The study of droplet deformation and motion in confined solid geometries is motivated by numerous applications in microfluidic devices, enhanced oil recovery and coating processes. A plethora of theoretical studies have investigated the axisymmetric droplet motion in cylindrical capillaries. However, droplet dynamics in non-axisymmetric channels has received less attention, even though these capillaries represent better models for the aforementioned applications.

In this work we consider the deformation and motion of droplets and bubbles in a rectangular microfluidic channel. We investigate the behavior for a single droplet as well as an array of identical droplets by applying non-periodic and periodic conditions respectively. The effects of droplet size, flow rate and viscosity ratio will be presented. We also investigate the motion of droplets set free at a location off the centerline. Our numerical results are compared with analytical predictions and experimental findings.