On the Trajectory of a Light Small Rigid Body in an Incompressible Viscous Fluid

In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid b...

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Bibliographic Details
Published in:Journal of nonlinear science 2024-06, Vol.34 (3), Article 42
Main Authors: Bravin, Marco, Nečasová, Šárka
Format: Article
Language:English
Subjects:
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Fluid flow
Incompressible flow
Incompressible fluids
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Rigid structures
Rigid-body dynamics
Theoretical
Viscous fluids
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Summary:In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity in the limit. We are able to consider the limit when the volume of the rigid bodies converges to zero while their densities are a fixed constant.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-024-10022-w