THE ELECTROSTATIC FORCE BETWEEN CHARGED SPHERES AT CONSTANT POTENTIAL FROM THE FREDHOLM INTEGRAL EQUATION

The electrostatic problem of two spheres held at constant, not necessarily equal, potential is solved from considerations of action-at-a-distance (Coulomb force) by the way of using a solution to the Fredholm integral equation of the second kind. The solution, written in series form, is obtained from Gauss generalization of the electrostatic force for distributed charges and yields the charge density distribution, important to liquid droplet stability, droplet deformation, and breakup. Evaluation of the electrostatic force is fast because the series expression for the charge distribution is rapidly converging, a characteristic trait for some Fredholm type equations.     

THE ELECTROSTATIC FORCE BETWEEN CHARGED SPHERES AT CONSTANT POTENTIAL FROM THE FREDHOLM INTEGRAL EQUATION

The electrostatic problem of two spheres held at constant, not necessarily equal, potential is solved from considerations of action-at-a-distance (Coulomb force) by the way of using a solution to the Fredholm integral equation of the second kind. The solution, written in series form, is obtained from Gauss generalization of the electrostatic force for distributed charges and yields the charge density distribution, important to liquid droplet stability, droplet deformation, and breakup. Evaluation of the electrostatic force is fast because the series expression for the charge distribution is rapidly converging, a characteristic trait for some Fredholm type equations.     

Numerical simulation of microscopic motion and deposition of nanoparticles via electrodynamic focusing

A computational model was developed to simulate microscopic motion and deposition of charged aerosols during the nanoparticle patterning process utilizing electrodynamic focusing concept (Kim et al., 2006). Our computational model includes Brownian random force, Coulomb and image forces, fluid drag and van der Waals force for determining Lagrangian particle trajectories after solving electrostatic fields in the deposition chamber. Our results are in agreement with the previous experimental findings. The effects of operation parameters such as surface charge density, applied voltage and particle charges were investigated. It was found that the electric field-induced motion of particles dominated over Brownian random motion of 10 nm nanoparticles near the surface and the inertial motion of charged nanoparticles under high electric field would be important to determine the precise deposition pattern within submicrometer scale structures.     

Effect of an external electric field on the charge distribution of electrostatic coagulation

This article analyzes the effect of an external electric field on the charge distribution of bipolar and unipolar charged particles numerically by solving the coagulation equation for charged particles, based on the analytical expression for the coagulation coefficient [Wang, L. Z., Zhang, X. R., & Zhu, K. Q. (2005). An analytical expression for the coagulation coefficient of bipolarly charged particles by an external electric field with the effect of Coulomb force. Journal of Aerosol Science, 36, 1050–1055]. For symmetric bipolar charged particles, the external electric field does not change the symmetry of the initial charge distribution as the coagulation time increases. In addition, the particle number concentration decays monotonically during coagulation regardless of the magnitude of the particle charge. For asymmetric bipolar charged and unipolar charged particles, however, the particle number concentration does not decay monotonically for each value of charge during coagulation, due to the effect of an external electric field.     

Development and Validation of a Simple Numerical Model for Estimating Workplace Aerosol Size Distribution Evolution Through Coagulation,Settling, and Diffusion

Recent research has indicated that the toxicity of inhaled ultrafine particles may be associated with the size of discrete particles deposited in the lungs. However, it has been speculated that in some occupational settings rapid coagulation will lead to relatively low exposures to discrete ultrafine particles. Investigation of likely occupational exposures to ultrafine particles following the generation of aerosols with complex size distributions is most appropriately addressed using validated numerical models. A numerical model has been developed to estimate the size-distribution time-evolution of compact and fractal-like aerosols within workplaces resulting from coagulation, diffusional deposition, and gravitational settling. Good agreement has been shown with an analytical solution to lognormal aerosol evolution, indicating good compatibility with previously published models. Validation using experimental data shows reasonable agreement when assuming spherical particles and coalescence on coagulation. Assuming the formation of fractal-like particles within a range of diameters led to good agreement between modeled and experimental data. The model appears well suited to estimating the relationship between the size distribution of emitted well-mixed ultrafine aerosols, and the aerosol that is ultimately inhaled where diffusion loses are small.     

Electrically Produced Standard Aerosols in a Wide Size Range

Non-uniformly charged particles cause a major problem in electrical methods for producing standard aerosols, imposing strict limitations on the usability of the obtained standard aerosols. This article gives a quick overview of this problem, examining the ways how differently charged particles affect the generation of standard aerosols, and presenting a new method for producing standard aerosols and avoiding the effects of multiply charged particles, with the key idea that the probability for small particles to have more than one charge is very low. A two-stage aerosol generator is used. Small silver particles (d< 40 nm) generated by homogeneous nucleation of silver vapors obtain in bipolar charger not more than one elementary charge. These condensation nuclei are enlarged by a condensational growth device. Big particles are now also not more than singly charged, and narrow size distribution can be obtained by electrical separation. Properties of standard aerosols produced experimentally by both the conventional and the new method, are compared and the validity of the new idea behind the new method is confirmed.     

Effects of submicrometer particulate silica addenda on the adhesion of micrometer-size particles to a polyester-composite substrate

The force needed to detach five sets of different size particles, having number-averaged diameters between 3.6 and 8.5 µm, from a composite substrate was measured using an ultracentrifuge. In addition to size variations, the asperity concentration for each size particle was adjusted by varying the silica concentration, adjusted so that the surface area concentration at each level was kept constant for the five sizes of particles. Due to the changing silica concentration and particle size, the charge per particle also varied. It was found that the detachment force appeared to be virtually independent of charge, with any correlation actually appearing slightly negative, if anything. However, the detachment force increased monotonically with increasing particle diameter and decreased monotonically with increasing silica concentration. Moreover, upon normalizing the detachment force to the particle diameter and the silica concentration to the surface area concentration of silica, it was found that the detachment force clustered into groups in which the force needed to separate the particle from the substrate depended only on the silica concentration. These results suggest that van der Waals interaction, rather than electrostatic forces, are the dominant mechanism controlling toner adhesion in this instance.     

Theoretical Study of Equilibrium Bipolar Charge Distribution on Nonuniform Primary Straight Chain Aggregate Aerosols

A general theory describing the equilibrium bipolar charge distribution for straight chain aggregate aerosols consisting of primary spheres of different diameters was derived from a theory previously developed for linear chain aggregate of uniform spheres. The present theory is based on the assumptions that (1) the individual primary particles of a straight chain aggregate are charged independently, (2) the probability that a particular primary particle has acquired q elementary charges is governed by the Gaussian distribution predicted by Boltzmann's law, based on particle size; and (3) the resultant charge of a straight chain aggregate is the algebraic sum of the charges carried by the constituent primary spheres. The present theory can be stated as follows: The equilibrium bipolar charge distribution of straight chain aggregate aerosols with nonuniform primary spheres can be expressed by Boltzmann's law with an equivalent diameter such that d_eL = Σ ⁿ _i=1 d_i . The limitations imposed by the assumptions are also discussed.     

Interpretation of Volatility Tandem Differential Mobility Analyzer (V-TDMA) data for accurate vapor pressure and enthalpy measurement: Operational considerations,multiple charging,and introduction to a new analysis program (TAO)

Abstract

Significant evaporation of pure aerosols in a Volatility Tandem Differential Mobility Analyzer (V-TDMA) creates two Condensation Particle Counter (CPC) response peaks. Two hypotheses for the observed peaks have been proposed: the existence of two phases or the separation of the singly charged experimental size distribution from the remaining experimental size distributions with charges greater than 1 (charge separation). To explore this observation, we atomized pure levoglucosan aerosol and evaporated the aerosol until two peaks formed. We used an additional classifier and neutralizer to select particles from each of the two peaks and assessed the number of charges on the particles. The smaller diameter peak contained singly charged particles, and the larger diameter peak contained the remaining charges. The charge separation hypothesis alone accounts for the two-peak observations. We used a new V-TDMA model named TAO and show that charge separation should occur in other pure components as well. The TAO model was then used to display the impact of different DMA transfer functions, different inlet size distributions, and different oven residence time distributions (RTDs) on the CPC response. Large errors are possible when direct measurement of the RTD is not performed or when wide RTDs are used. We recommend use of narrow transfer functions with narrow RTDs to detect charge separation. When the singly charged CPC response is isolated (smaller diameter peak in the two peak response), accurate estimations of vapor pressure can be recovered, assuming accurate values for gas phase diffusivity, surface energy, particle density, etc. are used.

Copyright © 2020 American Association for Aerosol Research     

Role of Interfacial Interactions in the Deposition of Colloidal Clay Particles in Porous Media

Colloidal clay particle transport under saturated conditions is believed to be controlled by its interactions with the surrounding environment. The dominating forces among these interactions are electrostatic forces that are determined by colloidal clay particle and porous medium surface charge density and Lifshitz–van der Waals forces that are determined by colloidal clay particle and porous medium surface thermodynamic properties. Electrostatic forces are greatly affected by solution chemistry in terms of solution ionic strength and pH. In this research, electrostatic and Lifshitz–van der Waals forces of natural colloidal clay particles with a model porous medium of silica sand were quantified at different ionic strength and pH conditions. At the same time, colloidal clay particle transport in the model medium of silica sand was conducted in a laboratory column. The maximum electrostatic forces, F ^EL (max), which occurred when the separation distance between colloidal clay particles and the porous medium was in the range of the sum of the double layer thicknesses of the colloidal clay particles and the porous medium, was found to be the determinant factor for colloidal clay particle deposition in the porous medium. Colloidal clay particle desorption in the porous media was related to the net effect of attractive Lifshitz–van der Waals forces and repulsive electrostatic forces, evaluated at the equilibrium distance where physical contact between the colloidal clay particle and silica sand actually occurred (i.e., affix force). Higher colloidal clay particle desorption was found to coincide with smaller affix force values.     

Modulation of silica layer properties by varying the granulometric state of tetraethyl orthosilicate precursor aerosols during combustion chemical vapor deposition (CCVD)

Abstract

For the purpose of silica surface layer modulation, a pneumatic-controlled two-substance atomizer with inertia-based coarse droplet separation was operated at different system pressures for tetraethyl orthosilicate precursor aerosol supply during combustion chemical vapor deposition. A comprehensive testing study was performed to characterize the atomizer’s performance characteristics, initial precursor aerosols at the atomizer’s outlet, transformed aerosols before combustion, combustion aerosols and formed layers. Laser diffraction spectrometry, differential electrical mobility analyses and condensation particle counting were used for aerosol characterization with regard to particle size and particle production quantities. Layers were characterized by scanning electron microscopy, atomic force microscopy, spectral ellipsometry, water contact angle measurements and light transmission concerning geometric properties (thickness, surface structure and roughness) and physical behaviors (i.e., optical behaviors, hydrophobicity). Results show a quasi-linear relationship of the ejection mass flow of the pneumatic-controlled atomizer and geometric layer properties which again show a direct relationship to the physical properties. No correlation was found between the aerosols before combustion and the combustion aerosols since the majority of combustion aerosol particles are synthesized solely from the gas phase based on evaporated precursor material.

Copyright © 2020 American Association for Aerosol Research     

Rear surface deposition of fine particles on spheres — eddy deposition or electrostatic effects?

The aim of this investigation is to show the demarcation of two possible mechanisms for surface deposition of fine particles on the rear surface of single spheres. By means of single particle trajectory computation, based on numerically determined flow fields (Re_max = 10³), it is shown that the mere existence of a wake is not in itself sufficient to produce eddy deposition. In addition, the particle's motion must undergo a lateral transfer promoted by fluid trubulence, in order to effect eddy deposition commencing at a Reynolds number of about 100. On the other hand, rear deposition, influenced by electrostatic forces, especially by the Coulomb force, is possible at any Reynolds number. Consequently, for Reynolds numbers of less than 100, only electrostatic effects can produce rear surface deposition. In the range of high Reynolds numbers, the coexistence of both mechanisms is possible. Very high Reynolds numbers (Re > 10³) and low Stokes numbers indicated the predominance of the electrostatic effect over eddy deposition, whereas at very high Reynolds numbers and medium to high Stokes numbers the electrostatic effect is only predominant in presence of high electrostatic charges.     

Electrostatic effects on inertial particle transport in bifurcated tubes

Most aerosols found naturally in the ambient environment or those dispersed from artificial devices such as dry powder inhalers, are electrically charged. It is known that a strong electrostatic charge on aerosols can result in transport behavior dramatically different from that of uncharged aerosols, even in the absence of an external electric field. In the present work, we study pneumatic transport of corona‐charged particles in bifurcated tubes. This is accomplished by tracking the motion of discrete particles numerically under the influence of drag, gravitational, and electrostatic forces. The model aerosol is fly ash powder, whose size and charge distributions have been determined experimentally. The electrical mobility of the charged particle cloud is modeled through coulombic interactions between discrete point charges. For the case of polydispersed particles electrically charged across a distribution, the deposition efficiency was found to be greater than what is indicated by the mean charge and size. In particular, use of negatively charged fly ash powder of mean size of 2 μm and mean charge of ?1.5 C/kg led to significant increase in deposition efficiency (～29%) compared with uncharged fly ash powder of the same size distribution (～8%). Analysis of particle residence times suggests significant interaction between electrical and drag forces. These findings could have implications for pneumatic powder conveying or pulmonary drug delivery applications. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Quantitative Assessment of the Effect of Surface Deposition and Coagulation on the Dynamics of Submicrometer Particles Indoors

Exposure to airborne particles indoors depends on particle concentration, which is affected by air filtration, ventilation, and particle dynamics. The aim of this work was quantitative assessment of the effects of coagulation, surface deposition, and ventilation on the submicrometer particle concentration indoors. The assessment was obtained from measured particle loss rate and deposition velocity parameters. The experiments were conducted in an experimental chamber for three different types of aerosols: environmental tobacco smoke, petrol smoke, and ambient air aerosols. Particle number concentration and size distribution were measured in the size range between 0.017 and 0.898 w m by SMPS. The average values for the overall deposition loss rates varied from 4.3 2 10 m 5 s m 1 (0.16 h m 1 ) to 1.1 2 10 m 4 s m 1 (0.39 h m 1 ). The overall deposition velocities associated with surface deposition and coagulation ranged from 9.6 2 10 m 4 cm s m 1 to 2.4 2 10 m 3 cm s m 1 , and for surface deposition only from 2.8 2 10 m 4 cm s m 1 to 6.3 2 10 m 4 cm s m 1 . For indoor conditions with an air exchange rate above 1.3 h m 1 , (natural ventilation, no filters) only a reduction in particle number of about 20% is attributed to the surface deposition and coagulation.     

Studying surface charge and suspension stability of hydroxyapatite powder in isopropyl alcohol to prepare stable suspension for electrophoretic deposition

Abstract

Suspension stability of hydroxyapatite powder in isopropyl alcohol was investigated by measuring zeta potential. In this study, isopropyl alcohol was used as a suspension media, and nitric acid, polyvinyl butyral and polyethylenimine were the dispersing agents. Fine grain particles with mean particle size and surface area of 2·54 μm and 5·8 m² g^?1 respectively, were prepared. Stable suspensions were made by mixing 40 g L^?1 milled powders in isopropyl alcohol. The zeta potential of the suspensions was measured by using zeta sizer equipment. The results showed that by adding nitric acid and polyvinyl butyral to the system, negative charge was introduced, while polyethylenimine donated positive charge to the surface of particles and induced electrostatic and steric stabilisation. It was concluded that the suspension which was stabilised with 4 g L^?1 polyethylenimine revealed the highest zeta potential and stability which is suitable for cathodic electrophoretic deposition.     

Simultaneous Elemental Composition and Size Distributions of Submicron Particles in Real Time Using Laser Atomization Ionization Mass Spectrometry

Composition and size of individual submicron particles have been measured using a laser atomization ionization mass spectrometry technique, the Particle Blaster. Individual particles are quantitatively converted to atomic cations, providing information on both their complete elemental composition and particle size. Measured average atomic ratios for 100 nm particles of sodium chloride is 1.12 +- 0.36 (Cl:Na), for 50 nm particles of silica is 1.93 +- 0.52 (O:Si), and for 64 nm polystyrene latex spheres (PSL) is 1.13 +- 0.19 (H:C), in excellent agreement with the empirical formulae. Calculated particle sizes agree well with electrostatic classifier or TEM measurements in the size range of 17-900 nm diameter for particles of sodium chloride, silicon, and PSL. Size distributions are also obtain able, giving narrower distributions than are measured with an electrostatic classifier, for particles of alumina, silica, sodium chloride, and PSL spheres. Comparison with TEM data shows comparable primary particle sizes, but numerous particle aggregates are detected by the Particle Blaster which are unreported by the TEM measurements.     

Thermophoretic interactions of aerosol particles with constant temperatures

This paper presents an analytical study of the thermophoretic motion of two free aerosol spheres with constant temperatures by using a method of reflections. The particles are allowed to differ in radius, in temperature, and in surface properties. The Knudsen numbers are assumed small so that a continuum model describes the fluid flow with a thermal creep and a hydrodynamic slip at the particle surfaces. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single sphere with constant temperature placed in an arbitrarily varying temperature field. The results for two-sphere interactions are correct to O(r₁₂⁻⁷), where r₁₂ is the distance between the particle centers. For the special situation of two identical spheres, the effect of particle interactions will drive the pair system approaching each other if the particle temperature is less than the temperature of the surrounding. While the temperature of the particles is higher than the surrounding temperature, the thermophoretic force obtains a repulsive effect between the particles. Based on a microscopic model the results for two-particle interactions are applied to find the effect of particle concentration on the average thermophoretic velocity in a bounded suspension. In general, the effect of interactions on thermophoretic coagulation of particles with constant temperatures can be stronger than that on sedimentation.     

Surface tension of Nanofluid-type fuels containing suspended nanomaterials

ABSTRACT: The surface tension of ethanol and n-decane based nanofluid fuels containing suspended aluminum (Al), aluminum oxide (Al2O3), and boron (B) nanoparticles as well as dispersible multi-wall carbon nanotubes (MWCNTs) were measured using the pendant drop method by solving the Young-Laplace equation. The effects of nanoparticle concentration, size and the presence of a dispersing agent (surfactant) on surface tension were determined. The results show that surface tension increases both with particle concentration (above a critical concentration) and particle size for all cases. This is because the Van der Waals force between particles at the liquid/gas interface increases surface free energy and thus increases surface tension. At low particle concentrations, however, addition of particles has little influence on surface tension because of the large distance between particles. An exception is when a surfactant was used or when (MWCNTs) was involved. For such cases, the surface tension decreases compared to the pure base fluid. The hypothesis is the polymer groups attached to (MWCNTs) and the surfactant layer between a particle and the surround fluid increases the electrostatic force between particles and thus reduce surface energy and surface tension.     

Growth and Deposition of Hygroscopic Particulate Matter in the Human Lungs

Transport and fate of inhaled particulate matter in the human lungs is calculated for realistic physicochemical conditions by a new dosimetry model. The model solves a variant of the general dynamic equation for the size evolution of respirable particles within the human tracheobronchial airways, starting at the tracheal entrance. We focus on ambient anthropogenic aerosols, which are of concern in inhalation toxicology because of their potential irritant and toxic effects on humans. The aerosols considered are polydisperse with respect to size and heterodisperse with respect to thermodynamic state and chemical composition, having initially bimodal lognormal size distribution that evolves with time as a result of condensation-evaporation and deposition processes. The architecture of the human lung is described by Weibel's symmetric bronchial tree. Simulations reveal that, due to the rapid growth of submicron-sized particles, increased number and mass fractions of the particle population can be found in the intermediate size range 0.1 < φ < 1