Investigation Of Wall Effects On Self-propulsion Of Micro-swimmer

Many microorganisms in nature,such as sperms,bacteria and so on,can propel themselves by undulating their flagella.Due to the very small size and low speed,the Reynolds number of the flow induced by the microorganism migration is extreme low and the migration is affected significantly by the external environments,such as the surface of the contractive tract.The study about the propulsion mechanisms of microswimmers is helpful to understand some interesting behaviors of microorganisms and modulate their migration.And it also provides the fundamental knowledge to develop bionic micro/nano-scale robots.In this thesis,numerical simulation and asymptotic analysis are used to study the migration of a micro-swimmer with a single flagellum through a channel and the influence of the channel wall with different configurations.The corresponding results and conclusions are briefly given as follows:Firstly,a numerical frame based on Immersed Boundary Method(IBM)and Lattice Boltzmann Method(LBM)is established to simulate the flow and the locomotion of the swimmer through a two-dimensional or three-dimensional channel with vibrating walls.To overcome the limitation of the simulation size and reduce the computation cost in regular LBM,a scaling coefficient is introduced to construct a similar flow where only the Reynolds number is identical with the original flow.Then the similar flow is simulated effectively and the variables of the original flow are obtained by the similarity transformation.The method is validated by several cases which are solved by perturbation analysis or other numerical methods.Compared to the simulation of the original flow,with a felicitous coefficient,the relative error of the present method for the similar flow is within 5%and the computation cost is reduced to 1%.Therefore,the present method has a good balance between the efficiency and the accuracy.Then,the migrations of the micro-swimmer are simulated in different channels using the present numerical method.It is shown that the influence of the wall can’t be neglected when the distance between the wall and the swimmer is less than the wavelength of the flagellum beating.With an identical beating motion of the flagellum,if the swimmer is closer to the wall,the propulsion speed as well as the work rate becomes larger.When the swimmer is close to a single plain wall,the swimmer is pulled towards the wall.However,in axisymmetric channel,the circular wall pushes the swimmer towards the axis.The influence of the wavy wall is similar to the plain wall,i.e.,the selfpropelled velocity by the flagellum is enhanced but no extra propulsion is generated.On the contrary,the waving wall has a significant impact on the swimmer migration and provides an additional propulsion with the same direction of the wall waving propagation.The propulsion of the waving wall is independent of the self-propulsion of the beating flagellum,which can be considered as a result of the linear characteristic of the flow with low Reynolds number,and the influences of the wall waving parameters on the propulsion speed are investigated in detail.The asymptotic analysis is used to study further the influence of the waving wall on the micro-swimmer migration.Due to the linear characteristics of low Reynolds number flow,the propulsion of the waving wall is isolated from the beating flagellum propulsion.Then,with the assumption of the waving amplitude is much smaller than the wavelength,the flow induced by waving wall is solved in two-dimensional channel and in axisymmetric tube respectively.The expressions of the solutions are different between the two-dimensional and axisymmetric flows,but the flow characteristics are similar.Zero-order solution is a static flow and the first order solution implies an oscillatory flow,which make no contribution to the propulsion.The second order solution contains a net flow with the same direction of wall waving,which is the fundament of the waving wall propulsion.Compared to numerical simulation results,the asymptotic solutions predict very well the migration of a finite swimmer propelled by the waving wall with a small amplitude in two-dimensional or asymmetric channel.When the amplitude increases,higher order solution should be considered to correct the prediction of the waving wall effect.The wall influence range in the axisymmetric tube is much larger than in the two-dimensional case.The axisymmetric solution correctly captures the vorticity feature in three-dimensional channel and is more appropriate for predicting the propulsion of the waving wall with small amplitude in real world.