On shear viscosity and the Reynolds number of magnetohydrodynamic turbulence in collisionless magnetized plasmas: Coulomb collisions, Landau damping, and Bohm diffusion

2009 ◽  
Vol 16 (8) ◽  
pp. 082307 ◽  
Author(s):  
Joseph E. Borovsky ◽  
S. Peter Gary
Keyword(s):  
Reynolds Number ◽  
Shear Viscosity ◽  
Landau Damping ◽  
Magnetized Plasmas ◽  
Magnetohydrodynamic Turbulence ◽  
Coulomb Collisions

scholarly journals Enskog kinetic theory for monodisperse gas–solid flows

2012 ◽  
Vol 712 ◽  
pp. 129-168 ◽  
Author(s):  
V. Garzó ◽  
S. Tenneti ◽  
S. Subramaniam ◽  
C. M. Hrenya
Keyword(s):  
Reynolds Number ◽  
Kinetic Theory ◽  
Gas Phase ◽  
Parameter Space ◽  
Shear Viscosity ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Solid Particles ◽  
Analytical Treatment ◽  
Starting Point

AbstractThe Enskog kinetic theory is used as a starting point to model a suspension of solid particles in a viscous gas. Unlike previous efforts for similar suspensions, the gas-phase contribution to the instantaneous particle acceleration appearing in the Enskog equation is modelled using a Langevin equation, which can be applied to a wide parameter space (e.g. high Reynolds number). Attention here is limited to low Reynolds number flow, however, in order to assess the influence of the gas phase on the constitutive relations, which was assumed to be negligible in a previous analytical treatment. The Chapman–Enskog method is used to derive the constitutive relations needed for the conservation of mass, momentum and granular energy. The results indicate that the Langevin model for instantaneous gas–solid force matches the form of the previous analytical treatment, indicating the promise of this method for regions of the parameter space outside of those attainable by analytical methods (e.g. higher Reynolds number). The results also indicate that the effect of the gas phase on the constitutive relations for the solid-phase shear viscosity and Dufour coefficient is non-negligible, particularly in relatively dilute systems. Moreover, unlike their granular (no gas phase) counterparts, the shear viscosity in gas–solid systems is found to be zero in the dilute limit and the Dufour coefficient is found to be non-zero in the elastic limit.

Admissible Reynolds numbers for Poiseuille flow in jet viscometer orifices

1975 ◽  
Vol 347 (1648) ◽  
pp. 47-60 ◽  
Keyword(s):  
Reynolds Number ◽  
Shear Viscosity ◽  
Reynolds Numbers ◽  
Viscosity Reduction ◽  
Fully Developed Flow ◽  
Low Reynolds Numbers ◽  
Constant Diameter ◽  
Low Reynolds ◽  
Low Rate ◽  
Poiseuille Equation

At low Reynolds numbers for which the flow through a jet viscometer orifice strictly obeys the Poiseuille equation, the effective hydrodynamic length L 0 which may be calculated from the volume flow rate, the applied pressure difference, the radius of the orifice, and the density and low rate of shear viscosity of the liquid is much larger than the length L of ‘constant diameter’ of the orifice. It was shown before that a close approach, say 95%, to fully developed flow in the ‘constant diameter’ section of these short orifices is possible at sufficiently low Reynolds numbers, but it is shown now that L 0 may be used to calculate the largest admissible Reynolds number for 95% approach to fully developed flow. The flow in jet visco-meter orifices may be described by the Poiseuille–Hagenbach equation. At very low Reynolds numbers there is strict Poiseuille flow. This is followed by a short range of Reynolds numbers in which the inertia force correction factor m ( see equation (1)) increases steeply with the Reynolds number to reach a plateau value at a diameter Reynolds number of about 20. Although L 0 is not constant over the whole range of admissible Reynolds numbers, it satisfies the Poiseuille-Hagenbach equation if it is used with the appropriate m -value for each orifice and flow condition. For quantitative measurements of the temporary viscosity reduction of a liquid by an applied shear stress, care must be taken to avoid the transition region in which m varies with Re , because the Reynolds number Re can only be calculated with the low rate of shear viscosity of the liquid. It is important to find the mean rate of shear for any particular temporary viscosity reduction. Within the admissible range of Reynolds numbers, this may be derived from the Poiseuille equation. It is shown that the temporary viscosity reduction curve of one liquid which was measured with three jet orifices of different m-Re characteristics was a unique curve.

scholarly journals Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number

2005 ◽  
Vol 17 (12) ◽  
pp. 125105 ◽  
Author(s):  
Anatoliy Vorobev ◽  
Oleg Zikanov ◽  
Peter A. Davidson ◽  
Bernard Knaepen
Keyword(s):  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Magnetohydrodynamic Turbulence

scholarly journals Shear viscosity due to Landau damping from the quark-pion interaction

2013 ◽  
Vol 88 (6) ◽  
Author(s):  
Sabyasachi Ghosh ◽  
Anirban Lahiri ◽  
Sarbani Majumder ◽  
Rajarshi Ray ◽  
Sanjay K. Ghosh
Keyword(s):  
Shear Viscosity ◽  
Landau Damping ◽  
Pion Interaction
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