A numerical study of droplet deformation in a flat funnelform microchannel

Motivated by recent reported experiments, droplet deformation in a flat funnelform diverging microfluidic channel has been numerically studied. The structure of our microchannel is composed of two consecutive elements including a straight channel and a diverging channel. In this work, instead of solving the 3D Stokes equation, we solve a depth-averaged problem which is labeled two-dimensional problem. Employing the boundary element method (BEM), we numerically solve the Darcy equation in the two-dimensional and investigate droplet motion and droplet deformation as the droplet enters the flat funnelform diverging channel. Numerical simulations indicate that when a deformable droplet approaches the intersection of straight channel and funnelform diverging channel, the droplet decelerates and deforms. We numerically find that maximum deformation of droplet depends on droplet size, capillary number, and channel geometry. Our numerical scaling is in good agreement with the experimental scaling reports.