Monte Carlo simulations based on a Spin-1 Ising Model for binary alloys have been used to investigate the non-equilibrium partition coefficient (kneq ) as a function of solid-liquid interface velocity and orientation. In simulations of Si with a second component kneq is greater in the  direction than the  direction in agreement with experimental results reported by Aziz et al. The simulated partition coefficient scales with the square of the step velocity divided by the diffusion coefficient of the secondary component in the liquid.
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Beatty, K.M., Jackson, K.A. Orientation and Velocity Dependence of the Nonequilibrium Partition Coefficient. MRS Online Proceedings Library 398, 113–118 (1995). https://doi.org/10.1557/PROC-398-113