In this work, the breakup of a droplet passing through an obstacle in an orthogonal cross section is numerically investigated. The relevant boundary data of the velocity field is numerically computed by solving the depth-averaged Brinkman equation via a self-consistent integral equation using the boundary element method. To study the dependence of the droplet breakup on the obstacle shape, two different shapes of obstacle, circular and elliptical, are considered in the present work. We investigate the effect of obstacle size, obstacle position, and capillary number on the breakup treatment of the droplet. Numerical results indicate that the critical capillary number depends on the obstacle shape, obstacle position and droplet size. In the elliptical obstacle, in addition, the results also show that the area ratio of daughter droplets depends on the capillary number. Results show that the area ratio of daughter droplets depends on the capillary number, obstacle shape, and obstacle position. Our results is in a good agreement with the previous studies.

在这项工作中，对通过正交截面中的障碍物的液滴的破裂进行了数值研究。使用边界元方法，通过自洽积分方程对深度平均的布林克曼方程进行求解，来数值计算速度场的相关边界数据。为了研究液滴破裂对障碍物形状的依赖性，在本工作中考虑了两种不同形状的障碍物：圆形和椭圆形。我们研究了障碍物尺寸，障碍物位置和毛细管数对液滴破碎处理的影响。数值结果表明，临界毛细管数取决于障碍物的形状，障碍物的位置和液滴的大小。此外，在椭圆形障碍物中，结果还表明，子液滴的面积比取决于毛细管数。结果表明，子液滴的面积比取决于毛细管数，障碍物形状和障碍物位置。我们的结果与以前的研究非常吻合。