EFFECTS OF BOUNDARY-CONDITIONS AND RELATIVE DIMENSIONS OF A SOLUTION SYSTEM ON SCALING LAWS

A two-dimensional hydrodynamic model is employed to analyze the charac teristics of crystal growth from solution with only the variation of t he solution density caused by the temperature change taken into accoun t. In that case all the characteristics of the solution system only de pend on three numbers: the Rayleigh number Pa, the Prandtl number Pr a nd the Schemidt number Sc. In certain regions of the parameter (Ra, Pr and Sc) spaces, some scaling laws are generated: the scales of the te mperature distribution index S-theta, the concentration distribution i ndex S-phi (see text), the fluid velocity and the growth rate of cryst al are given by power functions of Pa, Pr and Sc. The effects of the g eometrical shape and the boundary condition of the solution system on the scaling laws are studied. When the ratio lambda of the height to t he length of the solution system changes, the scaling laws are still v alid and only the coefficients of power functions are changed, which a re also power functions of lambda. The scaling laws are valid both und er the isothermal temperature boundary condition and the adiabatic bou ndary condition at the surfaces of the top and the bottom sides of the solution system. The only difference is that the ratio of S-theta to Pa is greater for the latter than for the former. In certain ranges of Pa, there are no differences. between the other power functions for t he two cases.