Numerical study on solutal Marangoni instability in finite systems with a miscibility gap

Abstract

Solutal Marangoni instability (SMI) is investigated both in 2D and 3D using a combined Cahn-Hilliard and Navier-Stokes model in a finite system. Fe-Sn is chosen as a representative alloy system since the phase diagram reveals a region with a miscibility gap, where two liquid phases, namely, the Fe-rich phase L1 and the Sn-rich phase L2, are in chemical equilibrium. In 3D, considering a perturbed liquid cylinder (L2 phase) with a length of λ and a radius of R0 embedded in the middle of a simulation box of λ × H × H (length × width × height) surrounded by the phase L1, we find that the perturbation induced Marangoni flow is either clockwise or anti-clockwise depending on the mean curvature difference between the convex and concave regions which is affected by the ratio of λ/R0. The critical ratio of λ/R0 for SMI is shown to be invariant for different Marangoni numbers as well as independent of the geometrical properties of the L1 phase. In 2D, a perturbed liquid pipe with a length of λ and a radius of R0 embedded in the middle of a simulation box of λ × H (length × height) is taken into account. Due to different curvature constitution, the critical ratio of λ/R0 for SMI depends on the height of the L1 phase.