scholarly journals On the slow motion of a self-propelled rigid body in a viscous incompressible fluid

2002 ◽  
Vol 274 (1) ◽  
pp. 203-227 ◽  
Author(s):  
Ana Leonor Silvestre
Keyword(s):  
Rigid Body ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Slow Motion

Slow Viscous Flow Between Rotating Concentric Infinite Cylinders With Axial Roughness

1962 ◽  
Vol 29 (1) ◽  
pp. 188-192 ◽  
Author(s):  
S. J. Citron
Keyword(s):  
Velocity Field ◽  
Incompressible Fluid ◽  
Viscous Flow ◽  
Viscous Incompressible Fluid ◽  
Slow Motion ◽  
Slow Viscous Flow ◽  
Angular Velocities ◽  
The Moment

This paper presents the solution to the problem of determining the velocity field and the moment necessary to sustain the motion of a viscous incompressible fluid between two concentric infinite cylinders, rotating with constant but different angular velocities, when the radii of the cylinders vary axially. The solution is obtained for cases when the equations of slow motion govern the problem. The roughness of each cylinder is assumed small compared to the smooth radius; the roughness need not be small compared to the spacing between the cylinders. Results are explicitly obtained for the case of sinusoidal roughness.

scholarly journals Controllability of low Reynolds numbers swimmers of ciliate type

2020 ◽  
Vol 26 ◽  
pp. 31
Author(s):  
Jérôme Lohéac ◽  
Takéo Takahashi
Keyword(s):  
Rigid Body ◽  
Incompressible Fluid ◽  
Control Problem ◽  
Vector Fields ◽  
Viscous Incompressible Fluid ◽  
Exact Controllability ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Minimal Dimension ◽  
Stokes Fluid

We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.

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