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Navier–Stokes Equations01:28

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Related Experiment Video

Updated: Feb 10, 2026

Simultaneous Measurement of Turbulence and Particle Kinematics Using Flow Imaging Techniques
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Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

B Lambert1, L Weynans1, M Bergmann1

  • 1Memphis Team, INRIA, F-33400 Talence, France.

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|May 20, 2018
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Summary

This study introduces a new lubrication model for simulating particle suspensions, improving accuracy in fluid dynamics simulations by accounting for short-range hydrodynamic forces. The method enhances predictions for particle interactions without assuming particle shape.

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Area of Science:

  • Fluid Dynamics
  • Computational Mechanics
  • Particle Physics

Background:

  • Lubrication forces are crucial for particle suspension dynamics.
  • These forces are often underestimated in direct numerical simulations.
  • Accurate modeling is essential for understanding particle-laden flows.

Purpose of the Study:

  • To develop a novel lubrication model for coupled solvers.
  • To accurately estimate unresolved hydrodynamic forces and torques.
  • To improve simulations of incompressible Navier-Stokes flows with particles.

Main Methods:

  • Coupling a volume penalization method with a discrete element method solver.
  • Implementing local corrections on particle surfaces.
  • Avoiding assumptions on global particle shape.

Main Results:

  • The model accurately estimates hydrodynamic forces and torques.
  • Corrections are applied locally, enhancing flexibility.
  • Validated against experimental data, showing comparable performance to existing models.

Conclusions:

  • The proposed model effectively captures lubrication forces in particle suspensions.
  • It offers a more versatile approach than models limited to spherical particles.
  • This advancement improves the fidelity of direct numerical simulations for complex particle flows.