Analysis for Free Dendritic Growth Model Applicable to Nondilute Alloys

An extended free dendritic growth model incorporating the nonisothermal and nonisosolutal nature of the solid–liquid interface

“…(16)- (19), into the transport balance Eqs. (20) and (21), one obtains the following results, at the tip of dendrite (set b ¼ 0):…”

“…In the present work, the version with solute drag is proposed (see Refs. [20,24,25] for details). For the present model, the linear liquidus and solidus lines are assumed.…”

“…For the free dendritic growth in undercooled melts, the temperature gradient in the solid phase is normally negligible under the condition that the solid-liquid interface is assumed to be isothermal [9][10][11][12][13][14][15][16][17][18][19][20]. For the nonisothermal interface, there is an additional temperature gradient G S ðbÞ, which can be described as:…”

“…As the first attempt, local equilibrium solute diffusion in bulk liquid and linear liquidus and solidus were assumed in the present model, to focus on the effects of the nonisothermal nature and the nonisosolutal nature of the interface. In further works, the model should be improved by adopting the curved phase boundary [15,18] or the more realistic Gibbs free energy data [19,20,35].…”

Analysis for free dendritic growth model incorporating the nonisothermal nature of solid–liquid interface

“…The Ivantsov model set the groundwork for the studies that follows. Numerous dendritic growth models were established later [2][3][4][5][6][7][8][9][10][11][12][13].…”