Gas properties

Mass-mobility relationship

This section sets the mass-mobility parameters and shape factor used throughout the rest of the web app. Note that ρeff,100 is the effective density of a particle having a mobility diameter of 100 nm. Default is for soot [a].
ρeff,100 kg/m3
Exponent (Dm)
Matl. density

Pre-factor (k, m0)
2.93×10-6
fg
m @ 100 nm (m100)
0.267
fg
ρeff,100
510
kg/m3
χ @ 100 nm
2.15
(
1.54
)

Equivalent sizes

Mass and effective density at the chosen mobility diameter are computed via the mass-mobility relation. Cunningham slip corrections are calculated via the expressions of Kim et al. For dynamic shape factor and aerodynamic diameter, the value in the brackets is the equivalent quantity when not accounting for the slip correction, giving an indication of the significance of this effect.

Mobility diameter nm
Knudsen number (Kn)
1.35×109
Mass
0.2670
fg
ρeff @ dm
510
kg/m3
Volume eq. diameter
64.97
nm
χ @ dm
2.15
(
1.54
)
Cunningham slip @ dm
2.88
Cunningham slip @ da
4.47
Aerodynamic diameter
57.48
(
71.41
) nm
Mechanical mobility (B)
167
m/(N·ns)
Electrical mobility (Zp)
2.68×10-4
cm2/(V·s)
Diffusion coefficient (D)
6.88×10-6
cm2/s
dp,100 nm
DTEM
dp @ dm
17.8
nm
Number of primaries (Np)
49
kf nm
Df
Radius of gyration
68.08
nm

Distribution moments

This section computed equivalent distribution moments using a combination of Hatch-Choate and the above size conversions. In the plot, the blue line corresponds to the number distribution and the red line to the mass distribution.

CMD nm
GSD
MMD
176.7
nm
CMAD
47.95
nm
MMAD
85.58
nm
GSD (for da)
1.43
CMM
0.1308
fg
MMM
1.095
fg
GSD (for mp)
4.30
75177CMDMMD5102050100200500100020000.51251020501002005001000200050000.00010.0010.010.11101001000Mobility diameter [nm]Aerodynamic diameter [nm]Single particle mass, mp [fg]

Acronyms
CMD - Count median (mobility) diameter
MMD - Mass median (mobility) diameter
CMAD - Count median aerodynamic diameter
MMAD - Mass median aerodynamic diameter
CMM - Count median single particle mass
MMM - Mass median single particle mass

Average charge algorithms

Footnotes
a Soot [1]: ρeff,100 = 510 kg/m3, ρm = 1860 kg/m3, Dm = 2.48
b NaCl [2]: ρeff,100 = 1940 kg/m3, ρm = 2160 kg/m3, Dm = 2.97
c Water/PSL: ρeff,100 = 1000 kg/m3, ρm = 1000 kg/m3, Dm = 3
* This web app is currently under construction and has not been fully validated.
* Roughly equivalent MATLAB code is available here.

References
[1] Olfert and Rogak, "Universal relations between soot effective density and primary particle size for common combustion sources", Aerosol Sci. Technol. (2019).
[2] For density of NaCl see Sipkens et al., "Comparison of measurement systems for assessing number- and mass-based particle filtration efficiency". (2022).