Preprint The effect of negative viscosity of a fluid flowing over a r...

Attributing viscosity to attractive interactions is a bit too simplistic, I am afraid. Gases certainly have a viscosity and can mostly be modelled as hard spheres without any attractive interactions. To me, the easiest way to think about (kinetic) viscosity \nu is to recall that it is the diffusion coefficient of momentum diffusion. Momentum diffuses, because particles scatter off each other and that happens with the collision frequency \omega and after path lengths of the mean free path \ell. And indeed, with the Boltzmann equation, one finds \nu ~ \ell^2\omega_c with a prefactor of order unity. No need for attractive interactions here. Just a finite scattering cross section.

Put differently, a negative viscosity would imply that velocity differences would inherently grow by themselves. I.e., a quiescent fluid would spontaneously decompose into counter-flowing regions. While something like that may exist, repulsive interactions are certainly not a sufficient ingredient

Prof. Samuel Reich

In calculating the damping of sound waves by bulk viscosity in reacting gases, several years ago, we got a negative bulk viscosity for very small ω τ values, the issue was the photo-ionized hydrogen plasm calculation. We calculated it in a non-self consistent way, but the net heat/cooling function L, strictly speaking with a self-consistent radiative transfer problem should be worked out should self-consistently in order to get the bulk viscosity positive for all ω τ values.

Best Regards.

The constitutive laws of classical fluid must verify the fundamental inequality of thermodynamics (second principle of thermodynamics). The hypothesis of the local state leads to the formulation of the Gibbs relation in terms of the material derivatives. Taking into account the equation of the rate of entropy production, this fundamental inequality indicates that the irreversibility in the fluid results from the processes of thermal conduction and the work of deformation of the medium by the viscous stresses; the rate of entropy production can be expressed as the sum of the rate of intrinsic dissipation and heat dissipation. So that theoretically the existence of negative viscosity does not contradict the second principle of thermodynamics if this sum (rate of production of entropy) remains positive.

See (in frensh):

(6) (PDF) Equations de la Mécanique du Fluide Classique ; Chapitre 2 : Lois de Conservation (researchgate.net)

Dear Colleague Contreras

Could you please provide us with references relating to your last post? I confess that I had trouble getting it.

Thank you in advance

Dear Colleague Till Kranz

Are you speaking about the Kinetic Theory of Gases?

As I wrote, negative viscosity requires repulsive force between the parts of the fluid. The energy for the resultant effect on flow comes from the potential energy of those forces. There breaking of conservation laws. An ideal gas cannot have it under normal conditions. There cannot be a much attraction to walls if there is to be negative vorticity near the walls.

Thank you for your reply

Do you consider that the hypothesis of the continuous medium remains valid in the situations mentioned?

Jamel Chahed

I see no reason things cannot be considered continuous but not uniform. It is hard to get a uniform sharply focused electron beam (the best candidate). The word focused means non-uniform. The whole question at present time just theory, until use can be found for it if it exists.

Got it ; thank you, Dear Samuel Reich

Dear Samuel Reich According to your statement, with a negative viscosity, the kinetic energy should be large on account of the potential. Also, the entropy of the entire material should be very high.

Hayder Ibrahim Mohammed

No, NO the potential gets converted to kinetic energy during the period of negative viscosity. I did not mean a very high velocity is always present. Potential is indication of lower entropy than the same thing with same energy at lower potential. It is the nature of world potential tends to become kinetic energy wit passage of time.

During the evolution of mesoscale vortices against the background of their deforming flow, one should expect the transfer of energy from vortices to filaments, i.e. from mesoscale movements to the submesoscale. This is a direct energy cascade, and it is connected with the unlimited pulling of vortices into filaments. According to theoretical calculations, the vortex energy decreases by 20-60% with a significant elongation of the core. Since only a vortex and a current are present in the physical system, it is natural to expect that the “lost” energy of the vortices will be redistributed back into the current. If we return to the idea of an ensemble of vortices as a geophysical turbulence, where vortices are generated by the flow and then interact energetically with it, then the phenomenon of energy return from turbulence during the flow is called the phenomenon of “negative viscosity” or reverse cascade of energy. Although there is still no complete clarity on the issue of vortex energy transfer over the size spectrum, nevertheless, the process of turning vortices into filaments should eventually lead to an integral redistribution of vortex energy from the mesoscale to the submesoscale (direct energy cascade), and a decrease in vortex energy during the same process of pulling returns energy to currents (reverse energy cascade or the phenomenon of negative viscosity).

From the second principle of thermodynamics to the formulation of the conservation equations of the Classical Fluid: The constitutive laws of classical fluid verify the fundamental inequality of thermodynamics (second principle of thermodynamics). The hypothesis of the local state leads to the formulation of the Gibbs relation in terms of the material derivatives. Taking into account the equation of the rate of entropy production, this fundamental inequality indicates that the irreversibility in the fluid results from the processes of thermal conduction and the work of deformation of the medium by the viscous stresses; the rate of entropy production can be expressed as the sum of the rate of intrinsic dissipation and heat dissipation. So, theoretically, the existence of negative viscosity does not contradict the second principle of thermodynamics if this sum (rate of production of entropy) remains positive. See more on (In French):

Chapter ECFM-Chapitre 2 : Lois de Conservation

Chapter ECFM-Chapitre 3 : Equations Générales du Fluide Classique

The Kinetic Molecular Theory is not limited to the dilute state of gases or the perfectly ordered state of crystal lattices, it also covers processes of reversible or irreversible changes. This book [1] shows how the kinetic theory of matter accommodates itself to apply to the progress of modern physics in classical statistical mechanics and in quantum statistical mechanics.

[1] Dorfman, J. R., van Beijeren, H., & Kirkpatrick, T. R. (2021). Contemporary kinetic theory of matter. Cambridge University Press.

Available on:

Book Contemporary Kinetic Theory of Matter

For a beam of charged particles (electrons, protons or ions but not mixed charges): The electro-static forces on each particle is in direction away from the center. The magnetic field is circumferential inducing a force on the outer particles also away from the center. All repulsive. Potential energy is released when the outer particles move. There is no violation energy conservation. The energy from the inner particles. If they charge a wall it repels them also. In tube the same happens. Negative viscosity can exist then.

It is obvious a medium of repealing particles will dynamics opposite that of one made of attracting particles. High positive vorticity is the result of attractive force between particles in a medium; examples are heavy weight motor oil and maple syrup. Electron beams are the medium with highest repulsion between parts.