Quasi-steady-state modeling of dendritic growth

A new method of the moving-boundary problem analysis is developed. After proposed coordinate transformation, the quasi-steady-state differential equation was reduced to equivalent Laplace equation. Transformed boundary conditions of a rescaled field distribution reflect the presence of rate-dependent sources on interface. Taking into account the local rate-dependence of the Neumann's boundary conditions, non-equilibrium pattern formation was considered. The problem of dendrite fractal growth was reduced to one of interaction of conformal to tips charged particles. Conditions of the quasi-steady growth and the recurrence formula for k-order dendrite spacing were derived. Theoretically obtained scaling laws for interface shape, dendrite spacing, critical sidebranch distance are confirmed by available experimental data.