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Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

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Transport coefficients for the hard-sphere granular fluid.

Aparna Baskaran¹, James W Dufty, J Javier Brey

¹Department of Physics, University of Florida, Gainesville, Florida 32611, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

This study details Navier-Stokes hydrodynamics for inelastic hard spheres, providing exact expressions for cooling rate and transport coefficients. Results are compared to elastic systems, offering insights into granular fluid behavior.

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Area of Science:

Physics
Fluid Dynamics
Statistical Mechanics

Background:

Linear response methods were previously used for general Navier-Stokes order hydrodynamics.
The prior analysis encompassed normal and granular fluids with diverse collision rules.

Purpose of the Study:

Specialize general hydrodynamic expressions to smooth, inelastic, hard spheres.
Derive explicit formulas for key physical parameters.
Compare inelastic results with those for elastic systems.

Main Methods:

Application of linear response theory.
Mathematical derivation for specific particle interactions (inelastic hard spheres).
Comparative analysis between inelastic and elastic hard sphere systems.

Main Results:

Formally exact expressions for cooling rate, pressure, and transport coefficients.
Quantitative comparison of transport properties in inelastic versus elastic granular fluids.
Demonstration of specialized hydrodynamic parameters for inelastic collisions.

Conclusions:

The derived expressions provide a foundation for further analytical and numerical studies.
Highlights the distinct behavior of granular fluids under inelastic collisions.
Confirms the utility of linear response methods for complex fluid systems.