Effect of weak convection on lamellar spacing of eutectics

An asymptotic expansion method is proposed to solve the convection–diffusion equation which governs the directional solidification of eutectic alloys under the condition of weak convection at low Peclet number. The so-called weak convection is defined here as the condition for which the velocity of convective flow and its gradient ahead of the S/L interface are both relatively small. Our analysis shows that such weak convective flow will give rise to an increase of eutectic lamellar spacing since the convection produces a slight shift of solute concentration profile at the interface and a decrease of eutectic growth undercooling. Our analytical results are compared with other models and have been applied to some practical cases such as weak forced convection induced by a rotating disk and natural convection induced by solutal and thermal differences in solidification processing. Calculations for two typical eutectic alloys, Pb–Sn and Al–Cu, are performed in order to reveal schematically the effect of weak convective flow on eutectic growth.