Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

The growth of a free dendrite having a non-axisymmetric morphology with arbitrary symmetry in a pure substance is considered with the interfacial effect of anisotropy and in the absence of convective flow. A stable mode of thermal dendritic growth with the n -fold crystal symmetry is formulated using the solvability theory. A complete set of nonlinear equations, consisting of the undercooling balance condition and the selection criterion, is derived. Theoretical predictions are compared with phase field modeling data in two and three dimensional geometry obtained for ice dendrites growing in pure water.