65 research outputs found
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
The leading effect of fluid inertia on the motion of rigid bodies at low Reynolds number
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
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
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