DENDRITIC GROWTH IN MICROGRAVITY AND FORCED-CONVECTION

A unified treatment of natural and forced convection, based on solutio ns of Navier-Stokes and energy equations, is used to analyze the exper imental data on dendritic crystal growth from undercooled succinonitri le melts. The melt velocities that have been induced in the experiment s reported for, mu g, 1g and forced convection differ by 10(5), the or der being 10(-5), 10(-2), 1 cm/s, respectively. Transport theory predi cts quite well the growth Peclet number, P = VR/2 alpha, as a function of the Stefan, St, Prandtl, Pr, and Grashof, Gr, or Reynolds, Re, num bers in thermal or forced convection. For mu g the theoretical simulat ions and the experiments suggest a relation P - P-IV = a P-IV + bGr(1/ 4), where P-IV is the growth Peclet number given by Ivantsov's conduct ion theory with equal melt and solid densities, rho(1) = rho(s), and a , b are constants. The microgravity (mu g) data show systematic deviat ions above and below Ivantsov's conduction theory for an isothermal de ndrite at low and high undercooling, respectively. We show here theore tically that convection in the melt, at low undercooling is partly res ponsible for the higher rates of growth. Conversely, advection, (rho(1 ) not equal rho(s)), solid phase conduction and the Gibbs-Thompson cur vature at large undercoolings could account for most of the deviations below Ivantsov's solution in the mu g experiments. At 1g, the convect ion theory of Ananth and Gill for an isothermal dendrite agrees well w ith the experiments over the entire range of undercoolings studied. Th e critical undercooling required to produce by convection a 1% change in P decreases with the level of gravity and is given approximately by the slowly varying function Delta T-c similar to (g/g(0))(0.15). Thus a large change in g/g(0) produces a small change in Delta T-c and the critical undercooling needed to render convection negligible is rathe r insensitive to the strength of the gravitational field. Existing the ories predict that the pattern selection parameter, sigma, is indepen dent of undercooling. However, the thermal (10(-5)-10(-2) cm/s) and fo rced (10(-1)-1 cm/s) convection data show that sigma does depend on b oth the undercooling and the intensity of convection at larger values of Re and depends only on Delta T at small Re. In the forced convectio n experiments, Re is large, and sigma clearly increases with Reynolds number at fixed values of the undercooling. In the thermal convection experiments, sigma increases with decreasing Delta T and is independ ent of the intensity (up to 0.01 cm/s) of convection because Re is sma ll. This dependence of sigma on Delta T and Re is not well understood and needs further study because of theoretical interest.