Surface segregation exists in two-phase zone continuous casting (TZCC) alloy with wide solid–liquid two phase zone. The surface segregation formation cannot be explained by the traditional solidification theories. ProCAST software was used to simulate the TZCC process for preparing the Cu–4.7 wt%Sn alloy with wide solid–liquid two phase zone. The Sn solute distribution in TZCC Cu–4.7 wt%Sn alloy was investigated, and the surface segregation mechanism of TZCC Cu–4.7 wt%Sn alloy was analyzed. The results showed that numerical simulation results were agreed with that of experimental. TZCC Cu–4.7 wt%Sn alloy in the center firstly started to solidify and resulted in “Λ” shape inclined solid/liquid (S/L) interface near the mold. Therefore, a narrow gap between the wall of the two-phase zone mold and the S/L interface formed. On the one hand, while Cu–4.7 wt%Sn alloy solidified along the opposite continuous casting direction, the solute redistribution between the solid and the liquid occurred, which lead to Sn solute decreased in solid and enriched in front of S/L interface. Because the narrow gap lies in front of inclined S/L interface near the two-phase zone mold, Sn solute enriches in liquid of the narrow gap. On the other hand, during the TZCC process, solid grains nucleate on the wall of the two-phase zone mold, while the melt feeds into the two-phase zone mold which the temperature is in the two-phase zone of the Cu–4.7 wt%Sn alloy. The solute redistribution also occurs while the solid grains grow, thus lead to Sn content increases in front of S/L interface near the wall of the two-phase zone mold. The enriched Sn solute is too late to diffuse, and will quickly flows into the narrow gap, resulting in further increasing of Sn content in the narrow gap. The liquid with enriched Sn solute in the narrow gap will become the surface layer after solidification, which lead to surface segregation layer during the TZCC Cu–4.7 wt%Sn alloy.
A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations
