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Pointe Aux Piments , Mauritius EFFECT OF A FORCED FLOW ON 3 D DENDRITIC GROWTH IN BINARY SYSTEMS

The effects of a forced flow on dendritic growth rate in binary systems are studied theoretically. By using the Oseen approximation of the Navier-Stokes equation, the linear stability analysis and the solvability criterion, one determines a scaling factor V D d T 2 0 * 2 ρ σ = as a function of the velocity of the forced flow and the impurity concentration in the melt in the three-dimensional model. The criterion obtained rallies analytic results for dendrite growth under forced convection in a pure system [1] and dendrite growth in a stagnant binary system [2]. INTRODUCTION It is well-known that the mechanisms of dendrite growth determine the microstructure evolution during solidification of melts and solutions [3-5]. These mechanisms are dependent, in particular, on the tip kinetics during free dendritic growth into undercooled liquid [6-8] as well as on effects of liquid convection [9] and diffusion of impurities partially rejected by the moving interface [2]. One of the theoretically and practically important problems consists in obtaining stable crystallization mode of the growing dendrite. The problem of finding a stability criterion for the growing dendrite comes from the linear and nonlinear stability theories [10-18]. After establishing robust stable conditions for the dendritic tip growing into a one-component stagnant liquid [19,20], these were extended to the one-component dendritic growth under forced flow [1,21,22] as well as to the binary dendritic growth in a stagnant media [2]. However, in many cases, knowledge of stable dendritic growth in binary system mode is a crucial question in evaluation and verification of the dendritic theory predictions in comparison with experimental data [23]. Therefore, the present analytical investigation extending the boundaries of the two-dimensional analysis of ref. [24] is devoted to the problem of a selection criterion for the crystalline dendritic tip growing into a binary liquid under forced convective flow within the framework of the threedimensional model.