  The process of rapid solidification of a binary mixture is considered in the
framework of local nonequilibrium model (LNM) based on the assumption that
there is no local equilibrium in solute diffusion in the bulk liquid and at the
solid-liquid interface. According to LNM the transition to complete solute
trapping and diffusionless solidification occurs at a finite interface velocity
$V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present
work, the boundary conditions at the phase interface moving with the velocity
$V$ close to $V_D$ ($V \lesssim V_D$) have been derived to find the
non-equilibrium solute partition coefficient. In the high-speed region, its
comparison with the partition coefficient from the work [Phys. Rev. E 76 (2007)
031606] is given.
