Cunningham Correction Factor Research Articles

Uncertainty assessment for the airborne nanoparticle collection efficiency of a TEM grid-equipped sampling system by Monte-Carlo calculation

A mini particle sampler (MPS) equipped with a transmission electron microscopy (TEM) grid enables convenient particle sampling to subsequent analysis. However, its sampling efficiency involves uncertainties, and accurate sampling efficiency is required for particle collection applications. In this study, the sampling efficiency uncertainties from measured data and models are quantified using Monte-Carlo methods. The Sobol variance-based sensitivity analysis is used to determine the contributions of parameters to the sampling efficiency uncertainties. The results reveal that the sampling efficiency uncertainties from experimental dispersion calibration and theoretical models are generally less than 1% and 9%, respectively. Most sampling efficiency measured data are covered by the efficiency uncertainty range simulated by theoretical models. Pore size and flowrate contribute significantly to the sampling efficiency uncertainties and require control to improve the sampling efficiency precision. Besides, the Cunningham correction factor is also a sensitivity parameter. The utilization of proper models is crucial to support simulations for further process optimization. This study offers a quantitative method for nanoparticle collection efficiency analysis, which will help assess nanomaterials’ workplace exposure.

A bimodal temom model for particle Brownian coagulation in the continuum-slip regime

In this paper, a bimodal Taylor-series expansion moment of method is proposed to deal with Brownian coagulation in the continuum-slip regime, where the non-linear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that both the number concentration and volume fraction decrease with time in the smaller mode due to the intra and inter coagulation, and the asymptotic behavior of the larger mode is as same as that in the continuum regime.

The influence of electric charge on minimum particle scavenging efficiency particle size during below-cloud scavenging processes

Below-cloud wet deposition scavenging processes are important for removing coarse and very fine particles from the atmosphere. This study investigated the influence of electric charge on particle deposition and estimated the scavenging gap particle size (the most penetrating particle size) along with the corresponding minimum collection efficiency and minimum scavenging coefficient particle size by using equations for below-cloud scavenging processes. A harmonic mean type approximation was used for calculations and the Cunningham correction factor was applied to include the slip effect of nuclei mode particles. Results based on the analytically approximated solution compared well with the numerically calculated results and previous studies that did not consider electric charging effects. The results showed that charge effects play an important role in determining the most penetrating particle size. This study also showed that use of the Cunningham correction factor may increase the most penetrating particle size under certain conditions. Subsequently, these results indicate that consideration of the electric charge effect with a Cunningham correction factor is important for estimating the most penetrating particle size.

Breathing Resistance and Ultrafine Particle Deposition in Nasal–Laryngeal Airways of a Newborn, an Infant, a Child, and an Adult

As a human grows from birth to adulthood, both airway anatomy and breathing conditions vary, altering the deposition rate and pattern of inhaled aerosols. However, deposition studies have typically focused on adult subjects, results of which may not be readily extrapolated to children. This study numerically evaluated the age-related effects on the airflow and aerosol dynamics in image-based nose-throat models of a 10-day-old newborn, a 7-month-old infant, a 5-year-old child, and a 53-year-old adult. Differences in airway physiology, breathing resistance, and aerosol filtering efficiency among the four models were quantified and compared. A high-fidelity fluid-particle transport model was employed to simulate the multi-regime airflows and particle transport within the nasal-laryngeal airways. Ultrafine particles were evaluated under breathing conditions ranging from sedentary to heavy activities. Results of this study indicate that the nasal-laryngeal airways at different ages, albeit differ significantly in morphology and dimension, do not significantly affect the total deposition fractions or maximum local deposition enhancement for ultrafine aerosols. Further, the deposition partitioning in the sub-regions of interest is different among the four models. Results of this study corroborate the use of the in vivo-based diffusion parameter (D(0.5)Q(-0.28)) over the replica-based parameter in correlating nasal-laryngeal depositions of ultrafine aerosols. Improved correlations have been developed for the four age groups by implementing this in vivo-based diffusion parameter as well as the Cunningham correction factor.

Improved theoretical modeling of a cyclone separator as a diesel soot particulate emission arrester

Particulate matter is considered to be the most harmful pollutant emitted into air from diesel engine exhaust, and its reduction is one of the most challenging problems in modern society. Several after-treatment retrofit programs have been proposed to control such emission, but to date, they suffer from high engineering complexity, high cost, thermal cracking, and increased back pressure, which in turn deteriorates diesel engine combustion performance. This paper proposes a solution for controlling diesel soot particulate emissions by an improved theoretical model for calculating the overall collection efficiency of a cyclone. The model considers the combined effect of collection efficiencies of both outer and inner vortices by introducing a particle distribution function to account for the non-uniform distribution of soot particles across the turbulent vortex section and by including the Cunningham correction factor for molecular slip of the particles. The cut size diameter model has also been modified and proposed by introducing the Cunningham correction factor for molecular slip of the separated soot particles under investigation. The results show good agreements with the existing theoretical and experimental studies of cyclones and diesel particulate filter flow characteristics of other applications.

Experimental study of filter clogging with monodisperse PSL particles

A fibrous filter is a common cleaning device often used to remove particle from industrial gas streams. The main question that often arises concerns the evolution of the pressure drop and the filtration efficiency during the filter clogging. The increase of pressure drop and filter efficiency was measured and was linked to both the clogging degree inside the filter bed and the deposit structure observed thanks to scanning electron micrograph. We have also studied the influence of various parameters such as air velocity, particle size, aerosol concentration and filter main characteristics. An empirical equation for predicting the pressure drop across the filter as a function of inverse particle diameter and Cunningham correction factor was suggested without considering the particle density in the cellulose paper filter. The values of porosity, obtained from the pressure drop responses of loading in the paper filter using Rudnick and First equation, were compared with other researchers.

A model for supersonic and hypersonic impactors for nanoparticles

In this study the performance of supersonic and hypersonic impactors for collection efficiency of nanoparticles (in the size range of 2–100 nm) under various operating conditions is analyzed. Axisymmetric forms of the compressible Navier–Stokes and energy equations are solved and the airflow and thermal condition in the impactor are evaluated. A Lagrangian particle trajectory analysis procedure is used and the deposition rates of different size particles under various operating conditions are studied. For dilute particle concentrations, the assumption of one-way interaction is used and the effect of particles on gas flow field is ignored. The importance of drag, lift and Brownian forces on particle motions in supersonic impactors is discussed. Sensitivity of the simulation results to the use of different assumptions for the Cunningham correction coefficient is studied. It is shown that accurate evaluation of the gas mean free path and the Cunningham correction factor is important for accurate simulation of nano-particle transport and deposition in supersonic/hypersonic impactors. The computer simulation results are compared favorably with the available experimental data.

Analytic Solution for Collection Efficiency of Electrostatic Precipitators for Polydisperse Aerosols

In this study, the analytic solution for collection efficiency of an electrostatic precipitator has been obtained. Aerosol particles were assumed to be polydisperse, and approximated to have a log-normal size distribution. The moment method was applied, and a particle charge equation and Cunningham correction factor (Cc) were modified to obtain the analytic solution. The analytic solution was compared with the existing numerical results, and showed good agreement. As a result of this study, it i s known that the analytic solution for the efficiency of an ESP for the polydisperse particles can be obtained without much loss of accuracy, and it can be applied in the place of those determined numerically.

Scaling dynamics of aerosol coagulation.

A combination of static and quasielastic light scattering and the theory of scaling solutions to Smoluchowski's equation was used to determine the absolute coagulation rate K0\ensuremath{'} and kernel homogeneity \ensuremath{\lambda} of a coagulating liquid-drop aerosol. Droplet sizes ranged from 0.23 to 0.42 \ensuremath{\mu}m, implying Knudsen numbers in the range 0.26 and 0.14. The temporal evolution of the number concentration M0 and the modal radius rM of an assumed zeroth-order log-normal distribution showed near-power-law behavior similar to that predicted by the scaling theory. From the temporal scaling behavior of M0(t) and rM(t), the absolute coagulation rate was calculated. The coagulation rates from each method were in good agreement. The rate also agreed well with theory that corrected the Brownian rate, good for the continuum regime, by the average Cunningham correction factor. In addition, the time dependence of the moments M0 and rM, hence the determination of K0\ensuremath{'}, was in good agreement with a real-time numerical solution of Smoluchowski's equation for initial conditions analogous to our experimental ones.

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Cunningham correction factor and accommodation coefficient: Interpretation of Millikan's data

A new fit to Millikan's data for the slip correction of spheres is explored, leading to Cunningham constants α, β and γ which differ slightly from those in the literature. Reinterpretation of the old data with some recently developed theoretical expressions yields a value of 0.809 for the momentum accommodation coefficient.

Mechanics of removing glass particulates from a solid surface

A series of experiments underscores the importance of the capillary force in the adhesion of a particulate to a surface. The capillary force resulting from a liquid film between a particulate and a surface remains even after the particulate-surface combination is baked above the boiling point of the liquid for 24 h. A mechanical scrubbing force is required to remove the particulate held to a surface by a capillary force. The force on a particulate applied by an air jet is calculated using Stokes's law modified by Cunningham's correction factor. Furthermore, the force required to roll a particulate off a surface is calculated from the theoretical adhesion force between a particulate and a surface and particulate deformation characteristics. The applied force is in good agreement with the theoretical force required to roll off a particulate.

On the Aerosol Particle Slip Correction Factor

The slip correction factor for equations of particle motion is an item to which apparently little thought is given these days. The fact that the constants are for the most part empirical and that the values used are specifically for an air/oil droplet system are not usually considered even when very different atmospheres and aerosols are under investigation. Fuchs and Stechkina have developed a completely theoretical expression which requires as a measurement only the percentage of gas molecules reflected diffusely from the particle. This development is presented in simplified form and its use encouraged as a direct replacement for the Cunningham correction factor.