An Empirical Modification of Nucleation Theory and Its Application to Boiling Heat Transfer Page: 14 of 38
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Surface conditions, such as roughness, wetting character, contami-
nation, and crystal structure, are known to affect considerably the heat
transfer in nucleate boiling. Unfortunately, the coexistence of different
roughness, different wetting, etc., at different fluid-surface combinations
prevents a distinctive separation of the variables which affect the heat trans-
fer and hence a clear definition of these vague terms. At any rate, it can
be stated that surface conditions control (a) the effective solid-liquid contact
area, (b) the mean size of the originating bubbles, (c) the frequency of bubble
generation from each site, (d) the number of active bubble sites, and (e) the
superheat of incipient boiling. All these factors can be considered to affect
nucleation. Thus, if the heat transfer problem is approached from the
nucleation viewpoint, it should be possible to consolidate all these effects
into one, or at most two, parameters, which are to be determined by experi-
ments for each kind of fluid-surface combinations.
Volmer(ll) was the first to apply the Maxwell-Boltzmann distribu-
tion law to the condensation of supersaturated vapor and to suggest that the
rate of nucleation be expressed by the following equation:
N = Noe(A )/KT (5)
where No is the frequency factor, / the gas constant per molecule, and
A( the maximum activation energy or the work required to form a bubble
of the critical size:
AD = 3 7tra r*2 (6)
Volmer's theory has been subsequently improved by Eyring(12) and many
others. According to Eyring, the frequency factor No is proportional to the
No = NA K T/H , (7)
where NA is the Avogadro number and H is Planck's constant. Eyring
has also modified the maximum activation energy by the addition of the free
energy of the molecule moving toward or away from the interface.
Although the kinetic theory has proved quite satisfactory to explain
nucleation qualitatively, quantitative calculation shows that boiling cannot be
started unless it is facilitated with very large superheat which, however, is
not what has been found in experiments. In order to overcome this difficulty,
many investigators(13,14) have considered the role of solid surfaces in the
modification of the activation energy in Eq. (5). However, such refinements
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Chang, Y. P. An Empirical Modification of Nucleation Theory and Its Application to Boiling Heat Transfer, report, February 1, 1961; United States. (https://digital.library.unt.edu/ark:/67531/metadc863296/m1/14/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.