Dendrite growth under forced convection: analysis methods and experimental tests
P.K. Galenkob,c aDepartment of Mathematical Physics, Ural Federal University named after the First President of Russia B. N. Yeltsin, prosp. Lenina 51, Ekaterinburg, 620083, Russian Federation bFriedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, Löbdergraben Strasse 32, Jena, 07743, Germany cInstitut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Köln, Germany
An analysis is given of the nonisothermal growth of a dendrite under forced fluid flow in a binary system. The theoretical model used employs a free moving crystal—liquid interface and makes use of the Oseen approximation for the equation of motion of the liquid. A criterion for the stable growth of a two-dimensional and a three-dimensional parabolic dendrite is derived under the assumption of an anisotropic surface tension at the crystal—liquid interface, which generalizes the previous known results for the stable growth of a dendrite with convection in a one-component liquid and for the growth of a dendrite in a two-component system at rest. The criterion obtained within the Oseen hydrodynamic approximation is extended to arbitrary Peclet numbers and dendrite growth with convection in a nonisothermal multicomponent system. Model predictions are compared with experimental data on crystal growth kinetics in droplets processed in electromagnetic and electrostatic levitation facilities. Theoretical and simulation methods currently being developed are applied to crystallization processes under Earth and reduced gravity conditions.