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Consider water flowing from a nozzle to a turbine vane. As the water hits the turbine vane, it exerts a force that causes it to move along the flow of direction. Force is an impact that changes an object's motion, shape, or orientation. Forces can be caused by physical contact, such as a push or pull, or through non-contact interactions, such as magnetic or gravitational forces. Force is a vector quantity with both magnitude and direction, and is measured in newtons (N) in the SI unit...
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Hydrodynamic interactions between two forced objects of arbitrary shape. II. Relative translation.

Tomer Goldfriend1, Haim Diamant2, Thomas A Witten3

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Hydrodynamic interactions between objects in viscous fluids typically don't cause relative translation. However, breaking spatial inversion symmetry, especially near boundaries, can induce object movement and repulsion.

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Area of Science:

  • Fluid dynamics
  • Low Reynolds number flows
  • Hydrodynamic interactions

Background:

  • Hydrodynamic interactions between two rigid spheres in unbounded fluids do not cause relative translation.
  • Effective pair-interactions vanish in configurations with spatial inversion symmetry.

Purpose of the Study:

  • Investigate relative translation of arbitrarily shaped objects in viscous fluids at zero Reynolds number.
  • Analyze how breaking inversion symmetry by system boundaries affects object interactions.
  • Examine time-dependent relative translation of self-aligning objects.

Main Methods:

  • Theoretical analysis of hydrodynamic interactions.
  • Numerical analysis extending previous work.
  • Study of objects in confined geometries and near obstacles.

Main Results:

  • Breaking inversion symmetry by boundaries induces interactions between spheres in confined geometries.
  • New predictions for object interactions near obstacles.
  • Interplay between orientational and translational interactions leads to object repulsion over time.

Conclusions:

  • System boundaries are crucial for inducing relative translation and repulsion between objects.
  • Repulsion dynamics differ for self-aligning objects (t^{1/3} separation) versus prolate spheroids (t separation).
  • Findings offer insights into particle dynamics in confined and complex fluid environments.