Bi-velocity Hydrodynamics

Howard Brenner (MIT)

Thursday 13th March, 2008 16:00-17:00 515


Based on Boltzmann equation-based rarefied gas kinetic theory in conjunction with the principles of linear irreversible thermodynamics it is shown theoretically that traditional continuum fluid mechanics cannot be correctly described by means of a single velocity field. In effect, the classical mono-velocity Navier-Stokes-Fourier equations are shown by this rarefied gas example to be incomplete, a conclusion presumably applicable to liquids as well. Rather, two independent velocities are shown to be required. These two are identified physically in terms of the different outcomes of colorimetric and tracer-particle experiments arising when monitoring the respective trajectorial velocities in a nonisothermal gas of: (i) a dye or coloring agent, and (ii) a small physicochemically inert nonBrownian solid particle introduced into the gas. These two velocities are shown to correspond respectively to the fluxes of mass and of volume, with the difference between them representing a diffuse flux of volume. Our finding of the need for more than one velocity is noted to possess philosophical consequences extending beyond the realm of fluid mechanics.

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