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Bivelocity hydrodynamics. Diffuse mass flux vs. diffuse volume flux

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  • Brenner, Howard

Abstract

An intimate physical connection exists between a fluid’s mass and its volume, with the density ρ serving as a proportionality factor relating these two extensive thermodynamic properties when the fluid is homogeneous. This linkage has led to the erroneous belief among many researchers that a fluid’s diffusive (dissipative) mass flux and its diffusive volume flux counterpart, both occurring in inhomogeneous fluids undergoing transport are, in fact, synonymous. However, the existence of a truly dissipative mass flux (that is, a mass flux that is physically dissipative) has recently and convincingly been shown to be a physical impossibility [H.C. Öttinger, H. Struchtrup, M. Liu, On the impossibility of a dissipative contribution to the mass flux in hydrodynamics, Phys. Rev. E 80 (2009) 056303], owing, among other things, to its violation of the principle of angular momentum conservation. Unfortunately, as a consequence of the erroneous belief in the equality of the diffuse volume and mass fluxes (sans an algebraic sign), this has led many researchers to wrongly conclude that a diffuse volume flux is equally impossible. As a consequence, owing to the fundamental role played by the diffuse volume flux in the theory of bivelocity hydrodynamics [H. Brenner, Beyond Navier–Stokes, Int. J. Eng. Sci. 54 (2012) 67–98], many researchers have been led to falsely dismiss, without due consideration, the possibility of bivelocity hydrodynamics constituting a potentially viable physical theory, which it is believed to be. The present paper corrects this misconception by using a simple concrete example involving an isothermal rotating rigid-body fluid motion to clearly confirm that whereas a diffuse mass flux is indeed impossible, this fact does not exclude the possible existence of a diffuse volume flux and, concomitantly, the possibility that bivelocity hydrodynamics is indeed a potentially viable branch of fluid mechanics.

Suggested Citation

  • Brenner, Howard, 2013. "Bivelocity hydrodynamics. Diffuse mass flux vs. diffuse volume flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 558-566.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:558-566 DOI: 10.1016/j.physa.2012.09.013
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    References listed on IDEAS

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    1. Bardow, André & Christian Öttinger, Hans, 2007. "Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 88-96.
    2. Brenner, Howard, 2005. "Kinematics of volume transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 11-59.
    3. Bedeaux, Dick & Kjelstrup, Signe & Christian Öttinger, Hans, 2006. "On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 177-187.
    4. Brenner, Howard, 2006. "Fluid mechanics revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 190-224.
    5. Brenner, Howard, 2005. "Navier–Stokes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 60-132.
    6. Brenner, Howard & Bielenberg, James R., 2005. "A continuum approach to phoretic motions: Thermophoresis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 251-273.
    7. Brenner, Howard, 2009. "Bi-velocity hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3391-3398.
    8. Brenner, Howard, 2011. "Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier–Stokes–Fourier equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3216-3244.
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