# Rotation matters - Direct numerical simulations of rectangular particles in suspensions at low to intermediate solid fraction

## TL;DR

This paper introduces a novel direct numerical simulation method for rectangular particles in suspensions, enabling detailed analysis of how particle rotation influences suspension dynamics at low to intermediate solid fractions.

## Contribution

The study develops a new numerical approach combining Lagrange multipliers and immersed boundary methods for simulating rectangular particles, including an efficient collision scheme.

## Key findings

- Particle rotations significantly influence suspension behavior.
- The numerical method accurately captures particle interactions and rotations.
- Rotational energy remains small compared to translational energy but still impacts dynamics.

## Abstract

Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual interfaces and hence resolve unprecedented detail. While most previous studies focus on spherical particles, we develop a direct numerical approach to capture rectangular particles. Our approach uses distributed Lagrange multipliers to enforce rigid-body motion in the solid domain in combination with an immersed boundary method to correctly enforce the no-slip constraint on the solid-fluid interfaces. An important component of our model is an efficient particle collision scheme that prevents overlap between particles of different shapes and allows for the transfer of both translational and angular momentum during particle collision. We verify and validate our numerical method through several benchmark cases. Applied to suspension flow, we test the hypothesize that particle rotations alter the aggregated dynamics of the suspension even if the relative rotational energy of the particles remains small as compared to the translational energy.