according to the TEM images. With the increase of flame temperature, the effective density decreases, which is caused by the slower particle growth rate at higher temperatures as shown by a series of evidences.

Robust metric for quantifying the importance of stochastic effects on nanoparticle growth

Comprehensive representation of nanoparticle dynamics is necessary for understanding nucleation and growth phenomena. This is critical in atmospheric physics, as airborne particles formed from vapors have significant but highly uncertain effects on climate. While the vapor–particle mass exchange driving particle growth can be described by a macroscopic, continuous substance for large enough particles, the growth dynamics of the smallest nanoparticles involve stochastic fluctuations in particle size due to discrete molecular collision and decay processes. To date, there have been no generalizable methods for quantifying the particle size regime where the discrete effects become negligible and condensation models can be applied. By discrete simulations of sub-10 nm particle populations, we demonstrate the importance of stochastic effects in the nanometer size range. We derive a novel, theory-based, simple and robust metric for identifying the exact sizes where these effects cannot be omitted for arbitrary molecular systems. The presented metric, based on examining the second- and first-order derivatives of the particle size distribution function, is directly applicable to experimental size distribution data. This tool enables quantifying the onset of condensational growth without prior information on the properties of the vapors and particles, thus allowing robust experimental resolving of nanoparticle formation physics.

Four-Channel Photoelectric Counter of Saltating Sand Particles

A four-channel photoelectric counter has been designed and manufactured for the measurements of saltating sand concentration fluctuations and size distribution function of particles with diameters >30 μm over desertified areas. The measurement results are given. It is shown that the vertical profile of the saltating sand concentration does not change on average in the altitude range from 3 to 7 cm over a desertified area in the neighborhood of the Volga. The distribution function of saltating sand particles over the desertified area is approximated with satisfactory accuracy by the lognormal distribution near the distribution maximum. Noticeable distinctions between the abovementioned distributions for large and small sand particles are observed.

Flame temperature effect on sp2 bonds on nascent carbon nanoparticles formed in premixed flames (T &gt; 2100 K): A Raman spectroscopy and particle mobility sizing study

Abstract The evolution in carbon particle size and carbon bonds was observed with increasing flame temperature for a fixed growth time (tp ∼ 13 ms) and equivalence ratio (Φ = 2.5) in set of sooting premixed stagnation flames. For carbon formed in each flame, detailed particle size distribution functions (PSDF) and Raman spectra (excitation energy of 2.33 eV) were measured as the maximum flame temperature increased from 1911 K

Results of the Study of Aerosol Characteristics in the Atmosphere of the Kara and Barents Seas in Summer and Autumn 2016

Measurement results of a complex of aerosol microphysical, chemical, and optical parameters in two cruises of the Akademik Mstislav Keldysh research vessel in 2016 are analyzed. The work was carried out in the Kara Sea from July 10 till August 20 and in the Barents Sea from August 25 till October 10. The mean values of the following aerosol characteristics are given: AOD of the atmosphere, fine and coarse components of AOD, number concentration of particles in the near-water air layer, mass concentrations of the absorbing matter (soot), water-soluble ions (Na+, Mg2+, Cl–, K+, Ca2+, $$\rm{NH}_4^+, \rm{NO}_3^-, \rm{SO}_4^{2-}$$ ), and gaseous admixtures (SO2, HCl, HNO3, and NH3). The characteristic particle size distribution functions are presented for different regions of the Kara and Barents Seas. It is shown that the levels of both aerosol turbidity of the atmospheric column (AOD) and the aerosol and soot concentrations in the near-water air layer were close to the long-term mean values in Arctic latitudes. The atmospheric turbidity during the period of measurements was noticeably affected by emissions of continental forest fire smokes. The contribution of smoke aerosol to, e.g., the mean shipborne-measured AOD at λ = 0.5 μm is about 44%.

On the theory of nucleation and nonstationary evolution of a polydisperse ensemble of crystals

The process of nucleation and unsteady-state growth of spherical crystals in a supersaturated solution is considered with allowance for the Weber-Volmer-Frenkel-Zel’dovich and Meirs kinetic mechanisms. The first two corrections to the steady-state growth rate of spherical crystals are found analytically as the solution of the moving boundary problem. On the basis of this solution, we formulate and solve the integro-differential model consisting of the Fokker-Planck type equation for the particle-size distribution function and of the balance equation for the system supersaturation. The distribution function dependent on the nucleation kinetics is found as a functional of the supersaturation. The integro-differential equation for the system supersaturation is solved by means of the saddle-point method. As a result, a complete analytical solution of the problem of nucleation and nonstationary evolution of a polydisperse ensemble of crystals in a metastable medium is constructed in a parametric form. How to use the obtained solutions for supercooled liquids is discussed.

Deformations of loess soils caused by changes in the microaggregate structure

Protracted degradation of the loess structure during technogenesis leads to changes in the microaggregate composition, density, and moisture. We have developed a model that predicts the value of the porosity coefficient of loess in a degraded state. The model is based on the previously obtained results of applying fractal theory to soils. The loess areas of Dnipro city (Ukraine) and its environs were studied. The granulometric composition of the samples was determined before and after filtration, compression. According to the results of the pipet analysis of one sample, the number of aggregates, the number of particles composing the aggregates, and the number of free particles (nonaggregates) were calculated for each of the fractions. The values of the fractal dimension of the particle size distribution function were also calculated. The predicted values of the porosity coefficient in the state of complete decomposition of microaggregates were calculated according to the new model. The difference of the porosity coefficients in the initial (natural) and predicted states characterizes the value of the volume deformation of the soil. The obtained results of calculations of volumetric deformation of loess do not contradict the known data on the deformation features of the deposits of the region formed in the epochs of interglacial and terrestrial glaciation.

The distillation curve and sooting propensity of a typical jet fuel

Real jet fuels are complex mixtures of many organic components, some of which are aromatic compounds. Towards the high-temperature end of the distillation curve, some of the fuel components are multi-ring compounds. A small amount of these high molecular weight species in the fuel could impact soot nucleation in practical engines especially when the fuel is injected as a spray. This work aims to highlight the variation of the sooting propensity of jet fuels as a function of distillate fractions and to examine the validity of a surrogate fuel in emulating soot production from real fuels. Particle size distribution functions and soot volume fractions are studied in a series of laminar premixed stretch-stabilized ethylene flames doped with Jet A, its various distillate fractions, and the 2nd generation MURI surrogate. Soot formation as a result of doping real jet fuel and its distillate fractions is also investigated in counterflow and coflow diffusion flames. The results show that the higher-boiling distillates mostly influence soot nucleation and produce substantially more soot in nucleation controlled flames than the light molecular fraction and jet fuel as received, while such an effect is seen to be small in flames where soot production is controlled by surface growth. The potential impact of distillate fractions on soot nucleation propensities is discussed.