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      Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model

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          Abstract

          Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for large-amplitude elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a ‘high viscosity’ parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5°–10°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.

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          Microscopic artificial swimmers.

          Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.
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            Boundary Integral and Singularity Methods for Linearized Viscous Flow

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              Flagellar Hydrodynamics

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                Author and article information

                Journal
                R Soc Open Sci
                R Soc Open Sci
                RSOS
                royopensci
                Royal Society Open Science
                The Royal Society Publishing
                2054-5703
                March 2015
                18 March 2015
                18 March 2015
                : 2
                : 3
                : 140475
                Affiliations
                [1 ]Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road , Cambridge CB3 0WA, UK
                [2 ]School of Mathematics, University of Birmingham , Edgbaston, Birmingham B15 2TT, UK
                [3 ]Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Mindelsohn Way, Edgbaston , Birmingham B15 2TG, UK
                [4 ]Wolfson Centre for Mathematical Biology, University of Oxford, Mathematical Institute , Woodstock Road OX2 6GG, UK
                [5 ]School of Engineering and Centre for Scientific Computing, University of Warwick , Coventry CV4 7AL, UK
                Author notes
                Author for correspondence: T. D. Montenegro-Johnson e-mail: tdj23@ 123456cam.ac.uk
                Article
                rsos140475
                10.1098/rsos.140475
                4448824
                d250725c-c9a5-4c03-b194-3d7e81fffb93
                © 2015 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
                : 25 November 2014
                : 17 February 2015
                Categories
                1001
                1009
                73
                25
                30
                Structural Biology and Biophysics
                Custom metadata
                March, 2015

                stokesian swimming,fluid–structure interaction,human sperm

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