The motion of a deforming capsule through a corner

TL;DR

This study uses advanced numerical simulations to analyze how deformable capsules behave when passing through a corner in a duct, revealing the influence of membrane elasticity on their trajectory, deformation, and tension.

Contribution

It introduces an accelerated boundary integral method for simulating deformable capsules in complex geometries, highlighting the effects of membrane elasticity on capsule dynamics.

Findings

Capsule trajectory follows streamlines regardless of capillary number.

Membrane elasticity affects deformation, velocity, and tension during passage.

Velocity overshoot occurs past the corner, increasing with confinement.

Abstract

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner.