Settling dynamics of an oloid: experiments and simulations

TL;DR

This study addresses how the oloid’s unique curved geometry governs the settling of anisotropic particles in quiescent fluids. It employs a combined experimental (two sizes, ranged $Ga$, density contrasts via water–glycerol) and numerical (immersed boundary with Newton–Euler dynamics) approach to identify two distinct falling modes: a stable, orientation-preserving regime with rotation about the vertical axis and a tilted orientation, and a tumbling regime with random orientation. Orientation and rotation statistics reveal a translation–rotation coupling in the stable regime and a transition toward randomness as $Ga$ increases, with the stable mode obeying Stokes-like drag and the tumbling mode dominated by turbulent drag. The findings advance understanding of shape–drag–rotation interactions for anisotropic particles and provide benchmarks for validating fluid–structure interaction models in applications ranging from sedimentation to robotic design.

Abstract

This study presents a combined experimental and computational investigation of an oloid shaped particle settling in a quiescent fluid. The oloid, a unique convex shape with anisotropic geometry, provides a distinctive model for exploring how a particle's shape and orientation affect its settling dynamics. The settling oloids are tracked experimentally for Galileo numbers $48 \leq \text{Ga} \leq 5.4 \cdot 10^3$, using two particle sizes ($D_{\text{eq}}$ = 21.6 mm, and $D_{\text{eq}}$ = 10.8 mm). The density ratio between the particle and fluid $Γ$ = $\frac{ρ_p}{ρ_f}$ ranges from $1.11 \leq Γ\leq 1.30$ in the experiments. Computationally, the Galileo numbers $10 \leq \text{Ga} \leq 100$ are simulated, with $Γ= 2$. The experimental findings and numerical results are in good agreement, and give a consistent idea of the oloid settling dynamics. Our results indicate two distinct falling modes for the oloid, separated by Galileo number. The stable mode is characterised by a preferential orientation, with a rotation around the vertical axis, whereas the tumbling mode has randomly distributed orientation and rotation statistics. We characterise the falling velocity, orientation, and rotation dynamics of the oloids over a range of Galileo numbers. Additionally, the influence of the initial orientation is revealed to determine the rotation dynamics at low Galileo numbers.

Figures (19)

• Figure 1: Photo of the 3D-printed oloid particles used in experiments (a), and a 3D visualisation of the oloid geometry (b), showing perpendicular discs intersecting through their centres, with lines illustrating the convex hull. The oloid in its reference orientation (c), where the red arrow indicates the chosen pointing vector used in our analysis.
• Figure 2: 3D visualisation of the settling tank used in experiments, along with the cameras shown in red and blue, and an oloid (not to scale) in orange. The dimensions of the settling tank are $h =$ 200 cm, $l = w =$ 40 cm, where $h$, $l$, and $w$ denote the height, length, and width of the tank (without supports), respectively.
• Figure 3: Plot of the parameter space of the oloid in water-glycerol mixture, based on documented properties of glycerine solutions at 20 ° C glycerine1963. The used oloids have an equivalent diameter of $D_{\text{eq}} =$ 10.8 mm, and $D_{\text{eq}} =$ 21.6 mm. The black dots show the parameter values used in experiments.
• Figure 4: A raw image of an oloid captured by one of the high-speed cameras (left panel), and a reconstruction of the oloid using our orientation tracking algorithm described in Flapper2025 (right panel). An animation of the camera recording and the reconstruction is shown in the supplementary material.
• Figure 5: Snapshots of the oloid orientation for the two observed settling modes. The red arrow shows a pointing vector of the oloid, the blue line shows the path of the centre of mass. Snapshots of an experimentally measured oloid displaying a stable settling mode (a) for $\text{Ga} = 210$, with snapshots 0.6 s apart. Snapshots of a simulated oloid showing a stable settling mode (b) for $\text{Ga} = 10$. Snapshots of an experimentally observed tumbling oloid (c) for $\text{Ga} = 3500$, with snapshots 0.2 s apart. Snapshots of a simulated tumbling oloid (d) for $\text{Ga} = 100$.