Exploring an approximation for the homogeneous freezing temperature of water droplets
In this work, based on the well-known formulae of classical nucleation theory (CNT), the temperature <i>T</i><sub><i>N</i><sub>c</sub> = 1</sub> at which the mean number of critical embryos inside a droplet is unity is derived from the Boltzmann dis...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2016-06-01
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| Series: | Atmospheric Chemistry and Physics |
| Online Access: | https://www.atmos-chem-phys.net/16/7239/2016/acp-16-7239-2016.pdf |
| Summary: | In this work, based on the well-known formulae of classical nucleation theory
(CNT), the temperature <i>T</i><sub><i>N</i><sub>c</sub> = 1</sub> at which the mean number of
critical embryos inside a droplet is unity is derived from the Boltzmann
distribution function and explored as an approximation for homogeneous
freezing temperature of water droplets. Without including the information of
the applied cooling rate <i>γ</i><sub>cooling</sub> and the number of
observed droplets <i>N</i><sub>total_droplets</sub> in the calculation, the
approximation <i>T</i><sub><i>N</i><sub>c</sub> = 1</sub> is able to reproduce the dependence of
homogeneous freezing temperature on drop size <i>V</i> and water activity
<i>a</i><sub>w</sub> of aqueous drops observed in a wide range of experimental
studies for droplet diameter > 10 µm and
<i>a</i><sub>w</sub> > 0.85, suggesting the effect of
<i>γ</i><sub>cooling</sub> and <i>N</i><sub>total_droplets</sub> may be secondary
compared to the effect of <i>V</i> and <i>a</i><sub>w</sub> on homogeneous freezing
temperatures in these size and water activity ranges under realistic
atmospheric conditions. We use the <i>T</i><sub><i>N</i><sub>c</sub> = 1</sub> approximation to
argue that the distribution of homogeneous freezing temperatures observed in
the experiments may be partly explained by the spread in the size
distribution of droplets used in the particular experiment. It thus appears
that the simplicity of this approximation makes it potentially useful for
predicting homogeneous freezing temperatures of water droplets in the
atmosphere. |
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| ISSN: | 1680-7316 1680-7324 |