Numerical simulations of particle sedimentation using the immersed boundary method

TL;DR

This paper presents numerical simulations of particle sedimentation in viscous fluids using the immersed boundary method, capturing realistic settling behaviors and interactions like drafting, kissing, and tumbling.

Contribution

It introduces a numerical approach combining the immersed boundary method with an added mass term for simulating particle sedimentation, validated against theoretical and experimental data.

Findings

Terminal velocities match theoretical and experimental results.

Single-particle dynamics are qualitatively accurate.

Two-particle interactions show realistic drafting-kissing-tumbling behavior.

Abstract

We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction problem is simulated numerically using the immersed boundary method, with an added mass term that is incorporated using a Boussinesq approximation. Simulations are performed with a single circular particle, and also with two particles in various initial configurations. The terminal settling velocities for the particles correspond closely with both theoretical and experimental results, and the single-particle dynamics reproduce expected behavior qualitatively. The two-particle simulations exhibit drafting-kissing-tumbling dynamics that is similar to what is observed in other experimental and numerical studies.