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