Abstract We present the results of a systematic analysis of the morphology of the thin lubrication film surrounding a long gas bubble transported by a liquid flow in a square capillary. Direct numerical simulations of the flow are performed using the Volume-Of-Fluid method implemented in OpenFOAM, for a range of capillary and Reynolds numbers Ca = 0.002 − 0.5 and Re = 1 − 2000 , and very long bubbles, up to 20 times the hydraulic diameter of the channel. The lubrication film surrounding the bubbles is always resolved by the computational mesh, and therefore the results are representative of a fully-wetting liquid. This study shows that when Ca ≥ 0.05, the long gas bubble exhibits an axisymmetric shape on the channel cross-section, whereas for lower capillary numbers the bubble flattens at the centre of the channel wall and thick liquid lobes are left at the corners. When Ca ≤ 0.01, the thin film at the centre of the wall assumes a saddle-like shape, which leads to the formation of two constrictions at the sides of the liquid film profile, where minimum cross-sectional values of the film thickness are observed. The resulting cross-stream capillary pressure gradients drain liquid out of the thin-film, whose thickness decreases indefinitely as a power-law of the distance from the bubble nose. Therefore, the film thickness depends on the length of the bubble, unlike flow in circular channels. We report detailed values of the centreline, diagonal and minimum film thickness along the bubble, bubble speed, and cross-sectional gas area fraction, at varying Ca and Re. Inertial effects retard the formation of the saddle-shaped thin-film at the channel centre, which may never form if the bubble is not sufficiently long. However, the film thins at a faster rate towards the bubble rear as the Reynolds number of the flow is increased.

中文翻译：

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长气泡在方形毛细管中传播的形态

摘要 我们介绍了对由方毛细管中的液体流传输的长气泡周围的薄润滑膜的形态进行系统分析的结果。使用 OpenFOAM 中实现的流体体积方法对流动进行直接数值模拟，对于一系列毛细管和雷诺数 Ca = 0.002 - 0.5 和 Re = 1 - 2000 以及非常长的气泡，高达 20 倍通道的水力直径。气泡周围的润滑膜始终由计算网格解析，因此结果代表完全润湿的液体。本研究表明，当 Ca ≥ 0.05 时，长气泡在通道截面上呈现轴对称形状，而对于较低的毛细管数，气泡在通道壁的中心变平，而在角落处留下厚厚的液体瓣。当 Ca ≤ 0.01 时，壁中心的薄膜呈马鞍状，导致液膜剖面两侧形成两个收缩区，观察到膜厚的最小横截面值. 由此产生的横流毛细管压力梯度将液体从薄膜中排出，薄膜的厚度随着距气泡鼻距离的幂律而无限减小。因此，与圆形通道中的流动不同，薄膜厚度取决于气泡的长度。我们报告了在不同 Ca 和 Re 下，沿气泡的中心线、对角线和最小薄膜厚度、气泡速度和横截面气体面积分数的详细值。惯性效应阻碍了通道中心鞍形薄膜的形成，如果气泡不够长，则可能永远不会形成。然而，随着流动雷诺数的增加，薄膜朝着气泡后部以更快的速度变薄。