dorsal/arxiv
View SchemaThe Molecular Diffusion of Ice Crystals of Various Shapes
| Authors | Hyun Youk, Roland List, Theophilus Ola |
|---|---|
| Categories | |
| ArXiv ID | physics/0404094 |
| URL | https://arxiv.org/abs/physics/0404094 |
| DOI | 10.1175/JAS3712.1 |
| Journal | Journal of the Atmospheric Sciences 63:1650-1657 (June 2006) |
Abstract
The growth by molecular diffusion (Reynold's number (Re) = 0) of ice crystals of different shapes, represented by the Sherwood number (Sh) is calculated using an electrical analog which relates capacity (C) to Sh. Although experimental data on dependence of Sh on Re for various ice crystals of interest in cloud physics have been previously obtained, extrapolation of the data to smaller particles for Re=0 has been unreliable. We present a simple computational algorithm for computing Sh at Re=0 for various crystals of interest, which will allow proper coverage over the whole Re range applicable to ice crystals. The method we present can be applied to any crystal of rectilinear shape. The approach was as follows: the model crystal is positioned in a box and an electric field is applied between the crystal and the box, simulating the initial growth stage of ice crystals. Using a finite Cartesian grid system of variable lattice separations, the corners of ice crystal are assigned to particular lattice points, thereby defining the geometry of the crystal. A discrete version of Gauss' flux law is developed and used for this lattice system. Sh (at Re=0) is obtained for hexagonal plates, hexagonal columns, broad branched crystals, stellar crystals, and capped columns. Our calculations reveal that our simple computational algorithm provides the values of Sh for these shapes to within 5% error from the values obtained through estimates in previous studies.
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"abstract": "The growth by molecular diffusion (Reynold\u0027s number (Re) = 0) of ice crystals\nof different shapes, represented by the Sherwood number (Sh) is calculated\nusing an electrical analog which relates capacity (C) to Sh. Although\nexperimental data on dependence of Sh on Re for various ice crystals of\ninterest in cloud physics have been previously obtained, extrapolation of the\ndata to smaller particles for Re=0 has been unreliable. We present a simple\ncomputational algorithm for computing Sh at Re=0 for various crystals of\ninterest, which will allow proper coverage over the whole Re range applicable\nto ice crystals. The method we present can be applied to any crystal of\nrectilinear shape. The approach was as follows: the model crystal is positioned\nin a box and an electric field is applied between the crystal and the box,\nsimulating the initial growth stage of ice crystals. Using a finite Cartesian\ngrid system of variable lattice separations, the corners of ice crystal are\nassigned to particular lattice points, thereby defining the geometry of the\ncrystal. A discrete version of Gauss\u0027 flux law is developed and used for this\nlattice system. Sh (at Re=0) is obtained for hexagonal plates, hexagonal\ncolumns, broad branched crystals, stellar crystals, and capped columns. Our\ncalculations reveal that our simple computational algorithm provides the values\nof Sh for these shapes to within 5% error from the values obtained through\nestimates in previous studies.",
"arxiv_id": "physics/0404094",
"authors": [
"Hyun Youk",
"Roland List",
"Theophilus Ola"
],
"categories": [
"physics.ao-ph",
"physics.comp-ph"
],
"doi": "10.1175/JAS3712.1",
"journal_ref": "Journal of the Atmospheric Sciences 63:1650-1657 (June 2006)",
"title": "The Molecular Diffusion of Ice Crystals of Various Shapes",
"url": "https://arxiv.org/abs/physics/0404094"
},
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