Computational modeling of capillary droplet breakup

The flow and breakup of droplets in confined geometries, such as obstacle arrays in microfluidic channels, is governed by the droplet surface tension, surrounding fluid viscosity, and the presence of non-uniform flow fields. We present a "deformable particle model' that captures the essential features of droplet deformation and breakup by discretizing only the droplet surface and captures the droplet shape change and motion under external and internal stresses. We also implement a geometry-based droplet breakup model, which describes the thinning of the droplet necks prior to breakup. We validated the deformable particle model by comparing the droplet shapes in the simulations with experimental data from oil-in-water emulsion droplets interacting with a single obstacle. We investigate how the size ratio of daughter droplets post-breakup depends on the impact parameter of the parent droplet with the obstacle. We show that the control parameter that determines whether the droplet breaks up or not depends on the size ratio of the parent droplet and the obstacle, and the capillary number of the flow. We then use the validated simulation model to study the motion of a single droplet through a random array of multiple obstacles, and calculate the size distribution of the daughter droplets as a function of the obstacle packing fraction, obstacle-to-droplet size ratio, and depth through the obstacle array.