Dendritic growth-A test of theory

Abstract

Steady-state theories of dendritic solidification are reviewed, and three nonisothermal theories, expressed as simple power laws, are chosen for experimental verification. Specifically, the axial growth rate,V, of a freely growing dendrite can be expressed asV =βGΔθ ⁿ, wheren andβ are the exponent and prefactor derived from each theory,G is a lumped material parameter, andΔθ is the supercooling. Succinonitrile, a low entropy-of-fusion plastic crystal, was prepared in several states of purity as the test system, and dendritic growth was studied both in the usual manner in long tubes, and in a novel apparatus in which the conditions for “free” dendritic growth were attained. Kinetic measurements show that only when “free” growth conditions obtain are the data reconcilable with current theory in the form discussed above. In particular, we show thatn = 2.6, in agreement with the theories of Nash and Glicksman and that of Trivedi; however, the prefactorsβ of those theories do not agree with the value determined for succinonitrile, which is the only substance for whichG is known accurately. Tip radius measurements, taken over a relatively narrow range of supercooling, when combined with the growth rate data prove that the Peclet number-supercooling relationship derived for each of the three nonisothermal steady-state theoriesall agree with experiment. This curious agreement, along with the inability to “decompose” the Peclet numbers into acceptable velocity-supercooling and tip radius-supercooling relationships is explained on the basis of the limitations imposed by the steady-state assumption itself. Directions for future theoretical and experimental investigation are discussed in the light of the findings presented.