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From: (Grant W. Petty)
Newsgroups: sci.geo.meteorology
Subject: Re: homogeneous vs. heterogeneous nucleation
Date: 1 May 1997 15:02:33 GMT

In article <5k8uv9$>,
Leon Gardner <> wrote:
>I have read that homogeneous nucleation requires a relative humidity
>of several hundred percent, while heterogeneous nucleation can occur
>at relative humidities of just above 100 percent, or even lower than
>100 percent for hygroscopic particles. I am wondering why this is the
>case. Any comments on this topic would be welcome.

Conventionally, "saturation" (and thus also dewpoint, relative
humidity, etc.) is defined with respect to a flat surface of pure
water.  In this case, saturation (or equilibrium) vapor pressure
e_s(T) is a function of temperature only.

But in reality, the saturation (or equilibrium) vapor pressure for a
water surface is a function not only of temperature but also of the
curvature of a water surface, owing to the interfacial energy (a.k.a.
surface tension).  Highly curved water surfaces have higher
equilibrium vapor pressures than flat water surfaces.  A very small
droplet of water with large curvature will therefore evaporate in an
environment which is exactly saturated (RH = 100%) according to the
conventional definition.  The smaller the droplet, the more pronounced
this effect is; in fact, the saturation vapor pressure is proportional
to exp(a/r), where a is a constant and r is the radius.  Thus, for r
approaching zero, the saturation vapor pressure for that droplet
approaches infinity.

A crude explanation is that the pressure inside the droplet due to
surface tension is inversely proportional to the droplet radius;
therefore, with decreasing radius, the energetics increasingly favor
the escape of water molecules from the droplet and oppose the return
of molecules from the vapor phase.

In order for homogeneous nucleation to occur, an incipient water
droplet created by random collisions of water vapor molecules would
have to achieve a size large enough so that it sees the environment as
at least saturated, otherwise it will immediately evaporate again.
The larger the ambient supersaturation (by the conventional
definition), the smaller this incipient droplet has to be in order to
survive.  And the smaller it has to be, the more likely that that size
can be achieved with some frequency by random collisions of vapor
molecules.  In practice, significant rates of homogeneous nucleation
become possible only when the relative humidity is several hundred

Heterogeneous nucleation entails condensation onto foreign particles
and occurs much more easily:

In the case of an insoluble, but wettable particle, the radius barrier
is partially overcome, because an incipient water droplet forming on
the surface of the particle has much less curvature in relation to its

In the case of a soluble particle, the required vapor pressure for
condensation is greatly reduced by the so-called "solute effect",
which is also the reason why salt and sugar tend to clump when the air
is humid.  However, the curvature effect still dominates at certain
intermediate droplet radii, hence activation to form an actual cloud
droplet still requires a slight degree of supersaturation.

A good discussion of the above may be found in chapter 4 of Wallace
and Hobbs "Atmospheric Science: An Introductory Survey"


Grant W. Petty                        |Assoc. Prof.,  Atmospheric Science
Dept. of Earth & Atmospheric Sciences |Voice:  (317)-494-2544
Purdue University                     |Fax:    (317)-496-1210
West Lafayette, IN 47907-1397, USA    |Email:

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