Supercooling and nucleation

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Supercooling, undercooling and nucleation.

Volmer and Weber kinetic model

Volmer and Weber kinetic model [1] results in the following nucleation rate:

Failed to parse (unknown function "\label"): {\displaystyle I^{VW} = N^{eq}(n^*) k^+(n^*) = k^+(n^*) N_A \exp \left( -\frac{W(n^*)}{k_BT} \right) \label{eq_IVW} }

Szilard nucleation model

Homogeneous nucleation temperature

The homogeneous nucleation temperature (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_H} ) is the temperature below which it is almost impossible to avoid spontaneous and rapid freezing.

Zeldovich factor

The Zeldovich factor [2] (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} ) modifies the Volmer and Weber expression \eqref{eq_IVW}, making it applicable to spherical clusters:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z= \sqrt{\frac{ \vert \Delta \mu \vert }{6 \pi k_B T n^*}} }

Zeldovich-Frenkel equation

Zeldovich-Frenkel master equation is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\partial N(n, t)}{\partial t} = \frac{\partial }{\partial n} \left( k^+ (n) N^{eq} (n) \frac{\partial }{\partial n} \left( \frac{N(n, t)}{N^{eq}(n)} \right) \right)}

See also

References

  1. ↑ M. Volmer and A. Weber "Keimbildung in übersättigten Gebilden", Zeitschrift für Physikalische Chemie 119 pp. 277-301 (1926)
  2. ↑ J. B. Zeldovich "On the theory of new phase formation, cavitation", Acta Physicochimica URSS 18 pp. 1-22 (1943)
Related reading
Books
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