Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 33, Issue 44, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-648X/ac1a2f
Keywords
elliptical paraboloids; dendrite tips; crystal growth
Categories
Funding
- Russian Science Foundation [21-19-00279]
- Russian Science Foundation [21-19-00279] Funding Source: Russian Science Foundation
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This review article summarizes current theories of dendrite growth in the form of elliptical paraboloids, analyzing dendrite tip shapes, temperature, and solute concentration distributions. A significant difference in analytical solutions for elliptical paraboloids compared to axisymmetric morphologies is shown. The developed theory is compared with experimental data on ice crystal growth.
This review article summarizes current theories of the steady-state growth mode of dendrites in the form of elliptical paraboloids. The shape of dendrite tips is analyzed, temperature and solute concentration distributions are described in its vicinity, and a solution of the hydrodynamic problem of a viscous incompressible fluid flowing against a dendrite tip is developed. A significant difference in analytical solutions describing a dendrite tip as an elliptic paraboloid as compared to an axisymmetric morphology is shown. The system of nonlinear equations for determining the stationary velocity of dendrite growth and the radii of curvature of the dendrite tip along the major and minor axis of the ellipse, respectively, is derived. The developed theory is compared with experimental data on the growth of ice crystals consisting of D2O or H2O.
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