Note on the Correction for Diffusion and Drag in the Slip Regime

The Mobility of Fractal Aggregates: A Review

“…However, the random error in the Millikan data are about 5%, which is half the discrepancy incurred by using the constant A. Moreover, as pointed out by Sorensen and Wang (2000), the 10% error is comparable to other uncertainties endemic in aerosol transport and kinetics studies. Hence use of Equation (A4) barely warrants the additional complexity.…”

“…The constant can be evaluated for α = 1, a reasonable value, as A = 1.612. With a constant A = 1.612, Sorensen and Wang (2000) demonstrated that the predicted value of the drag coefficient is accurate at the limits Kn = 0 and Kn 1, and is in error by as much as 10% too small near Kn = 0.5 relative to the standard Cunningham correction. The Cunningham correction would replace the constant A in Equation (A3) with…”

“…Then f = 6πηR m /C (Kn) [12] for all Kn where C(Kn) is the Cunningham slip correction factor which is a function of the Knudsen number Kn (Friedlander 2000). A simple, general formula good for all Kn is the harmonic sum (Sorensen and Wang 2000) f…”

Re-evaluation of the slip correction parameter of certified PSL spheres using a nanometer differential mobility analyzer (NDMA)

“…Although Chapmann and Enskog's theoretical formulation is valid for specular type interactions between the gas and the particle, the equation cannot account for the more complex interaction between gas and particle for particle sizes of a few nanometers and larger. To correct this problem, many articles (Annis et al, 1972;Epstein, 1924;Fernandez de la Mora et al, 2003;Friedlander, 1977;Li & Wang, 2003a, b; Phillips, 1975;Sorensen & Wang, 2000;Tammet, 1995) have been reported modifying the Epstein's equation analytically. Li & Wang (2003a, b) considered an intermolecular potential energy for gas molecule interactions and obtained the following expression for the drag force:…”

Mobility radius of fractal aggregates growing in the slip regime

“…This causes the increase in aggregate internal permeability as compared to that, which is valid in the continuum regime. The diffusion coefficient of a particle that applies at both the slip and continuum regimes is postulated (Sorensen & Wang, 2000) to be the sum of Einstein (1956) and Epstein (1924) coefficients:…”