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Toward a Theory of the Evolution of Drop Morphology and Splintering by Freezing

Alexander StaroselskyaDepartment of Physical Sciences, Raytheon Technologies Research Center, East Hartford, Connecticut

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Ranadip AcharyaaDepartment of Physical Sciences, Raytheon Technologies Research Center, East Hartford, Connecticut

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Alexander KhainbInstitute of Earth Science, Hebrew University of Jerusalem, Jerusalem, Israel

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Abstract

The drop freezing process is described by a phase-field model. Two cases are considered: when the freezing is triggered by central nucleation and when nucleation occurs on the drop surface. Depending on the environmental temperature and drop size, different morphological structures develop. Detailed dendritic growth was simulated at the first stage of drop freezing. Independent of the nucleation location, a decrease in temperature within the range from ~−5° to −25°C led to an increase in the number of dendrites and a decrease in their width and the interdendritic space. At temperatures lower than about −25°C, a planar front developed following surface nucleation, while dendrites formed a granular-like structure with small interdendritic distances following bulk nucleation. An ice shell grew in at the same time (but slower) as dendrites following surface nucleation, while it started forming once the dendrites have reached the drop surface in the case of central nucleation. The formed ice morphology at the first freezing stage predefined the splintering probability. We assume that stresses needed to break the ice shell arose from freezing of the water in the interdendritic spaces. Under this assumption, the number of possible splinters/fragments was proportional to the number of dendrites, and the maximum rate of splintering/fragmentation occurred within a temperature range of about −10° to −20°C, is in agreement with available laboratory and in situ measurements. At temperatures < −25°C, freezing did not lead to the formation of significant stresses, making splintering unlikely. The number of dendrites increased with drop size, causing a corresponding increase in the number of splinters. Examples of morphology that favors drop cracking are presented, and the duration of the freezing stages is evaluated. Sensitivity of the freezing process to the surface fluxes is discussed.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alexander Khain, alexander.khain@mail.huji.ac.il

Abstract

The drop freezing process is described by a phase-field model. Two cases are considered: when the freezing is triggered by central nucleation and when nucleation occurs on the drop surface. Depending on the environmental temperature and drop size, different morphological structures develop. Detailed dendritic growth was simulated at the first stage of drop freezing. Independent of the nucleation location, a decrease in temperature within the range from ~−5° to −25°C led to an increase in the number of dendrites and a decrease in their width and the interdendritic space. At temperatures lower than about −25°C, a planar front developed following surface nucleation, while dendrites formed a granular-like structure with small interdendritic distances following bulk nucleation. An ice shell grew in at the same time (but slower) as dendrites following surface nucleation, while it started forming once the dendrites have reached the drop surface in the case of central nucleation. The formed ice morphology at the first freezing stage predefined the splintering probability. We assume that stresses needed to break the ice shell arose from freezing of the water in the interdendritic spaces. Under this assumption, the number of possible splinters/fragments was proportional to the number of dendrites, and the maximum rate of splintering/fragmentation occurred within a temperature range of about −10° to −20°C, is in agreement with available laboratory and in situ measurements. At temperatures < −25°C, freezing did not lead to the formation of significant stresses, making splintering unlikely. The number of dendrites increased with drop size, causing a corresponding increase in the number of splinters. Examples of morphology that favors drop cracking are presented, and the duration of the freezing stages is evaluated. Sensitivity of the freezing process to the surface fluxes is discussed.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alexander Khain, alexander.khain@mail.huji.ac.il
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