Selection criterion for the growing dendritic tip at the inner core boundary

A free dendrite growth at the Earth's inner core boundary is analyzed using a sharp interface model. A new selection criterion of the dendrite tip's stable growth into non-isothermal binary melt with convection and pressure effects for the 2D and 3D axisymmetric models is derived. The criterion obtained combines known analytic results for the dendrite growth under forced convection in a pure system and dendrite growth in a stagnant binary system. The generalized selection criterion represents a condition connecting the main physical parameters of the Earth's inner core. (paper)