| An experimental study of the dendritic growth of ice crystals in quiescent pure water was extended to small subcoolings of 0.035 K {dollar}<{dollar} {dollar}Delta{dollar}T {dollar}<{dollar} 1.000 K, where natural convection is prevalent. Quantitative measurements of growth velocity, V{dollar}sb{lcub}rm G{rcub}{dollar}, and tip radii of the edge and basal planes, R{dollar}sb1{dollar} and R{dollar}sb2{dollar}, were made simultaneously.; It was found that the characteristic fluid velocity driven by natural convection begins to contribute significantly to the growth velocity of ice dendrites at subcooling of about 0.35 K and the effect of natural convection on dendritic growth of ice becomes stronger as subcooling decreases. Consequently, the growth kinetics becomes higher than the prediction by the conduction theory of Horvay and Cahn, with an aspect ratio of 28 at subcooling less than 0.35 K.; The present experimental data show that the stability parameter of ice dendrites,{dollar}{dollar}rmsigmasp* left(={lcub}2alpha dsb0over Vsb{lcub}G{rcub}Rsb{lcub}m{rcub}sp2{rcub}right),{dollar}{dollar}is a constant and equals 0.075. The degree of anisotropy in the surface energy of the edge plane was estimated to be 0.3 and that of the basal plane to be 0.001-0.003; these values were obtained by observation of the shape of the water droplet in an ice matrix. In the light of microscopic solvability theory, tip splitting in ice dendrites, which also occurs at subcooling less than about 0.35 K (i.e., at the {dollar}Delta{dollar}T where natural convection is dominant), seems to be a morphological instability caused by the coupling between the lack of anisotropy of surface energy in the basal plane and natural convection.; The moving boundary solutions of the three-dimensional Navier-Stokes and energy equations for the dendritic growth with an elliptical paraboloid shape were obtained in the presence of Stokes flow. Experimental results of growth velocity, V{dollar}sb{lcub}rm G{rcub}{dollar}, and tip radii, R{dollar}sb1{dollar} and R{dollar}sb2{dollar}, seems to be in reasonable agreement with these solutions when the thermal convection analogy and stability parameter are applied. A comparison between present experiments and these solutions with the thermal convection analogy, Gr = Re{dollar}sp2{dollar}, suggests that the lengthscale of ice dendrites might be the harmonic average of the tip radii of the edge and basal planes, i.e., {dollar}rm Rsb{lcub}m{rcub} = {lcub}2Rsb1Rsb2 over Rsb1 + Rsb2 {rcub}.{dollar}... |
