Numerical Study On The Propulsion Of Flexible Flagella At Low Reynolds Number

Microorganisms are ubiquitous in nature and affect many biological processes such as reproduction and infection.Most microorganisms swim at low Reynolds number and use flexible flagella for propulsion.The beat pattern of a flexible flagellum is the result of the combined effect of its structure and external flow.The study of the propulsion of flexible flagella facilitates the development of miniature swimming robots which could be used inside the human body in the future.In this thesis,we considered flexi-ble flagella as elastic filaments with bending plane waves to understand the propulsion mechanism of flagella at low Reynolds number.Asymptotic analysis and numerical simulation were used to study the effects of flagellar structure,and internal/external driving on the propulsion of flexible flagella,and to explore some strategies to improve the propulsion performance of bionic flagella.In order to investigate the influence of the interactions between the different parts of microswimmer,different methods were adopted for the treatment of viscous flow and swimming head,such as asymptotic analysis and the regularized Stokeslets method in free-space and outside a solid sphere.The comparative analysis shows that when the parts of the microswimmer are close to each other,the hydrodynamic interactions is enhanced,which brings significant quantitative differences on propulsion performance.Inspired by the swimming of biflagellate alga Chlamydomonas reinhardtii,we studied the influence of the uniform intrinsic curvature of filament on its thrust.The results show that the intrinsic curvature of filaments affects the magnitude and direc-tion of the thrust generated by the flagella.When the intrinsic curvature is small,the deflection angle of the direction of thrust is linearly related to the intrinsic curvature.According to the understanding of this directional characteristic,a symmetrically actu-ated double-filament was constructed.The magnitude and direction of the thrust can be directly controlled by the tilt angle and the intrinsic curvature,and the maximum thrust can be several times the filament with zero intrinsic curvature.For the displacement-driven hinged filaments,the introduction of intrinsic curvature can significantly increase the thrust,and the maximum gain can be more than three times.According to the understanding of thrust,we designed a microswimmer consisting of a spherical head and a pair of symmetrically actuated elastic filaments.Asymptotic analysis and numerical simulation were carried out to study the propulsion performance of the microswimmer.We investigated the effects of the uniform intrinsic curvature,tilt angle,head size and oscillation amplitude on the swimming speed and propulsion effi-ciency of the microswimmer.It was found that by adjusting the intrinsic curvature and tilt angle of the filaments,the swimming speed and propulsion efficiency can be greatly improved.It is interesting to find that the swimming direction can also be reversed:a swimmer with filaments bent inwardly swims toward the head,whereas a swimmer with filaments bent outwardly swims toward the tail.Furthermore,when the filament is close to the head,the hydrodynamic interactions between the filament and the head can significantly enhance the propulsion performance of the swimmer.Based on the sliding control model of biological flagella,we numerically studied the problem of self-organized swimming with a filament undergoing spontaneous os-cillations driven by the internal molecular motor.The results show that as the motor activity increases,the waveform of filament changes from a tip-to-base(retrograde)wave to a base-to-tip(anterograde)wave.Meanwhile,the swimming direction reverses from backward swimming to forward swimming,and the speed of swimming increases significantly after the transition.The component analysis of the waveform shows that the principal modes before and after the transition are significantly different and the waveform after the transition is closer to that of a real spermatozoon.