Elastohydrodynamics of actuated slender bodies in Stokes flows: methods, tools, and simulations of microscale motility

Hall-McNair, Atticus L. ORCID: 0000-0002-3142-5621 (2022). Elastohydrodynamics of actuated slender bodies in Stokes flows: methods, tools, and simulations of microscale motility. University of Birmingham. Ph.D.

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Countless microorganisms use slender elastic filaments to affect and traverse their surroundings. From the metachronal synchronisation of tracheal cilia to transport mu- cus, to the propulsive undulatory motion of sperm flagella, cells of all shapes and sizes use filament-like structures in a variety of fluid environments. The key physics in such environments arise from the interactions between slender-body filament-like elastic structures comprising the organism and surrounding viscous fluid. Understanding the coupled elastohydrodynamics of microscale propulsive mechanisms can provide in- sights into cell ultrastructure and rheology, paving the way for experimental studies and data interpretation, and suggesting novel diagnostics useful to researchers and clinicians alike.

In this thesis, we present two mathematical models for describing the dynamics of elastohydrodynamic filaments, in particular for simulating the motion of human sper- matozoa. Both methods are accompanied by bespoke implementations in open source MATLAB® code. The methods, dubbed the EIF and SPX methods, differ principally in dependent variables, which is the angle made between the filament centreline and a fixed axis in the EIF, and nonplanar centreline position, tension, and twist curvature in the SPX model. Key considerations in both approaches are (a) accuracy, improving upon many de-facto standard approaches by considering nonlocal hydrodynamic in- teractions and nonlinear geometries, (b) generalisability, so that the proposed methods can be applied to a variety of problems in a straightforward manner, and (c) efficiency, to reduce the formidable computational requirements that have historically stood as barriers to entry for rapid and reliable simulation studies. The methods developed de- rive from exploiting the slenderness property of the propulsive structures (i.e. cilia and flagella); auxiliary structures such as cell bodies or heads are not required to be slender provided the overall cell length is much longer than the width.

The EIF method is formulated and applied to simulate groups of planar active and passive filaments in quiescent fluid, shear flows, and sedimenting due to gravity. By using novel discretisation techniques and exploitation of optimised MATLAB® built-in algorithms, the resulting numerical implementation enables rapid simulations on even modest readily-available computer hardware.

Expanding upon the EIF, the SPX method provides a model for simulating filaments and monoflagellate cells moving in three dimensions. Maintaining accuracy and non- local interactions in the fluid dynamics through the method of regularised stokeslets, the elasticity model is generalised to account for arbitrary bend and twist deforma- tions. The presented tools and methodology are applied to simulate human spermato- zoa locomoting through a rhythmic twist and bend motion. Results indicate that the rate of axial rolling exhibited by nonplanar swimmers is reduced in the presence of a plane wall, with the rate of reduction dependent on the angle of approach towards the boundary and a dimensionless parameter characterising the relative ratio of twist drag to viscous drag in the system.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Smith, David J.UNSPECIFIEDorcid.org/0000-0002-3427-0936
Gallagher, Meurig T.UNSPECIFIEDorcid.org/0000-0002-6512-4472
Licence: All rights reserved
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/12569


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