Side-branch growth in two-dimensional dendrites. I. Experiments

Abstract

The dynamics of growth of dendrites' side branches is investigated experimentally during the crystallization of solutions of ammonium bromide in a quasi-two-dimensional cell. Two regimes are observed. At small values of the Peclet number a self-affine fractal forms. In this regime it is known that the mean lateral front grows as t 0.5 . Here the length of each individual branch is shown to grow ͑before being screened off͒ with a power-law behavior t ␣ n . The value of the exponent ␣ n ͑0.5ഛ ␣ n ഛ 1͒ is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small ␣ n are screened off by their neighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometrical position relative to its dominant neighbors. These results show that the branch structure results from a deterministic growth of initially random disturbances. At large values of the Peclet number, the faster of the side branches escape and become independent dendrites. The global structure then covers a finite fraction of the two-dimensional space. The crossover between the two regimes and the spacing of these independent branches are characterized.

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification

“…33 We have shown that, as long as sidebranching is frequent enough for competition among branches to occur, the exact choice of the input parameters N and DN has little influence on the final selected spacings. 15 One limitation of the current implementation is that it does not describe the lateral movement of dendrites.…”

The transient growth of ammonium chloride dendrites

“…Other experiments with more rapid transients have seen large sets of sidebranches generated [23,24,25,26]. We also saw no evidence of any transition to doublons, as has been observed in xenon dendrites [27,28].…”

Atomistic to continuum modeling of solidification microstructures

“…However, quantitative predictions of those properties remain scarce for alloys. Atomistic [33] -by a network of thin needle crystals that interact through the solute field, as illustrated in (b). The growth dynamics of each individual needle branch is obtained by combining two independent conditions at two distinct length scales: (c) a solute conservation equation at a length scale much larger than the needle tip radius q but much smaller than the diffusion length D=V, and (d) a solvability condition at the scale of the needle tip radius q [138].…”