Inertial effects on the flow of capsules in cylindrical channels

A front-tracking method was used to study moderate to large-sized capsules flowing in cylindrical channels at Reynolds numbers ranging from 0.1 to 225. Two different constitutive equations, the Neo-Hookean and Skalak laws were considered to describe the mechanics of the thin membrane. The effect of capsule size, elastic capillary number, and Reynolds number on the shape, migration velocity, and extra pressure loss were determined. The deformation of the capsules was strongly tied to the size of the capsule compared with the channel diameter with larger capsules deforming more due to the confining effect of the wall. As the Reynolds number was increased, capsules were more elongated in the direction of flow. The effect of Reynolds number was more apparent as the elastic capillary number was increased. Both the migration velocity and extra pressure loss were seen to depend primarily on the size of the capsule with deformation playing a secondary role. The Neo-Hookean membrane showed a larger deformation than the Skalak law due to its strain softening nature. The Neo-Hookean membrane also displayed a failure phenomenon of continuous deformation at large enough elastic capillary numbers not seen in the Skalak law membranes. This limiting elastic capillary number was shown to decrease as Reynolds number became larger. The membrane strain was largest at the front of the capsule indicating the most likely region where the capsule would fail.