How a growing dendritic crystal reaches its stationary crystallization velocity

Abstract Motivated by important applications in materials science, geo- and biophysics, we develop a theory answering the question of how a growing dendritic crystal reaches its stationary crystallization velocity . To do this, we compare existing theoretical approaches, computational simulations and experimental data for crystal growth laws at certain time intervals. Taking these laws into account, we stitch together all known asymptotics and derive two generalized expressions for the crystal growth velocity as a function of time. We analyze a behaviour of these generalized laws and compare them with experiments. Both expressions have similar behaviour and well describe the experimental data. Therefore, the choice between these expressions is more a matter of taste.