Dendrite tips as elliptical paraboloids

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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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.