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Thermal convection, morphological stability and the dendritic growth of crystals
Author(s) -
Koo KeeKahb,
Ananth Ramagopal,
Gill William N.
Publication year - 1992
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690380615
Subject(s) - subcooling , natural convection , convection , thermodynamics , thermal , dendrite (mathematics) , crystal growth , mechanics , forced convection , materials science , physics , chemistry , heat transfer , geometry , mathematics
New data on the dendritic growth and microstructure of ice crystals in quiescent pure water are reported for small subcoolings of 0.035 K <ΔT<1.000 K, where thermal or natural convection is prevalent. Accurate and systematic measurements of the growth velocity V G and the tip radii of the edge and basal planes R 1 and R 2 were made as functions of time. The central point of this work is that with the harmonic mean of the tip radii R m as the lengthscale, the intensity of natural convection can be correlated accurately by using the thermal convection analogy, Gr = Re 2 . On this basis, natural convection has a crucial effect on dendritic growth of ice at ΔT<0.35 K, the region of subcooling in which the tip of the dendrite splits consistently. The experiments show that the morphological stability parameter C* is independent of subcooling and equals 0.075, when the lengthscale is R m . With the observed values of R 1 and R 2 , the aspect ratio is 28, and the growth velocity for small ΔT is significantly higher than that predicted by the conduction theory of Horvay and Cahn (1961). Thus, the effect of convection on the growth of ice crystals is more important as the subcooling decreases. Moving boundary solutions of the three‐dimensional Navier‐Stokes and energy equations for the dendritic growth of an elliptical paraboloid were obtained here with the Stokes flow approximation. Experimental observations of the quantities, V G , R 1 , and R 2 , agree well with predictions of this theory when Gr=Re m 2 is based on R m . In contrast, if convection is neglected in the theory, it does not agree with the experiments and the difference increases significantly as the subcooling is decreased.