Numerical pancake droplets: from capturing to versatile microfluidics

This article proposes a numerical model for microfluidic two-phase flows in flat channels, also called Hele-Shaw cells. The initially three-dimensional problem is simplified to two-dimensions by depth averaging in the thin direction. The 2D partial differential equation is then numerically solved using the Boundary Element Method (BEM), which leads to an efficient algorithm for the evolution of free interface problems. Using this method we investigate a flow in a flat microchannel, where a droplet driven by a carrier fluid becomes anchored to a hole, placed in one of the channel walls. The numerical method is compared to experiments and a model with analytic solution. These examples demonstrate that the model equation and the numerical scheme are basically able to describe flow in simple three-dimensional geometries.