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Side-branch growth in two-dimensional dendrits. Part I: Experiments
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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 off) with a power-law behavior
t
α
n
. The value of the exponent
α
n
(
0.5
⩽
α
n
⩽
1
)
is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small
α
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.
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COUDER, Yves, et al. Side-branch growth in two-dimensional dendrits. Part I: Experiments. Physical Review E. 2005. Vol. E71, num. 031602-1-031602-12. ISSN 1063-651X. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/18745