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Fluid mechanics in fluids at rest.

Howard Brenner1

  • 1Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA. hbrenner@mit.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Independent tracer measurements yield different velocities in compressible flows, contrary to current fluid mechanics understanding. This discovery necessitates a new bipartite theory for fluid dynamics, applicable to both liquids and gases.

Area of Science:

  • Fluid mechanics
  • Continuum mechanics
  • Chemical engineering

Background:

  • Conventional fluid mechanics assumes a single fluid velocity, applicable to both compressible and incompressible flows.
  • Current experimental techniques using tracers like dyes or particles often assume they measure the same local fluid velocity.
  • The perception of liquids as incompressible can obscure the need for distinct velocity measures in non-isothermal flows.

Purpose of the Study:

  • To challenge the assumption of single fluid velocity measurements in compressible flows.
  • To demonstrate that different tracers measure fundamentally different fluid velocities in compressible flows.
  • To introduce the concept of bivelocity hydrodynamics for a more accurate modeling of fluid behavior.

Main Methods:

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  • Analysis of experimental thermophoretic particle-velocity data.
  • Theoretical examination of tracer behavior in compressible and incompressible fluid flows.
  • Comparison of dye-tracer (mass velocity) and particle-tracer (volume velocity) measurements.

    • Main Results:

    • Tracer-velocity equality holds only for incompressible flows.
    • In compressible fluids, dye tracers measure mass velocity (v), while inert particles measure volume velocity (v(v)).
    • Compressibility effects include pressure and temperature influences on fluid density.

    Conclusions:

    • Contemporary fluid mechanics, including Navier-Stokes-Fourier equations, is limited to incompressible flows.
    • A new bipartite theory, bivelocity hydrodynamics, is required for accurate modeling of compressible fluid dynamics.
    • This new framework is applicable to both liquids and gases, unifying their fluid mechanical descriptions.