The boundary integral equation for unsteady crystal growth in a channel
Ekaterina A. Titova, Alexandra E. Glebova, Irina E. Koroznikova, Dmitri V. Alexandrov · Journal of Physics A Mathematical and Theoretical · 2025
Abstract The boundary integral equation for an unsteady growth mode of dendritic crystal in an undercooled binary liquid in a channel with allowance for convection and nonlinear growth kinetics is found. A limit transition to the previously known steady-state boundary integral is obtained. The present boundary integral theory enables us to derive the dendrite tip velocity as a function of the melt undercooling and channel width. The boundary integral under consideration is verified by comparing obtained results with experimental data and numerical simulations.