Universality of time evolution for the unsteady dendrite

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).