Drag Force and Slip Correction of Aggregate Aerosols

The mobility of a nonspherical particle is a function of both particle shape and orientation. Thus, unlike spherical particles, the mobility, through its orientation, depends on the magnitude of the electric field. In this work, we develop a general theory, based on an extension of the work of Happel and Brenner (1965), for the orientation-averaged mobility applicable to any axially symmetric particle for which the friction tensor and the polarization energy are known. By using a Boltzmann probability distribution for the orientation, we employ a tensor formulation for computing the orientation-averaged mobility rather than a scalar analysis previously employed by Kim et al. (2007) for nanowires. The resulting equation for the average electrical mobility is much simpler than the expression based on the scalar approach, and can be applied to any axially symmetric structures such as rods, ellipsoids, and touching spheres. The theory is applied to the specific case of nanowires and the experimental results on the mobility of carbon nanotubes (CNT). A set of working formulas of additional mobility expressions for nanorods and prolate spheroids in the free molecular, continuum, and transition regimes are also presented. Finally, we examine the expression of dynamic shape factor common in the literature, and propose a clearer definition based on the tensor approach. Mathematica codes for the electrical mobility evaluations for five cases are provided in the Supplemental Information.

Section: Defining the Dynamic Shape Factormentioning

confidence: 92%

Section: Defining the Dynamic Shape Factormentioning

confidence: 99%

The Effect of Orientation on the Mobility and Dynamic Shape Factor of Charged Axially Symmetric Particles in an Electric Field

Mulholland

Zachariah

2012

“…Early measurements of apparent particle density were accomplished by using Millikan cells and are reviewed by Fuchs (1964). More recently, Allen and Raabe (1985) and Cheng et al (1988) have used Millikan cells to measure the slip correction factor and dynamic shape factor of aggregated latex spheres. Though highly accurate, Millikan cell measurements yield information on only singleparticle characteristics.…”

Section: Previous Density and Shape Factor Measurement Techniquesmentioning

confidence: 99%

Measurement of Particle Density by Inertial Classification of Differential Mobility Analyzer–Generated Monodisperse Aerosols

Kelly

McMurry

1992

174

140

A density measurement technique based on the selection of a monodisperse aerosol with a differential mobility analyzer followed by classification according to aerodynamic diameter with an impactor has been designed and tested. Experimental results were obtained for several laboratory aerosols (dioctyl phthalate, (NH,),SO,, NaCI, and H,S04 a t a range of hnmidities) by using four different microorifice uniform deposit impactor stages with aerodynamic diameter cutoffs of 0.12-0.56 pm. The average error in measured particle densities is 4% and a maximum error of 8% is observed for all of the materials tested except NaCI, for which the measured effective density is 14% smaller than the true density. The discrepancy for NaCl is attributed to nonspherical particle shape. The system will be applied in the future to measure the densities of submicrometer atmospheric particles.

“…Values of dynamic shape factors ( x,), and adjusted sphere diameters (d,) used to predict x,,/C values for these aggregates (long axes in parallel and oriented vertically with respect to the flow [Horvath, 1974;Cheng et al, 1988;Cheng, 19911) are listed in Table 1. Figure 5 shows that for the smallest particles (largest Knudsen numbers sampled under near Stokesian conditions), the experimental data agreed quite well with predictions for doublets, triangular triplets, and tetrahedral quadruplets, assuming that these particles moved in each case with their long axis perpendicular to the direction of the flow.…”

Section: Aggregate Microspheresmentioning

confidence: 99%

Behavior of Compact Nonspherical Particles in the TSI Aerodynamic Particle Sizer Model APS33B: Ultra-Stokesian Drag Forces

Cheng

Chen

Yeh

et al. 1993

The aerodynamic behavior of aggregates consisting of uniform polystyrene latex (PSL) spheres and unaggregated cuboidal Natrojarosite particles in a TSI aerodynamic particle sizer (Model APS33B) has been studied. In initial tests, monodisperse PSL microspheres ranging from 0.3 to 7 y m in geometric diameter were generated from aqueous suspensions using a Lovelace nebulizer. APS33B responses for these uniform-sized particles showed multiple peaks. The major (primary) peak, which resulted from the smallest particle, corresponded to the unaggregated single spheres (singlets); the second, third, and fourth peaks were identified as doublets, triangular triplets, and tetrahedral quadruplets, respectively. Both doublets and triplets moved with their long axes in perpendicular (maximum drag) orientation to the flow direction in the APS33B. In contrast, the tetrahedral particles were isometric and had the same dynamic shape factor (drag resistance) for all three primary orientations. The particle Reynolds numbers (Re,) for these particles were calculated and ranged from 0.2 to 30 in the sensing volume of the APS33B detector (i.e., ultraStokesian conditions). Ultra-Stokesian drag forces for all three types of aggregates were, therefore, estimated and expressed as a function of an empirical factor (1 + a~e , b ) to the Stokesian drag force. The ultraStokesian drag of a Natrojarosite particle was measured in the range 20 < Re, < 50 and could be described with a similar expression. This approach facilitates the study of the dynamic behavior of nonspherical particles and yields new information about the characteristics of drag forces in the ultra-Stokesian regime.