Fractal scaling of coated soot aggregates

Recent field observations have shown soot aggregates (SAs) to contain significant amounts of surface coatings of organic compounds which obfuscate their native fractal morphology and make them visually appear as “near-spherical.” Morphologies of these aggregates are currently parameterized using fractal dimension (D_f) values greater than the universal 1.8. This is done to account for the supposedly morphological restructuring of an aggregate to a more compact form upon condensation of organic materials. Using multiple-angle light scattering analysis, it has been experimentally shown that restructuring of SA morphology only takes place during the evaporation process, not condensation. Based on this seminal finding, here we formulate the correct parameterizations to describe the morphology of surface coated aggregates. We perform detailed three-dimensional morphological characterization of computer simulated coated aggregates that mimic atmospheric SAs and show that their D_f remains invariant at 1.8 with increasing coating mass by as much as 18 fold. We find coating to affect only the fractal prefactor k₀, an understudied parameter which controls the aggregate shape anisotropy and local packing fraction of monomers. Specifically, k₀ was observed to scale with the ratio of aggregate's total (coating + bare) mass M_total to bare mass M_bare as k₀ = 1.34*(M_total/M_bare)^0.56.

Copyright © 2017 American Association for Aerosol Research     

The effect of electric-field-induced alignment on the electrical mobility of fractal aggregates

We study the effects of electric field strength on the mobility of soot-like fractal aggregates (fractal dimension of 1.78). The probability distribution for the particle orientation is governed by the ratio of the interaction energy between the electric field and the induced dipole in the particle to the energy associated with Brownian forces in the surrounding medium. We use our extended Kirkwood–Riseman method to calculate the friction tensor for aggregates of up to 2000 spheres, with primary sphere sizes in the transition and near-free molecule regimes. Our results for electrical mobility versus field strength are in good agreement with published experimental data for soot, which show an increase in mobility on the order of 8% from random to aligned orientations. Our calculations show that particles become aligned at decreasing field strength as particle size increases because particle polarizability increases with volume. Large aggregates are at least partially aligned at field strengths below 1000 V/cm, though a small change in mobility means that alignment is not an issue in many practical applications. However, improved differential mobility analyzers would be required to take advantage of small changes in mobility to provide shape characterization.

Copyright © 2018 American Association for Aerosol Research     

Enhanced growth rates of nanodroplets in the free molecular regime: The role of long-range interactions

Recently, Pathak et al. (2013) Pathak, H., Mullick, K., Tanimura, S., and Wyslouzil, B. E. (2013). Nonisothermal Droplet Growth in the Free Molecular Regime. Aerosol Sci. Technol., 47:1310–1324.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] conducted a series of non-isothermal D₂O nanodroplet growth studies in the free molecular regime. They found that under highly non-equilibrium conditions, the condensation (q_c) and evaporation coefficients (q_e) can differ from each other and from the expected value of 1. Here, we confirm these observations by analyzing comparable experiments using n-propanol. We show that the best agreement with the non-isothermal Hertz–Knudsen growth law corresponds to setting (q_c, q_e) = (1, 0.6) or (q_c, q_e) = (1.3, 1). The approach of retarded evaporation yields values close to those observed by Pathak et al. for D₂O, but is difficult to justify theoretically. Enhancing the condensation coefficient is consistent with long-range attractive interactions between the vapor molecules and droplets in the nanometer size range.

© 2016 American Association for Aerosol Research     

Dynamic characteristics for the normal impact process of micro-particles with a flat surface

A dynamic model has been developed to simulate the normal impact of an elastic-plastic adhesive sphere with a flat surface. The model combines the extended JKR theory considering both adhesion and plastic deformation with Newton's motion equation to describe the rebound behavior of the impacting particles. Theoretical expressions for velocity, contact time and restitution coefficient are obtained. The models were validated by comparison with the experimental results. Especially, a new empirical critical capture velocity expression was proposed which can be used to determine whether the particle will stick or bounce off the surface after the impact.

Copyright © 2018 American Association for Aerosol Research     

Examining the ability of empirical correlations to predict subject specific in vivo extrathoracic aerosol deposition during tidal breathing

The accuracy of five extrathoracic deposition equations was examined by comparing model predictions with in vivo deposition measurements of ^99mTc-DTPA radiolabeled 0.9% saline delivered via PARI LC Sprint nebulizers in 19 healthy human subjects. The average extrathoracic deposition fraction measured in vivo was 0.19 ± 0.10 (average ± standard deviation). Comparing to this average value, the extrathoracic deposition fraction predicted by Golshahi et al. equation was the most accurate (0.18 ± 0.08), followed by the model described by the ICRP (0.16 ± 0.03). However, prediction of subject-specific deposition proved more challenging; the Golshahi et al. model performed the best of the examined equations, yet showed only a small positive correlation between measured and predicted deposition in individual subjects with a Pearson correlation coefficient of 0.34. The difficulties in predicting subject-specific deposition likely result from geometric dissimilarity both within and between subjects, and may require more complicated modeling methods than algebraic equations of the kind examined in this study.

Copyright © 2017 American Association for Aerosol Research     

Deposition of droplets from the trachea or bronchus in the respiratory tract during exhalation: A steady-state numerical investigation

Abstract

Respiratory droplets are bioaerosols that originate from the respiratory tract. Knowing their deposition characteristics during exhalation would facilitate the understanding of the source of large respiratory droplets and their importance in the spread of respiratory infectious diseases. In this study, computational fluid dynamics is used to simulate the motion and deposition of droplets released from either trachea or bronchi in a realistic reconstruction of the human respiratory tract. Influences of airflow structures and locations of droplet generation on droplet deposition are studied, and droplets with diameters between 1 and 50?µm are examined. The deposition of droplets is found to be influenced mainly by the droplet diameter and the flow rate of exhalation. The number of droplets released from the trachea or bronchi that can escape into the environment decreases as the flow rate increases. When the flow rate is low (10?L/min), the critical diameter of droplets generated in the lower respiratory system that can escape into the air is approximately 12?µm, but this diameter is approximately 5?µm when the flow rate is medium (30 to 60?L/min) or large (90?L/min). The larynx is the dominant site of deposition for droplets smaller than the critical diameter, while trachea and bronchus are more important locations that account for the deposition of larger droplets. This study indicates that the lower respiratory tract is an important source of fine droplets (<5?µm) in indoor environments, and larger droplets probably originate from the upper respiratory tract, which needs further investigation.

Copyright © 2020 American Association for Aerosol Research     

Effect of friction coefficient and density on mixing particles in the rolling regime

In this work, optical imaging is used to quantify the mixing dynamics of granular materials. Two different methods (GLCM and Multivariate RGB analysis) are combined to extract surface information and the time to achieve a specific degree of mixing. In particular, the effect of density, friction coefficient, surface quality and particle geometry was studied. The results show that the Froude number alone is not enough to completely characterize the rolling regime. In addition, the filling ratio must be in a specific range which depends on the material properties.     

Novel method for determining the dynamic friction coefficient of explosives

A new method for determining the dynamic friction coefficient of explosives is presented. The method combines the physical model of friction sensitivity with theoretical analysis and numerical calculations. Experimental measurements of the dynamic friction coefficient of steel indicate that the proposed method is effective, provides secure and reliable data, and can be used to calculate the dynamic friction coefficient between cyclonite (RDX) and steel.     

Analytical estimate of the heating regime for a recuperative glass-melting furnace

The results of an analytical evaluation of the heat transfer processes in the working space of the furnace are presented. Four atomizers located under the nozzle of the burner are used for heating. The calculations are performed using a three-dimensional heat transfer zonal model for three variants of the thermal load distribution between the atomizers, as well as for heating of the furnace with natural gas (non-luminous flames).     

Mobility radius of fractal aggregates growing in the slip regime

A method is presented for the calculation of the mobility radius of fractal aggregates. The connection between the aggregate permeability and the monomer friction factor is derived, which makes it possible to convert the permeability in the continuum regime to that in the slip regime. The method elaborated here estimates the permeability of an aggregate treated either as impermeable sphere of the size equal to mobility radius or a permeable self-similar structure consisting of impermeable monomers. The internal permeability of a fractal aggregate growing in the slip regime is analyzed assuming that the aggregate consists of no more than twelve effective impermeable monomers, the number being a result of hydrodynamic considerations. The method makes it possible to estimate the aggregation number dependence of the mobility radius. A system of carbonaceous flame soot aerosol containing fractal aggregates with D=1.8 is analyzed. The mobility radius-aggregation number relation is found to be very close to that obtained experimentally. For large aggregation numbers this relation tends to that, which is valid for the dynamic radius.     

Observations on the coefficient of friction of polypropylene film

Data are presented relating the time change of the coefficient of friction of cast polypropylene films to changes in film density and concentration of surface lubricant. It is shown that during aging the density of polypropylene increases, thus causing a decrease in the friction coefficient. It is also shown that although the lubricant added to the polymer will diffuse to the surface of copolymer films, no diffusion occurred in polypropylene films.     

Taylor-expansion moment method for agglomerate coagulation due to Brownian motion in the entire size regime

Through applying the Taylor-expansion technique to the particle general dynamic equation, the newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation due to Brownian motion in the entire size regime. The TEMOM model disposed by Dahneke's solution (TEMOM–Dahneke) is proved to be more accurate than by harmonic mean solution (TEMOM–harmonic) through comparing their results with the reference sectional model (SM) for different fractal dimensions. In the transition regime, the TEMOM–Dahneke gives the more accurate results than the quadrature method of moments with three nodes (QMOM3). The mass fractal dimension is found to play an important role in determining the decay of agglomerate number and the spectrum of agglomerate size distribution, but the effect decreases with decreasing agglomerate Knudsen number. The self-preserving size distribution (SPSD) theory and linear decay law for agglomerate number are only applicable to be in the free molecular regime and continuum plus near-continuum regime, but not perfectly in the transition regime.     

Variation of the aerosol charge neutralization coefficient in the entire particle size range

The rate at which the mean charge on aerosol particles relaxes to its steady-state value under bipolar charging is characterized by the neutralization rate constant, β (s⁻¹). It is an important parameter for fixing the nt product in charge neutralizers as well as in the theory of charging-induced diffusion. Here we compute the neutralization coefficient, β/n (where n is the mean ion density), as a function of particle size through the use of ion-particle combination coefficients provided by the recent theories. The results indicate that β/n decreases from a continuum limit value of 3.1 × 10⁻⁶ cm³ s⁻¹, to a free molecular limit value of 1.4 × 10⁻⁶ cm³ s⁻¹. The changeover occurs rapidly in the transitional regime (10–100 nm). This clearly indicates that the nt product required to attain steady state is higher for nano particles than for larger ones. The paper also presents the variations of the mean square variance of charge, the coefficients of charging-induced drift and diffusion, as a function of particle size.     

Friction coefficient and mass of silver agglomerates in the transition regime

The dynamic shape factor and the exponents, $\eta$ and $D_{\mathit{fm}}$, which characterize the power law dependence of friction coefficient on the number of primary spheres and the mass on the mobility diameter, have been determined for silver agglomerates using the differential mobility-aerosol particle mass (DMA-APM) analyzer method. This method provides characterization of nearly monodisperse agglomerates and is able to analyze thousands of particles over a 10 min period. A quantitative uncertainty analysis finds that the calibration of the APM is the major source of uncertainty and that the combined uncertainties are about 6–7% for the dynamic shape factor and about 3% for the exponents $\eta$ and $D_{\mathit{fm}}$. The dynamic shape factor obtained based on free molecular analysis is larger than the measured results. The observed decrease in $\eta$ by about 15% with increasing agglomerate size compared to almost constant values for the model predictions suggests a flow interaction between the primary particles not included in the models which are based on free molecular dynamics. An empirical equation is given for the N dependence of the ratio of the measured friction coefficient to a free molecular expression based on a computer simulation. Model predictions indicate that $\eta$ is independent of agglomerate size while $D_{\mathit{fm}}$ is sensitive to agglomerate size. Experimentally, it appears the opposite is true: the dependence of $\eta$ on particle size is greater than for $D_{\mathit{fm}}$. The near constancy for the measured $D_{\mathit{fm}}$ results from the decreasing value in $\eta$ being compensated by the slip correction term in the expression relating $d_m$ to the friction coefficient.     

Measurement of the coefficient of dynamic friction at extrusion processing conditions

The dynamic friction coefficients of several polymers have been investigated using a specific rotating device similar to an extruder. The increase in temperature during the measurements made it necessary to develop a theoretical approach in order to interpret the experimental data correctly. The rotation speed and particle shapes were found to have little influence on the friction coefficient. For HDPE and PVC, the friction coefficient decreased slightly with interfacial temperature, whereas it remained constant for PP. The order of magnitude of the friction coefficients was similar to what has already been published in the literature.     

Viscosity of polypropylene oxide solutions over the entire concentration range

An empirical equation is presented which describes polymer solution viscosity, η, over the entire concentration range from a knowledge of intrinsic viscosity, [η], Huggins constant, k′, and bulk flow viscosity of polymer, η₀. The equation is: \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\eta _{sp}}}{{C[\eta]}} = \exp \left\{{\frac{{{\rm k'[}\eta {\rm]C}}}{{1 - bC}}} \right\} $\end{document} where solution viscosity, η, is contained in η_sp. No arbitrary parameters are invoked since b can be evaluated at bulk polymer (C = polymer density) where everything else is known. The equation accurately portrays the viscosity of polypropylene oxide (PPG 2025) from infinite dilution to bulk polymer in a very good solvent (benzene) and in a somewhat poorer (～ θ) solvent (methylcyclohexane). The hydrodynamic consequences of the thermodynamic interactions between polymer and solvent are reflected in the constants. This equation should be applicable to other polymer/solvent systems, and thus be immediately useful to those working with concentrated polymer solutions.     

Role of the friction coefficient in the frictional heating ignition of explosives

An expression is developed for the friction coefficient of a material in terms of the parameters that control the friction shear. This expression in conjunction with the frictional heating equation describes the hot spot temperature produced in a friction event. Hot spot temperature increases with an increase in the particle size and shear strength of the explosive material, with an increase in the (shock) loading pressure and friction velocity, and with a decrease in material thermal conductivity. The equations are discussed in terms of their implications regarding the factors that control the sensitivity of an explosive or propellant to frictional heating under various conditions, and the results of experimental studies given in the literature.