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

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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.