The flow of droplets and capsules in channels is important for a variety of industrial and biological applications. Droplet flow is common in microfluidic devices and emulsion processing as well as oil recovery from porous materials. Capsules are used to encapsulate sensitive materials and can be used to study the mechanical properties of biological cells. A computational method was developed to study the two-phase flow of drops with and without surfactants, and capsules surrounded by a thin elastic membrane. This new computational method allowed for the inclusion of inertial effects on droplet and capsule flow which has not received much attention in the past. Results are presented for both the steady flow in straight cylindrical channels, and the transient flow in response to sudden expansions or contractions in the channel diameter. Increasing the Reynolds number was seen to cause non-monotonic trends in the capsule deformation and velocity. Parameters such as the drop viscosity and presence of surfactants were seen to have smaller effects when the Reynolds number became large. Capsules flowing in channels were seen to have limiting elastic capillary numbers above which no stable shape could be found. The transient deformation of drops and capsules moving through expansions depended strongly on the shape of the drop upstream of the expansion. The transient deformation increased with the capillary number up to a limiting value. The flow of droplets through channels was seen to produce large deformations that could break the drop apart at low viscosity ratios. The inclusion of inertial effects caused increases in the transient deformation as well as oscillations as the drops relaxed back into their steady shape.
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