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Updated: Apr 18, 2026

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Published on: February 17, 2019
Hydrodynamic interactions between a sphere and a number of small particles
Maria L Ekiel-Jeżewska1, B U Felderhof2
1Department of Mechanics and Physics of Fluids, Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiegop 5B, 02-106 Warsaw, Poland.
This study provides exact formulas for hydrodynamic interactions between a sphere and small particles in a viscous fluid. These findings advance understanding of low Reynolds number fluid dynamics for particle systems.
Area of Science:
- Fluid dynamics
- Low Reynolds number hydrodynamics
- Multibody particle interactions
Background:
- Understanding hydrodynamic interactions is crucial in fluid dynamics.
- Previous models often simplify complex particle behaviors in viscous fluids.
Purpose of the Study:
- To derive exact mathematical expressions for hydrodynamic interactions.
- To analyze interactions involving a sphere and multiple small particles in a viscous fluid.
Main Methods:
- Utilizing Stokes equations for low Reynolds number flow.
- Combining solutions for flow around a sphere (Stokes, Kirchhoff).
- Applying Oseen's solution for the Green tensor in a sphere's presence.
Main Results:
- Exact expressions for pair and three-body hydrodynamic interactions.
- Detailed analysis of fluid flow influenced by particle configurations.
Conclusions:
- The derived expressions offer precise predictions for particle dynamics.
- This work provides a foundational tool for simulating complex fluid-particle systems.
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