STL-to-Stokeslet Computation of Mobility Tensors and Sedimentation Dynamics for Shaped Particles

TL;DR

This paper introduces an efficient numerical method to compute the hydrodynamic mobility tensor of shaped particles from STL files, enabling accurate prediction of sedimentation and motion in low Reynolds number fluids.

Contribution

It presents a novel surface discretization approach using stokeslets to calculate mobility tensors from 3D object files, validated against analytical and experimental data.

Findings

Validated against analytical solutions and experiments.

Demonstrated the impact of center of mass shifts on particle motion.

Provided a user-friendly tool for diverse applications in fluid mechanics and biophysics.

Abstract

Sedimentation is extremely common in nature, occurring throughout the atmosphere and oceans, and in every laboratory centrifuge. The shape and mass distribution of a particle uniquely determines its motion at low Reynolds number, and complex dynamics can emerge from even simple particle shapes. The dynamics are governed by the particle's hydrodynamic mobility tensor, which dictates the translational and rotational velocities given the forces and torques. However, to date the inference of the mobility tensor from the object shape has been cumbersome and tricky. Starting with an input file representing an object for a 3D printer, such as an STL file, here we present an efficient numerical framework to compute the mobility tensor by discretizing the particle surface into distributed point drag forces called stokeslets. We validate our results against analytical solutions of simple geometries and recent experimental measurements. With our calculated mobility tensors in hand, using standard transformation laws, we demonstrate the dramatic effect of shifting the center of mass from a center of symmetry: all initial orientations evolve into one, two, or three particular final motions dictated by the object. By providing a user-friendly and efficient framework to compute the mobility tensor and resulting particle dynamics, this work offers a broadly applicable tool for the soft-matter, fluid-mechanics, and biophysics communities, and facilitates the design of steerable particles under diverse external forces, with relevance to colloidal transport, biological locomotion, diffusion, and self-assembly.