Join us for this seminar by Maria Tatulea-Codrean (Cambridge) as part of the North West Seminar Series in Mathematical Biology and Data Sciences. Details of the full series can be found here https://www.cms.livjm.ac.uk/APMSeminar/
The talk will be hosted by the University of Liverpool and streamed via Zoom please contact carl.whitfield@manchester.ac.uk or bnvasiev@liverpool.ac.uk for the link, or sign up to the mailing list.
Abstract: Microswimmer motility has been a topic of great interest in the fields of mathematical biology and fluid mechanics, particularly in the last two decades. Microswimmers have had their every move watched by microscopes and every step predicted by equations of motion. Amongst them is the model organism Escherichia coli, a motile bacterium with a decidedly finite number of propellers or “flagella” (by which we mean that N>1 but not >>1). Bacteria with a single flagellum (N=1) can be reasonably well understood using the force-balance type of arguments put forward by Purcell (1976) and later improved on by Higdon (1979), while swimmers covered in cilia (N>>1) can be approached using the squirmer model proposed by Lighthill (1952) and extended by Blake (1971). But the N-flagella problem posed by multi-flagellated bacteria remains unsolved to this day.
In this talk, we will present recent theoretical advancements towards modelling the interactions between a pair of bacterial flagella (N=2); both short-range steric interactions due to the helical geometry of flagellar filaments 1 and long-range hydrodynamic interactions 2,3. Our approach builds on well-established asymptotic theories such as the slender-body theory of hydrodynamics and the method of multiple scales. We find novel applications of these methods to the topic of bacterial motility, and we investigate whether two rotating bacterial flagella can remain tangle-free and synchronize in phase with each other due to steric and hydrodynamic interactions, respectively. In the last part of the talk, we demonstrate that hydrodynamic interactions within a bundle of filaments (N>2) can lead to surprising effects on the swimming speed of a multi-flagellated bacterium 4.
References:
1 M. T?tulea-Codrean & E. Lauga. (2020) Geometrical constraints on the tangling of bacterial flagellar filaments. Scientific Reports, 10: 8406.
2 M. T?tulea-Codrean & E. Lauga. (2021) Asymptotic theory of hydrodynamic interactions between slender filaments. Physical Review Fluids, 6: 074103.
3 M. T?tulea-Codrean & E. Lauga. (2022) Elastohydrodynamic synchronization of rotating bacterial flagella. Physical Review Letters, 128: 208101.
4 M. T?tulea-Codrean & E. Lauga. (2023) In preparation.
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