The passage of a rising bubble through immiscible fluids is encountered in bath smelting. In order to investigate characteristics of bubble deformation in immiscible fluids, the bubble shape change at the interface and the relationship between the bubble aspect ratio (E) and dimensionless number of forces were obtained. A three-dimensional model was established, and the free-floating behavior of a single bubble in immiscible fluids was numerically simulated by phase-field method. The simulation results are in good agreement with experimental results. The results indicate that when the bubble passes through the interface, the bubble shape is divided into four types in turn: “pear”, inverted “pear”, “convex” and “droplet” shape. In the lower liquid, the relationship of E to Weber number (We), Tadaki number (Ta), and Reynolds number (Re) is distributed between two intersecting lines. The relationship of E to Eötvös number (Eo), a dimensionless group, and Galilei number (Ga) is distributed near the lines with slopes of − 3.325 × 10^–5, − 0.0855, and − 8.73 × 10^–4, respectively. In the upper liquid, the relationship of E to We, Ta, and Re is distributed between two parallel lines. Compared with gravity, the inertial force plays a leading role in the bubble shape in the lower and upper liquid. Compared with the viscous force, the surface tension dominates the bubble shape in the lower liquid.

在熔池熔炼中会遇到上升的气泡穿过不混溶的流体。为了研究非混相流体中气泡的变形特性，得到了界面处气泡形状的变化以及气泡纵横比（E）与无量纲力数的关系。建立三维模型，采用相场法数值模拟了单个气泡在不混溶流体中的自由漂浮行为。仿真结果与实验结果吻合较好。结果表明，当气泡通过界面时，气泡形状依次分为“梨形”、倒“梨形”、“凸形”和“水滴形”四种。在下层液体中，E的关系韦伯数 ( We )、忠木数 ( Ta ) 和雷诺数 ( Re ) 分布在两条相交的线之间。E与无量纲群Eötvös 数 ( Eo )和伽利略数 ( Ga ) 的关系分布在斜率分别为 − 3.325 × 10 ^–5、− 0.0855 和 − 8.73 × 10 ^–4的线附近。在上层液体中，E与We、Ta和Re的关系分布在两条平行线之间。与重力相比，惯性力对下层和上层液体中的气泡形状起主导作用。与粘性力相比，表面张力主导下层液体中的气泡形状。