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 |
| _version_ | 1818171949958823936 |
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| author | K.-T. O R. Wood |
| author_facet | K.-T. O R. Wood |
| author_sort | K.-T. O |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T19:04:51Z |
| format | Article |
| id | doaj.art-d8f615beb20349a3ba86b9f6f5d6adf9 |
| institution | Directory Open Access Journal |
| issn | 1680-7316 1680-7324 |
| language | English |
| last_indexed | 2024-12-11T19:04:51Z |
| publishDate | 2016-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Atmospheric Chemistry and Physics |
| spelling | doaj.art-d8f615beb20349a3ba86b9f6f5d6adf92022-12-22T00:53:55ZengCopernicus PublicationsAtmospheric Chemistry and Physics1680-73161680-73242016-06-01167239724910.5194/acp-16-7239-2016Exploring an approximation for the homogeneous freezing temperature of water dropletsK.-T. O0R. Wood1University of Washington, Department of Atmospheric Sciences, Seattle, WA, USAUniversity of Washington, Department of Atmospheric Sciences, Seattle, WA, USAIn 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.https://www.atmos-chem-phys.net/16/7239/2016/acp-16-7239-2016.pdf |
| spellingShingle | K.-T. O R. Wood Exploring an approximation for the homogeneous freezing temperature of water droplets Atmospheric Chemistry and Physics |
| title | Exploring an approximation for the homogeneous freezing temperature of water droplets |
| title_full | Exploring an approximation for the homogeneous freezing temperature of water droplets |
| title_fullStr | Exploring an approximation for the homogeneous freezing temperature of water droplets |
| title_full_unstemmed | Exploring an approximation for the homogeneous freezing temperature of water droplets |
| title_short | Exploring an approximation for the homogeneous freezing temperature of water droplets |
| title_sort | exploring an approximation for the homogeneous freezing temperature of water droplets |
| url | https://www.atmos-chem-phys.net/16/7239/2016/acp-16-7239-2016.pdf |
| work_keys_str_mv | AT kto exploringanapproximationforthehomogeneousfreezingtemperatureofwaterdroplets AT rwood exploringanapproximationforthehomogeneousfreezingtemperatureofwaterdroplets |