Computations of the Growth of Cloud Drops by Condensation 
Using an Electronic Digital Computer 
M. NEIBURGER AND C. W. CHIEN 
Department of Meteorology, University of California, Los Angeles, California’ 
Abstract—The growth of cloud drops by condensation was computed for four cases 
involving three different assumptions concerning the manner of cooling and two differ- 
ent size distributions of hygroscopic nuclei. All cas 
show that the smallest nuclei grow 
fS) 
only until the maximum supersaturation has been reached, and then shrink slowly, 
while the larger nuclei continue to grow rapidly, resulting in a gap in the size spectrum 
between the cloud drops and the imactivated nuclei. In the cooling models correspond- 
ing to Cumulonimbus and trade-wind Cumulus a sufficient number of large drops are 
formed to initiate drop growth by coalescence and warm-cloud precipitation. 
List of symbols—The following symbols are used 
in this paper. 
a Cunningham constant 
c Average molecular velocity 
c Specific heat of cloud drop 
D (Dz ,Dre ,Dr) Coefficient of molecular diffusion 
Dy Thermal diffusion coefficient 
e Vapor pressure 
e, Vapor pressure at surface of drop of radius 7 
e; Saturation vapor pressure 
e, Ambient vapor pressure in air parcel 
Fy, Flux of mass of water vapor 
F, Flux of heat 
g Acceleration of gravity 
H Heat 
K Coefficient of thermal conduction 
k Boltzmann’s constant 
L Latent heat of condensation 
M_~ Mass of drop 
m, Mass of water vapor molecule 
No Number of cloud drops per unit volume 
Number of drops per cm’ larger than r; (cu- 
mulative frequency) 
n Number of molecules (of all kinds) per unit 
volume 
P Pressure 
R, Gas constant of water vapor 
r Radius of drop 
ro Equivalent radius of nucleus 
8 Parameter introduced by Rooth 
T Temperature (°K); T,, T,,, values of T at 
drop surface and in environment 
t Time, seconds 
w Vapor mixing ratio 
wy, Liquid content 
a Accommodation coefficient 
T Consolidated hygroscopic factor 
Y Parameter introduced by Frisch and Collins 
6 Fractional difference between temperature of 
drop and ambient temperature 
1U.C.L.A. Department of Meteorology, Contri- 
butions to Meteorology No. 40. 
191 
Ratio of molecular weights of water vapor 
and dry air (0.622) 
n Fractional frequency of cloud drops 
N Molecular free path 
m Molecular viscosity of air 
Pa Density of air 
pr Density of nucleus 
ps Density of cloud drops 
p» Density of water vapor; por , pr. , Values at 
drop surface and in distant (undisturbed) 
environment 
Drop-size frequency function 
o Surface tension 
nm 
6 
Introduction—It is a remarkable fact that meas- 
urement of drop-size distribution in all sorts of 
clouds at various locations throughout the world 
almost always shows a mode, or most frequent 
size, in the range of 5 to 10 microns radius [Diem, 
1948; Netburger, 1949; Weickmann and aufm 
Kampe, 1953]. Methods of measurement which 
are able to count the very small droplets show 
that there are in addition a large number of sub- 
micron droplets and nuclei in the clouds [Eld- 
ridge, 1957]. We undertook the study we are re- 
porting on here to see whether drop growth by 
condensation alone could explain the remarkable 
uniformity of the drop-size distributions in clouds 
formed under quite different conditions, and also 
explain the development of bimodal size distri- 
butions from the uni-modal distributions which 
are almost always found in nucleus counts. In 
addition, we were interested in seeing whether 
drop growth by condensation on the observed 
wide range of nucleus sizes would give enough 
large drops to initiate the growth of precipitation 
by coalescence. 
The problem of the growth of drops by con- 
densation involves two transport processes in the 
