Universality of time evolution for the unsteady dendrite

TL;DR

This paper investigates the unsteady growth of ammonium chloride dendrites, confirming a universal ratio in their area evolution and proposing a mathematical model describing their growth dynamics.

Contribution

It introduces a universal ratio hypothesis for dendrite growth and develops a parametric exponential model for area evolution during unsteady crystallization.

Findings

Confirmed the ratio S'(t)/S(t) is consistent across different dendrite parts.

Derived a growth curve model S(t)=const*exp(-b*t)*t^a with parameters fitted to data.

Identified a universal parameter a approximately equal to 1.7+/-0.2.

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).