Modeling and simulation of contact in micro-swimming

[VLCeline]

The objective of my internship is to model and simulate the contact between rigid bodies placed in a fluid or between a rigid body and the boundary of the fluid domain. Collision models are added to the fluid-rigid body interaction problem. There are many different collision models. We implemented a model based on a repulsive force that allows to avoid the direct contact between the bodies during the interactions. We have considered this force for spherical rigid bodies, bodies of complex shape and articulated bodies, in particular the three-sphere swimmer. I will show some examples for each of these cases.

Collisions between spherical bodies

1. Spherical rigid body - spherical rigid body collision in 2D

This simulation represents a phenomenon called drafting, kissing and tumbling : the lower body creates a pressure drop reducing the fluid resistance for the upper body. Therefore, the upper body falls faster until it collides with the lower one, leading to a rotation of the two bodies. Finally, the repulsive forces cause the separation of the two bodies.

2. Multi-collisions between spherical rigid bodies in 2D

During the simulation, the bodies close to the right and left wall fall slower than the bodies initially located at the center. At final time, all bodies are settled at the bottom of the computational domain.

Collisions between complex shaped bodies

1. Rigid ellipse - bottom collision in 2D

During the simulation, the ellipse is rotating until it touches the bottom. Its large side becomes horizontal.

2. Particle suspension in a 2D symmetric stenotic artery

Two particles are located asymmetrically to the horizontal centerline in an artery. They move under the effect of hydrodynamic forces caused by a pressure difference between the inlet and the outlet. The two particles pass the stenotic throat due to this slight asymmetry. The particles move side by side, represented by the snapshot 1 − 9, until they are near the stenotic throat, snapshot 10. This latter indicates that the upper particle stops and moves back to allow the lower particle, that keeps moving, to pass the throat. Once passed, the upper particle changes direction and follows the first particle through the artery, shown by snapshot 11 − 17.

Collisions with articulated rigid bodies

1. Mobile three-sphere swimmer near boundary in 2D

During this simulation, the swimmer retracts and extends his arms in order to move. Due to its initial orientation, the swimmer approaches the bottom of the channel. Then, when the right sphere is in the lubrication zone, collision forces are applied on it. The swimmer begins to change direction : the right sphere moves upward, and the swimmer occupies a horizontal position. The swimmer continues to rotate until the left sphere is in the lubrication zone. Finally, the collision forces force the swimmer to move upwards.

More information on the collision model and simulations can be found under the following link: https://feelpp.github.io/swimmer/swimmer/latest/StageCeline/Introduction.html.