Universality of time evolution for the unsteady dendrite

Leonid M. Martyushev; Pavel S. Terentiev

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arXiv · 1202.4252

Universality of time evolution for the unsteady dendrite

Leonid M. Martyushev·Pavel S. Terentiev

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Abstract

Unsteady growth of ammonium chloride dendrites during crystallization from an aqueous solution in a thin capillary is experimentally investigated. Dependency of the crystal area S on the time t for various sectors located along a primary branch and sidebranches is measured. A hypothesis of the same ratio between the area change and the area itself (S'(t)/S(t)) for different but simultaneously growing parts of an unsteady dendrite is advanced and confirmed. This conclusion allows proposing a curve for describing the evolution of the dendrite area (or its part) of the form S(t)=const*exp(-b*t)*t^a, where a and b are the parameters, whose values are determined in the paper. The nondimensionalization of S(t) and S'(t)/S(t) (using the full dendrite growth time) results in simple one-parameter functions depending on a single parameter (a) (which is presumably associated only with physical and chemical characteristics of the crystallized system and, in our case, equals 1.7+/-0.2).

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Leonid M. Martyushev, Pavel S. Terentiev. 2012-02-20. Universality of time evolution for the unsteady dendrite. https://arxiv.org/abs/1202.4252

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