Tip Velocities and Radii of Curvature of Pivalic Acid Dendrites under Convection-Free Conditions

Abstract

The growth of dendrites is governed by the interplay between two simple and familiar processes: the irreversible diffusion of energy and the reversible work done in the formation of new surface area via phase transformation. In this article, we present benchmark data using pivalic acid (PVA) in an apparent-microgravity environment, where convection effects were essentially eliminated so that we could test independently both components of dendritic growth theory, thermal diffusion, and interface stability. Our data indicate three main sets of conclusions. (1) Pivalic dendrites are not well described by assuming a single-parameter paraboloid or a two-parameter quartic of revolution, but rather by a two-parameter hyperboloid. (2) Peclet numbers predicted by Ivantsov’s solution do not agree with the convection-free data, as may be expected given the assumption of a paraboloid shape, but do agree reasonably well with point source models based on a hyperboloidal dendrite tip shape. This validates the role of thermal diffusion in dendritic growth theory provided that one makes a proper accounting of thermal sources and sinks. Last, we conclude that (3) the scaling/selection parameter data from both convection-free and diffusoconvective experiments are indistinguishable from each other, and the experimentally determined scaling/selection parameter does not appear to be a constant over the full supercooling range of these experiments and does not appear to agree with current predicted scaling/selection rule values.