Reciprocal swimming at intermediate Reynolds number

Derr, Nicholas J.; Dombrowski, Thomas; Rycroft, Chris H.; Klotsa, Daphne

doi:10.48550/arxiv.2202.03669

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The expressions similar to Eqs. (6.3) and (6.4) derived by Derr et al 9 are the same apart from numerical factors. The potential flow appears only in the single sphere added mass.…”

Section: Small Amplitudesupporting

confidence: 64%

“…However, the numerical solution of the Navier-Stokes equations by Dombrowski and Klotsa 8 showed that at high frequency the system shows a transition with a reversal of the direction of swimming. Recently Derr et al 9 analyzed the flow about an oscillating dimer at small amplitudes on the basis of the Navier-Stokes equations. They found a reversal of swimming velocity at high frequency due to a boundary layer effect, similar to that found by Riley for steady streaming about a single sphere 10 .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing the Mean Swimming Velocity of a Model Two-sphere Swimmer

Felderhof

2022

Preprint

View full text Add to dashboard Cite

The swimming of a two-sphere system oscillating in a viscous fluid is studied on the basis of simplified equations of motion which take account of both friction and inertial effects. In the model the friction follows from an Oseen approximation to the mobility matrix, and the inertial effects follow from a dipole approximation to the added mass matrix. The resulting mean swimming velocity is evaluated analytically in a first harmonics approximation. For specific choices of the parameters this is compared with the exact result following from a numerical calculation including higher harmonics. The Oseen-Dipole model is compared with the simpler Oseen* model, in which the added mass effects are approximated by just the effective mass of the single spheres and dipole interactions are neglected. The expression for the mean swimming velocity can be reduced to a dimensionless scaling form. For given viscosity and mass density of the fluid the frequency of the stroke and the ratio of radii can be chosen such that the swimming velocity is optimized.

show abstract

“…The expressions similar to Eqs. (6.3) and (6.4) derived by Derr et al 9 are the same apart from numerical factors. The potential flow appears only in the single sphere added mass.…”

Section: Small Amplitudesupporting

confidence: 64%