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      The three-dimensional coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics

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          Abstract

          Elastic filaments are vital to biological, physical and engineering systems, from cilia driving fluid in the lungs to artificial swimmers and micro-robotics. Simulating slender structures requires intricate balance of elastic, body, active and hydrodynamic moments, all in three dimensions. Here, we present a generalized three-dimensional (3D) coarse-graining formulation that is efficient, simple-to-implement, readily extendable and usable for a wide array of applications. Our method allows for simulation of collections of 3D elastic filaments, capable of full flexural and torsional deformations, coupled non-locally via hydrodynamic interactions, and including multi-body microhydrodynamics of structures with arbitrary geometry. The method exploits the exponential mapping of quaternions for tracking 3D rotations of each interacting element in the system, allowing for computation times up to 150 times faster than a direct quaternion implementation. Spheres are used as a ‘building block’ of both filaments and solid microstructures for straightforward and intuitive construction of arbitrary three-dimensional geometries present in the environment. We highlight the strengths of the method in a series of non-trivial applications including bi-flagellated swimming, sperm–egg scattering and particle transport by cilia arrays. Applications to lab-on-a-chip devices, multi-filaments, mono-to-multi flagellated microorganisms, Brownian polymers, and micro-robotics are straightforward. A Matlab code is provided for further customization and generalizations.

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          Most cited references84

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          The hydrodynamics of swimming microorganisms

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            Development of a sperm-flagella driven micro-bio-robot.

            A new biohybrid micro-robot is developed by capturing bovine sperm cells inside magnetic microtubes that use the motile cells as driving force. These micro-bio-robots can be remotely controlled by an external magnetic field. The performance of micro-robots is described in dependence on tube radius, cell penetration, and temperature. The combination of a biological power source and a microdevice is a compelling approach to the development of new microrobotic devices with fascinating future applications.
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              Physics of microswimmers—single particle motion and collective behavior: a review

              Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
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                Author and article information

                Contributors
                Role: Formal analysisRole: InvestigationRole: MethodologyRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: SupervisionRole: Writing – original draftRole: Writing – review & editing
                Journal
                J R Soc Interface
                J R Soc Interface
                RSIF
                royinterface
                Journal of the Royal Society Interface
                The Royal Society
                1742-5689
                1742-5662
                May 31, 2023
                May 2023
                May 31, 2023
                : 20
                : 202
                : 20230021
                Affiliations
                Department of Engineering Mathematics and Bristol Robotics Laboratory, University of Bristol, , Bristol, UK
                Author information
                http://orcid.org/0000-0002-1385-5492
                http://orcid.org/0000-0001-8053-9249
                Article
                rsif20230021
                10.1098/rsif.2023.0021
                10230328
                37254703
                f2a655d5-aba7-47fa-bfe1-9d70c90c8c9a
                © 2023 The Authors.

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                : January 15, 2023
                : April 28, 2023
                Funding
                Funded by: Engineering and Physical Sciences Research Council, http://dx.doi.org/10.13039/501100000266;
                Categories
                1004
                30
                18
                25
                Life Sciences–Mathematics interface
                Research Articles

                Life sciences
                elastohydrodynamics of filaments,microhydrodynamics,fluid–structure interaction,elastic filaments in three dimensions,cilia and flagella,microorganisms and microswimmers

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