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The three-dimensional coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body
Paul Fuchter1, Hermes Bloomfield-Gadêlha1
1Department of Engineering Mathematics and Bristol Robotics Laboratory, University of Bristol, Bristol, UK.
Journal of the Royal Society, Interface
|May 31, 2023
Summary
A new 3D coarse-graining method efficiently simulates elastic filaments, crucial for biological and engineering systems. This approach accelerates computations for complex structures like cilia and micro-robots, enabling broader research applications.
Area of Science:
- Computational physics and biophysics
- Mechanics of soft and biological matter
- Microfluidics and micro-robotics
Background:
- Elastic filaments are fundamental in biological and engineering systems, including cilia and artificial swimmers.
- Simulating these slender structures in 3D demands balancing elastic, body, active, and hydrodynamic forces.
- Existing methods often face challenges in efficiency and implementation for complex geometries and interactions.
Purpose of the Study:
- To present a generalized, efficient, and extensible 3D coarse-graining formulation for simulating elastic filaments.
- To enable the simulation of collections of 3D elastic filaments with full flexural and torsional deformations.
- To couple these filaments via non-local hydrodynamic interactions and include multi-body microhydrodynamics for arbitrary geometries.
Main Methods:
- Developed a 3D coarse-graining formulation utilizing exponential mapping of quaternions for efficient rotation tracking.
- Employed spheres as building blocks for constructing filaments and microstructures of arbitrary 3D geometry.
- Integrated non-local hydrodynamic interactions and multi-body microhydrodynamics for coupled simulations.
Main Results:
- Achieved computation times up to 150 times faster than direct quaternion implementations.
- Demonstrated the method's capability to simulate complex phenomena like bi-flagellated swimming and particle transport by cilia arrays.
- Validated the straightforward construction of arbitrary 3D geometries using spherical building blocks.
Conclusions:
- The presented 3D coarse-graining method offers an efficient and versatile tool for simulating elastic filaments in diverse applications.
- The formulation simplifies the simulation of complex micro-scale systems, including biological microorganisms and engineered micro-robots.
- The provided Matlab code facilitates further customization and extension for research in microhydrodynamics and soft matter physics.
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