186 We 
= surface tension 
mech equiv. of heat 
= latent heat of water 
= density of water 
heat diffusion coefficient 
lta te He | 
ll 
= vapor pressure 
s = saturation vapor pressure 
When (5) is substituted in (4) the equation be- 
comes 
1 dn’ 2a1 A(2a — 1) 
= SS = | Spa = 6) 
n’ dt ria | ‘ v a(a + 1) | 
The objective now is to see how the terms in 
oo FD 
ll 
10.5 
63+ 
(g/m3) 
© Condensed woter 
42 
217 
Fic. 1—The concentration of liquid water on 
droplets growing by condensation on a spectrum 
of different size condensation nuclei; the spectrum 
was characteristic of spectra measured by Wood- 
cock at cloud base over the open sea in a Beaufort 
Force 4 wind; note how quickly the liquid water 
is concentrated on the smallest one or two size 
categories of droplets; the mean radius derived 
from the total liquid water content therefore does 
not differ much from the minimum droplet radius 
as used in the present calculations [Mordy, 1959] 
A. MORDY 
(6) vary as time proceeds. In the writer’s previ- 
ous study it was shown how the bulk of the liquid 
water lies in the smallest one or two categories of 
cloud droplets in such a model (see Fig. 1), hence 
the mean volume radius will represent nearly 
the radius of droplets which contain the largest 
part of the liquid water. It will serve as a good 
index, therefore, for this discussion to consider 
collisions between this volume mean radius (7) 
and larger or smaller droplets in the spectrum. 
The volume mean radius is defined by 
4en7%p = Mm 
; (6b) 
= mean mass of the droplets 
In the model we are considering, the liquid 
water is very nearly equal to a constant times 
the height above cloud base, which is to say 
Vv a dz ou 
l a TPL asi aa (7) 
where dx/dz = the change in mixing ratio in a 
moist adiabatic expansion (~2 X 
10-* egs at 800mb and 10°C) 
z = ht above cloud base 
N = X(N, + Nz ---) = const. 
By differentiating, (7) can be written 
A)p = (8) 
where z = vt in the model. 
The term containing (s* — A) here has been 
substituted from the condensation growth equa- 
tion (5). If these expressions in (7) and (8) are 
used to replace 7? and (s* — A) in (6) the equa- 
tion becomes: 
adn’ _(2\ (AY, , 
n' dt \8a t 
when it is assumed that p = 1 
If the two equations for drop growth (5) are 
subtracted the following equation may be ob- 
tained in quite an analogous way 
1 dn — 7) -1 i 
1 — FT dt sat 
Now putting 
A(2Qa — 1) 4raN (9) 
a(a + 1) cv 
acv 
AdmaN | (10) 
cv 
LS 
eA 
and 
Ar =m — 7 
