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B. U. Felderhof

Publications and source records attributed to B. U. Felderhof.

At least 37 records · Page 2Linked to original sources
arXiv2016

Swimming at small Reynolds number of a collinear assembly of spheres in an incompressible viscous fluid

Swimming at small Reynolds number of a linear assembly of identical spheres immersed in a viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The swimming velocity is deduced from the momentum balance equation for the assembly of spheres, and the mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocity and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated in terms of prescribed periodic displacements. Explicit calculations are performed for a linear chain of three identical spheres.

physics.flu-dyn↗
arXiv2016

Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia

An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation the flow potential near a small sphere is assumed to be dipolar, but near the large sphere it involves all higher order multipoles. The analysis is based on an exact result for the potential of a magnetic dipole in the presence of a superconducting sphere. Subsequently, the approximate added mass hydrodynamic interactions are used in a calculation of the swimming velocity and rate of dissipation of linear chain structures consisting of a number of small spheres and a single large one, with account also of frictional hydrodynamic interactions. The results derived for periodic swimming on the basis of a kinematic approach are compared with bilinear theory, valid for small amplitude of stroke, and with the numerical solution of the approximate equations of motion. The calculations cover the whole range of scale number between the friction-dominated Stokes limit and the inertia-dominated regime.

physics.flu-dyn↗
arXiv2016

Effect of fluid inertia on the motion of a collinear swimmer

The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be non-vanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.

physics.flu-dyn↗
arXiv2016

Stokesian swimming of a prolate spheroid at low Reynolds number

The swimming of a spheroid immersed in a viscous fluid and performing surface deformations periodically in time is studied on the basis of Stokes equations of low Reynolds number hydrodynamics. The average over a period of time of the swimming velocity and the rate of dissipation are given by integral expressions of second order in the amplitude of surface deformations. The first order flow velocity and pressure, as functions of spheroidal coordinates, are expressed as sums of basic solutions of Stokes equations. Sets of superposition coefficients of these solutions which optimize the mean swimming speed for given power are derived from an eigenvalue problem. The maximum eigenvalue is a measure of the efficiency of the optimal stroke within the chosen class of motions. The maximum eigenvalue for sets of low order is found to be a strongly increasing function of the aspect ratio of the spheroid.

physics.flu-dyn↗
arXiv2016

Stokesian swimming of a sphere at low Reynolds number

Explicit expressions are derived for the matrices determining the mean translational and rotational swimming velocities and the mean rate of dissipation for Stokesian swimming at low Reynolds number of a distorting sphere in a viscous incompressible fluid. As an application an efficient helical propeller-type stroke is found and its properties are calculated.

physics.flu-dyn↗
arXiv2016

Stokesian swimming of a sphere by radial helical surface wave

The swimming of a sphere by means of radial helical surface waves is studied on the basis of the Stokes equations. Explicit expressions are derived for the matrices characterizing the mean translational and rotational swimming velocities and the mean rate of dissipation to second order in the wave amplitude.

physics.flu-dyn↗
arXiv2016

Spinning swimming of Volvox by tangential helical wave

The swimming of a sphere by means of tangential helical waves running along its surface is studied on the basis of the Stokes equations. Two types of tangential waves are found. The first of these is associated with a pressure disturbance and leads to a higher rate of net rotation than the second one for the same power. It is suggested that the helical waves are relevant for the rotational swimming of Volvox.

physics.flu-dyn↗
arXiv2015

Effect of inertia on laminar swimming and flying of an assembly of rigid spheres in an incompressible viscous fluid

A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.

physics.flu-dyn↗
arXiv2015

Efficient swimming of an assembly of rigid spheres at low Reynolds number

The swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent is studied in low Reynolds number hydrodynamics. The instantaneous swimming velocity and rate of dissipation are expressed in terms of the time-dependent displacements of sphere centers about their collective motion. For small amplitude swimming with periodically oscillating displacements, optimization of the mean swimming speed at given mean power leads to an eigenvalue problem involving a velocity matrix and a power matrix. The corresponding optimal stroke permits generalization to large amplitude motion in a model of spheres with harmonic interactions and corresponding actuating forces. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres. A model of three collinear spheres with motion along the common axis is studied as an example.

physics.flu-dyn↗
arXiv2015

Optimization of flagellar swimming by a model sperm

The swimming of a bead-spring chain in a viscous incompressible fluid as a model of a sperm is studied in the framework of low Reynolds number hydrodynamics. The optimal mode in the class of planar flagellar strokes of small amplitude is determined on the basis of a generalized eigenvalue problem involving two matrices which can be evaluated from the mobility matrix of the set of spheres constituting the chain. For an elastic chain with a cargo constraint for its spherical head, the actuating forces yielding a nearly optimal stroke can be determined. These can be used in a Stokesian dynamics simulation of large amplitude swimming.

physics.flu-dyn↗
arXiv2015

Stokesian swimmers and active particles

The net steady state flow pattern of a distorting sphere is studied in the framework of the bilinear theory of swimming at low Reynolds number. It is argued that the starting point of a theory of interacting active particles should be based on such a calculation, since any arbitrarily chosen steady state flow pattern is not necessarily the result of a swimming motion. Furthermore, it is stressed that as a rule the phase of stroke is relevant in hydrodynamic interactions, so that the net flow pattern must be used with caution.

physics.flu-dyn↗
arXiv2014

Self-propulsion of a spherical electric or magnetic microbot in a polar viscous fluid

The self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field which polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.

physics.flu-dyn↗
arXiv2014

Collinear swimmer propelling a cargo sphere at low Reynolds number

The swimming velocity and rate of dissipation of a linear chain consisting of two or three little spheres and a big sphere is studied on the basis of low Reynolds number hydrodynamics. The big sphere is treated as a passive cargo, driven by the tail of little spheres via hydrodynamic and direct elastic interaction. The fundamental solution of Stokes' equations in the presence of a sphere with no-slip boundary condition, as derived by Oseen, is used to model the hydrodynamic interactions between the big sphere and the little spheres.

physics.flu-dyn↗
arXiv2014

Swimming of an assembly of rigid spheres at low Reynolds number

A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may interact with elastic forces. The analysis is based on the Stokes mobility matrix of the set of spheres, defined in low Reynolds number hydrodynamics. For small amplitude swimming optimization of the swimming speed at given power leads to an eigenvalue problem. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres.

cond-mat.soft↗
arXiv2014

Hydrodynamic interactions between a sphere and a number of small particles

Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirchhoff, and the result derived by Oseen for the Green tensor of Stokes' equations in the presence of a fixed sphere.

physics.flu-dyn↗
arXiv2014

Optimal translational swimming of a sphere at low Reynolds number

Swimming velocity and rate of dissipation of a sphere with surface distortions are discussed on the basis of the Stokes equations of low Reynolds number hydrodynamics. At first the surface distortions are assumed to cause an irrotational axisymmetric flow pattern. The efficiency of swimming is optimized within this class of flows. Subsequently more general axisymmetric polar flows with vorticity are considered. This leads to a considerably higher maximum efficiency. An additional measure of swimming performance is proposed based on the energy consumption for given amplitude of stroke.

physics.flu-dyn↗
arXiv2014

Jittery velocity relaxation of an elastic sphere immersed in a viscous incompressible fluid

Velocity relaxation of an elastic sphere immersed in a viscous incompressible fluid is studied on the basis of the equations of linear elasticity and the linearized Navier-Stokes equations. It is found that both translational motion after a sudden impulse and rotational motion after a sudden twist show jittery behavior in the long-time regime, with many reversals of velocity if the sphere is sufficiently flexible. In the extreme long-time regime the translational and rotational velocity relaxation functions each decay with a universal algebraic long-time tail. The added mass and the added moment of inertia of the sphere are found to vanish.

physics.flu-dyn↗