Force on a sphere via the generalized reciprocal theorem

An approach based on the generalized reciprocal theorem is presented to derive the well-known result for the drag force exerted on a rigid sphere translating in a viscous fluid in an arbitrary manner. The use of generalized reciprocal theorem allows one to bypass the calculation of stress distribution over the particle surface in order to compute the force

The leading effect of fluid inertia on the motion of rigid bodies at low Reynolds number

We investigate the influence of fluid inertia on the motion of a finite assemblage of solid spherical particles in slowly changing uniform flow at small Reynolds number, Re, and moderate Strouhal number, Sl. We show that the first effect of fluid inertia on particle velocities for times much larger than the viscous time scales as rootSl Re given that the Stokeslet associated with the disturbance flow field changes with time. Our theory predicts that the correction to the particle motion from that predicted by the zero-Re theory has the form of a Basset integral. As a particular example, we calculate the Basset integral for the case of two unequal particles approaching (receding) with a constant velocity along the line of their centres. On the other hand, when the Stokeslet strength is independent of time, the first effect of fluid inertia reduces to a higher order of magnitude and scales as Re. This condition is fulfilled, for example, in the classical problem of sedimentation of particles in a constant gravity field

A frictionless microswimmer

We investigate the self-locomotion of an elongated microswimmer by virtue of the unidirectional tangential surface treadmilling. We show that the propulsion could be almost frictionless, as the microswimmer is propelled forward with the speed of the backward surface motion, i.e. it moves throughout an almost quiescent fluid. We investigate this swimming technique using the special spheroidal coordinates and also find an explicit closed-form optimal solution for a two-dimensional treadmiler via complex-variable techniques.Comment: 6 pages, 4 figure

Stokesian jellyfish: Viscous locomotion of bilayer vesicles

Motivated by recent advances in vesicle engineering, we consider theoretically the locomotion of shape-changing bilayer vesicles at low Reynolds number. By modulating their volume and membrane composition, the vesicles can be made to change shape quasi-statically in thermal equilibrium. When the control parameters are tuned appropriately to yield periodic shape changes which are not time-reversible, the result is a net swimming motion over one cycle of shape deformation. For two classical vesicle models (spontaneous curvature and bilayer coupling), we determine numerically the sequence of vesicle shapes through an enthalpy minimization, as well as the fluid-body interactions by solving a boundary integral formulation of the Stokes equations. For both models, net locomotion can be obtained either by continuously modulating fore-aft asymmetric vesicle shapes, or by crossing a continuous shape-transition region and alternating between fore-aft asymmetric and fore-aft symmetric shapes. The obtained hydrodynamic efficiencies are similar to that of other low Reynolds number biological swimmers, and suggest that shape-changing vesicles might provide an alternative to flagella-based synthetic microswimmers

A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin

We develop a qualitative geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body theory. We then apply the theory to derive the basic qualitative properties of Purcell's swimmer.Comment: 24 pages, 12 figure

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.Comment: 14 pages, 5 figure

On the Mysterious Propulsion of Synechococcus

We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in the form of small amplitude traveling ridges along the S-layer above the helical track. The resulting fluid motion adjacent to the helical ribbon provides the propulsive thrust. A variation on the helical rotor model of [1] allows the motors to be anchored to the peptidoglycan layer, where they drive rotation of the track creating traveling helical waves along the S-layer. We derive expressions relating the swimming speed to the amplitude, wavelength, and velocity of the surface waves induced by the helical rotor, and show that they fall in reasonable ranges to explain the velocity and rotation rate of swimming Synechococcus