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.