Quasi‐Self‐Preserving Log‐Normal Size Distributions in the Transition Regime

Abstract

A log-normal model, based on the extended SIMPLER-tion moments. Applying the log-normal model a simple algorithm utilizing the Modal Aerosol Dynamics Modelling coagulation model consisting of a closed set of five equations Technique, and a sectional model are compared for Brownian is developed that does not require the solution of ordinary difcoagulation in the transition regime. The models are in good ferential equations. agreement with respect to the calculated particle size distribu-

A new analytical solution for solving the population balance equation in the continuum-slip regime

“…This is because in the continuum-slip regime only the PSPSD distribution rather than SPSD distribution exists. This is absolutely different from the free molecular and continuum regimes where individual constant geometric standard deviation exists (Lee et al, 1997;Otto et al, 1994). However, it is not possible to go through all the Knudsen numbers and geometric standard deviations for verification in practice, thus, some representative cases have to be selected and investigated, just as the performance in this work.…”

“…In both the free molecular and continuum regimes, asymptotic solutions exist because the asymptotic status for the size distribution, i.e., self-preserving size distribution (SPSD), has been verified in both the regimes (Friedlander, 2000). However, in the continuum-slip regime, especially as the Knudsen number ranges from $ 0.1000 to $ 5.0000 (also called the near-continuum regime), the geometric standard deviation (GSD) of number distribution always varies with the Knudsen number (Otto et al, 1994;Park et al, 1999;Yu et al, 2011). In this case, the asymptotic solution will no longer exist.…”

Evolution of primary and aggregate particle‐size distributions by coagulation and sintering

“…in the free-molecular and transition regime Kn f 7 , the g bigger the aggregates are the faster the coagulation rate is and the wider the resulting particle-size distribution becomes Ž . Otto et al, 1994 . The sintering time proposed by Kobata et Ž .…”

“…As sintering time increases, it tends to broaden the particle-size distribution and shift it to larger size scales. Low sintering rates lead to bigger aggregates, which grow faster in the Ž free-molecular-transition regime Akhtar et al, 1991;Otto et . al., 1994 , shifting the particle-size distribution to the right.…”

Asymptotic Particle Size Distributions Attained during Coagulation Processes

“…Conventionally, in the self-preserving formulation, the dimensionless particle volume is defined as η = v/ṽ, [25] and the dimensionless size distribution density function as = nṽ/N [26] whereṽ [=M 1 /N ] is the arithmetic mean particle volume. Since the plot of against a log scale of η does not provide a correct shape of the size distribution, a plot of η versus η was used, so that a symmetric curve is obtained for a log-normal size distribution.…”