Motion and deformation of capsules flowing through a corner in the inertial and non-inertial regimes

Abstract

We investigate the inertial and non-inertial dynamics of three-dimensional elastic capsules flowing through a square channel presenting a sharp corner. Our study analyzes the trajectory, surface area, velocity and membrane stress of the capsules in the case of a single capsule, a system of two interacting capsules and a train of ten capsules released upstream of the corner. The channel Reynolds number $Re$ ranges from 0.01 to 50 and the Capillary number $Ca$, which measures the ratio of the viscous and elastic stresses, ranges from 0.075 to 0.35. We find that in the inertial regime, the membrane stretch and stress increase dramatically as compared to the non-inertial case, and that the velocity overshoot inside the corner is also enhanced. The maximum capsule deformation is observed to depend nearly linearly on $Ca$ and $Re$. Additionally, we report a repelling mechanism between two confined capsules when their initial interspacing distance $d$ is smaller than a critical value $d_c$. The deformation of the leading capsule is found to be mitigated by the presence of the following capsule. In the case of multiple capsules flowing through the corner, we observe that the increase in the maximum surface area of the trailing capsules eventually saturates at the tail of the train. Moreover, we find that the corner tends to separate the capsules regardless of their upstream interspacing distances $d$. This study contributes to the elaboration of practical guidelines for controlling capsule breakup and predicting throughput in both inertial and non-inertial microfluidic experiments.