Dendritic growth in microgravity and forced convection

A unified treatment of natural and forced convection, based on solutions of Navier-Stokes and energy equations, is used to analyze the experimental data on dendritic crystal growth from undercooled succinonitrile melts. The melt velocities that have been induced in the experiments reported for, mu g, 1g and forced convection differ by 10(5), the order being 10(-5), 10(-2), 1 cm/s, respectively. Transport theory predicts 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, numbers in thermal or forced convection. For mu g the theoretical simulations 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 conduction theory with equal melt and solid densities, rho(1) = rho(s), and a, b are constants. The microgravity (mu g) data show systematic deviations above and below Ivantsov's conduction theory for an isothermal dendrite at low and high undercooling, respectively. We show here theoretically that convection in the melt, at low undercooling is partly responsible for the higher rates of growth. Conversely, advection, (rho(1) not equal rho(s)), solid phase conduction and the Gibbs-Thompson curvature at large undercoolings could account for most of the deviations below Ivantsov's solution in the mu g experiments. At 1g, the convection theory of Ananth and Gill for an isothermal dendrite agrees well with the experiments over the entire range of undercoolings studied. The 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 rather insensitive to the strength of the gravitational field. Existing theories predict that the pattern selection parameter, sigma*, is independent of undercooling. However, the thermal (10(-5)-10(-2) cm/s) and forced (10(-1)-1 cm/s) convection data show that sigma* does depend on both the undercooling and the intensity of convection at larger values of Re and depends only on Delta T at small Re. In the forced convection 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 independent of the intensity (up to 0.01 cm/s) of convection because Re is small. This dependence of sigma* on Delta T and Re is not well understood and needs further study because of theoretical interest.