Numerical simulations of a drop crossing a plane liquid-liquid interface in a centrifugal field are performed using the level-set method. The objective is to characterize the hydrodynamical parameters controlling the coating volume of the droplet, which results from the rupture of the liquid column of the lighter phase entrained by the droplet during the crossing of the interface in the tailing regime. The numerical method is validated first in two-phase flow simulations of a drop rising in a stagnant liquid and then in three-phase flow configurations to reproduce the theoretical critical condition for a drop to cross an interface in static conditions (without initial velocity). Then, in inertial conditions, extensive simulations of crossing droplets are performed in a wide range of flow parameters and phase properties for two types of drop: solidlike droplets (mimicking rigid particles) and deformable drops. The crossing criterion is found to remain very close to that given by the theory in static conditions, for either a spherical or a deformed droplet. For each case studied, the crossing time, the maximum length of the column of liquid pulled by the droplet, and the volume encapsulating the drop after crossing are computed and scaled as a function of an inertia parameter, which is the ratio $F^{*}$ between the inertial stresses pushing on the interface, defined from the minimum drop velocity reached during crossing as the characteristic velocity, and the opposite stress pulling back the entrained column towards the interface. The maximal column length increases with $F^{*}$ (when rescaled by the minimal inertial required for crossing) under two distinct growth rates according to the flow regime in the column. For solidlike drops, the final coating volume is a unique function of $F^{*}$ and grows with $F^{*}$ at large inertia. In the case of deformable droplets, the coating volume evolution can also be well predicted by $F^{*}$ but corrected by the drop-to-film viscosity ratio, which strongly affects the drainage rate of the film along the drop surface during the encapsulation process.

中文翻译：

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液滴穿越液-液界面的数值模拟

使用水平集方法对在离心场中穿过平面液-液界面的液滴进行了数值模拟。目的是表征控制液滴的涂层体积的流体力学参数，该流体力学参数是由于在尾矿状态下界面的越过期间液滴夹带的较轻相的液柱的破裂而产生的。首先在停滞的液体中上升的液滴的两相流模拟中然后在三相流动配置中验证了该数值方法，以重现液滴在静态条件下（没有初始速度）穿过界面的理论临界条件。然后，在惯性条件下，针对两种类型的液滴，在宽范围的流动参数和相位特性中执行了交叉液滴的广泛模拟：固态液滴（模仿刚性颗粒）和可变形液滴。对于球形或变形液滴，发现在静态条件下，交叉准则与理论给出的准则非常接近。对于所研究的每种情况，均会计算出穿越时间，液滴拉动的液体柱的最大长度以及穿越后封装液滴的体积，并根据惯性参数（比例）进行缩放$F^{*}$施加在界面上的惯性应力（由交叉过程中达到的最小降落速度定义为特征速度）之间的反作用力和相反的应力将夹带的柱子拉回界面。最大列长随$F^{*}$（当根据交叉所需的最小惯性进行重新缩放时），将根据列中的流态在两个不同的增长率下进行。对于固体滴，最终的涂层体积是$F^{*}$ 和一起成长 $F^{*}$大惯性 对于可变形的液滴，也可以通过以下方式很好地预测涂层体积的演变：$F^{*}$ 但可以通过液滴与膜的粘度比进行校正，该比率会严重影响膜在封装过程中沿液滴表面的排液速率。