Method of evaluation for the non-stationary period of primary dendritic crystallization

Theoretical predictions by many models of solidification kinetics rest on assumption of the steady-state regime of crystal growth with constant velocity. Such approximation holds if the time for solidification of a region under study is much longer than the non-stationarity time for solidification velocity. Even though a lot of experimental evidences which support the existence of long quasi-stationary periods of crystal growth or solidifying layers with constant velocity exists, direct quantitative estimations of such regimes are given usually for planar fronts or essential simplifications which, for instance, do not take into account the finiteness of solidifying bulk. The present work suggests a method to quantify non-stationary periods of crystal growth in comparison with solidification time of finite bulks. In essence we discuss and quantify limits of applicability of steady state crystal growth theories. With this aim, an acceleration- and velocity-dependent interfacial condition [A. Salhoumi, P.K. Galenko, Physica A 447 (2016) 161] is used for the analysis of various regimes of dendrite growth as particular case of crystalline solidification. The time dependence of the dendrite tip velocity is obtained for the growth from a pure (chemically one component) undercooled liquid. The developed theoretical model shows a drastic reducing the non-stationarity time with the increase of undercooling. The present model can be advanced to the arbitrary undercooling and further compared with data of experimental measurements on crystal growth kinetics.