Breakup a droplet passing through an obstacle in an orthogonal cross-section microchannel

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.