Development of a numerical method for interface dynamics by using the two-phase lattice Boltzmann method

为了研究液-液或气-液两相流动，我们采用两相晶格玻尔兹曼方法建立了一种新的两相流动数值计算方法。将该方法应用于两个基本两相流问题的计算。一种是剪切流动中液滴的变形和破碎，另一种是重力作用下液体中气泡的行为。本研究的结果如下：1。本文对剪切流中液滴变形和破裂的研究结果与已有的低雷诺数下的理论、实验和数值结果吻合较好。随着雷诺数的增加，液滴更容易变形和破裂。当液滴与悬浮液的粘度比接近于1时，液滴容易变形。在高粘度比的情况下，液滴的行为类似于刚体。在液体中气泡的计算中，当密度比达到1000.5时，得到了稳定的结果。对于不同的Eotvos和Morton数，计算了气泡上升的行为。当厄托沃斯数较低时，气泡会合并成一个大的芭蕾舞状气泡。另一方面，对于高厄托弗斯数，气泡反复合并和破裂，形成许多复杂的形状。

In order to investigate liquid-liquid or gas-liquid two-phase flows, we developed a new numerical method for two-phase flows by using a two-phase lattice Boltzmann method. The method was applied to the calculations of two fundamental two-phase flow problems. One is the drop deformation and breakup in shear flows, and the other is the behavior of bubbles in liquid under gravity effect.The results of this study are as follows.1. The present results for the drop deformation and breakup in shear flows are in good agreement with available theoretical, experimental, and numerical results at very low Reynolds numbers.2. As the Reynolds number increases, the drop is easier to deform and to be ruptured.3. When the viscosity ratio between the drop and the suspending fluid is close to unity, the drop easily deforms. In the case of high viscosity ratios, the drop behaves similarly to a rigid body.4. In the calculations of bubbles in liquid, stable results are obtained with the density ratio up to 1000.5. For various Eotvos and Morton numbers, the behavior of rising bubbles is calculated. For low Eotvos numbers, the bubbles coalesce into a large ballet-shape bubble. For high Eotvos numbers, on the other hand, the bubbles repeatedly coalesce and rupture, forming into many complicated shapes.