Bulk Viscosity

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Bulk viscosity is a measure of a fluid's resistance to uniform compression or expansion, reflecting its ability to dissipate energy during volumetric changes. It quantifies the internal friction within a fluid when subjected to pressure variations, influencing the dynamics of fluid flow in various physical and engineering contexts.

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The Polyakov loop dependence of bulk viscosity of QCD matter

by Debmalya Mukhopadhyay

In this work, we show the dependence of bulk viscosity on Polyakov loop in 3+1 dimensional topologically massive model (TMM). This model contains equally massive non-Abelian gauge fields without spontaneous symmetry breaking. In earlier... more

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Black Holes in Bulk Viscous Cosmology

by Francesco Paolis

2010, International Journal of Theoretical Physics

We investigate the effects of the accretion of phantom energy with non-zero bulk viscosity onto a Schwarzschild black hole and show that black holes accreting viscous phantom energy will lose mass rapidly compared to the non-viscous case.... more

IG. 1: For an initial mass of black hole Mp = 10°’kg, the evolution of the mass parameter

FIG. 2: For an initial mass of black hole Mo = 10**kg, the evolution of m is plotted against the time n = M/Mpo — 1 is plotted against the logarithmic time with a = 10~° and ty = 101s.

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Buoyancy driven convection in near-critical and supercritical fluids

by Nusair Hasan

2012, International Journal of Heat and Mass Transfer

Buoyancy driven thermal transport in a pure fluid (carbon dioxide) near its gas-liquid critical point is investigated using a two-dimensional numerical model. A square enclosure is considered with side heating. For all cases considered,... more

In thermodynamics, a critical point specifies the conditions (temperature and pressure) at which a phase boundary ceases to Fig. 2 shows the density and specific heat vs. temperature dia- gram for carbon dioxide with changing pressure. The density at atmospheric pressure is almost constant, while the density in the supercritical-pressure condition widely varies across the phase interface from the liquid or gas phase to the supercritical fluid phase. Hence, even around 10K above the critical temperature Fig. 1. The p-v diagram for carbon dioxide. 2. Thermo-physical properties at supercritical state

Fig. 3. Ratio of bulk viscosity to shear viscosity (1,/{:) as a function of pressure and temperature for near-critical carbon dioxide. Fig. 2. Variation of density () and specific heat (cp) as functions of pressure and temperature for near-critical carbon dioxide.

study, the set of equations developed by Onuki [25] was used fo the determination of the bulk viscosity of supercritical carbor dioxide. Fig. 3 shows the ratio of bulk viscosity to shear viscosity ({/~) of supercritical carbon dioxide as a function of pressure and temperature near the critical point. The bulk viscosity tends to infinity when temperature and pressure approach critica values.

Fig. 6. Contours of steady state temperature inside the side heated enclosure filled with supercritical carbon dioxide far from the critical point (p;= 12.0 MPa, Tm = 325.0K) with Ra=10°, p’=6.26 x 107-', T=6.86 x 10°? and Th = 8.71 x 10-7; at (a) t=1.0s and (b) steady state. [Tmax = 325.3 K (left wall), Tmin = 324.7 K (right wall), 5T = 60 mK]. Fig. 5. Contours of steady state temperature inside the side heated enclosure filled with supercritical carbon dioxide near the critical point (p; = 7.38 MPa, T,, = 305.0 K) with Ra = 10°, p’ = 3.66 x 10-4, T =2.9 x 10-3 and T¢ = 3-88 x 10° at (a) t=1.0s and (b) steady state. [Tmax = 305.05 K (left wall), Twin = 304.95 K (right wall), oT = 10 mK].

Fig. 7. Velocity vectors (Ra= 10%) inside the side heated enclosure filled with supercritical carbon dioxide (a) near the critical point (p; = 7.38 MPa, T,, = 305.0 K, p' = 3.66 x 10-4, T = 2.9 x 10-? and T;,, = 3.88 x 10-°) and (b) far from the critical point (p; = 12.0 MPa, Tm = 325.0 K, p’ = 6.26 x 10-1, T =6.86 x 10°? and T,, = 8.71 x 10-7) at steady state.

Fig. 8. Variation of steady state spatially averaged Nusselt (Nu) number along the vertical walls as a function of Rayleigh (Ra) number for supercritical carbon dioxide far from the critical point.

Fig. 9. Variation of steady state spatially averaged Nusselt number as a function of T= (= 7) for different p’ = (252) for near-critical carbon dioxide with (a) 8 8 ° 8 Ra=5 x10 (b) Ra=1x10 and(c)Ra=5x10.

Fig. 10. Steady state spatially averaged Nusselt number (Nu) surface map as a function of the dimensionless temperature T’ = (;-"*) and pressure p’ = (22) for near-critical carbon dioxide at Ra = 10°.

Fig. 11. Variation of steady state spatially averaged Nusselt (Nu) number as a function of Rayleigh (Ra) number for supercritical carbon dioxide with different values of the parameter ‘f.

Fig. 12. Contours of temperatures inside a bottom heated enclosure at t= 1.5 s for near critical carbon dioxide (p;=7.38MPa, 1;=304.3K, p’=3.66 x 10-4, T =5.65 x 10-4 and T,, = 3.88 x 10°*) and Ra = 7.35 x 10° (a) with and (b) without the inclusion of bulk viscosity. [Tmax = 304.4 K (bottom wall), Tmin = 304.3 K (top wall), 6T = 1.0 mK].

Fig. 13. Velocity vectors inside a bottom heated enclosure at t=1.5s for near- critical carbon dioxide (p; = 7.38 MPa, T; = 304.3 K, p’ = 3.66 x 10~4, T’ =5.65 x 10-4 and T,,, = 3.88 x 10~°) and Ra = 7.35 x 10° (a) with and (b) without the inclusion of bulk viscosity.

Fig. 14. Spatial variation of temperature inside the enclosure at mid-plane (X/ L=0.5) at t=1.5s for near-critical carbon dioxide (p;= 7.38 MPa, T;= 304.3 K, p' =3.66 x 10-4, 7 =5.65 x 10-4 and Tc = 3.88 x 10-°) and Ra=7.35 x 10° with and without the effect of bulk viscosity.

Fig. 15. Temporal variation of spatially averaged Nusselt number (Nu) at the left wall (X/L=0.0) of the enclosure at t=1.5s for near-critical carbon dioxide (p; = 7.38 MPa, T; = 304.3 K, p' = 3.66 x 10-4, T’ =5.65 x 10-4 and T,, = 3.88 x 10-°) and Ra = 7.35 x 10° with and without the effect of bulk viscosity.

Fig. 16. Contours of viscosity ratio (j1,/44) inside a bottom heated enclosure at t=1.5s for near-critical carbon dioxide (p; = 7.38 MPa, T; = 304.3 K, p! = 3.66 x 1074, T =5.65 x 10-4 and T,,¢ = 3.88 x 10-5) and Ra=7.35 x 108 [(jtp//)max = 1200 (top wall), ({p//0)min = 50 (bottom wall), 5({tp/p0) = 50]. The temporal variation of spatially averaged Nusselt number at the left (heated) wall of the enclosure is shown in Fig. 15. At the beginning, the temporal heat transfer rate at the left wall is very high due to the heating. The value decreases as the system ap- proaches thermal equilibrium. It is observed that the case includ- ing the bulk viscosity effects exhibits a relatively smaller Nusselt number compared to that without the effect of bulk viscosity. This is mainly due to the larger effective viscosity in the system. For the case without the inclusion of bulk viscosity, the rapid increase and decrease in temporal Nusselt number around 1.0 ~ 1.3 s indicates the collapse of the bottom boundary layer and release of thermal

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Rotational relaxation and transition to turbulence

by Oleg Nerushev

1997, Physics Letters A

Using the same apparatus, it is experimentally shown that the transition from laminar flow to turbulence for two nearly identical gasses, CO and N,, is not identical, giving rise to the interpretation that rotational relaxation is... more

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Nonlinear bulk viscosity in FRW cosmology: a phase space analysis

by Giovanni Acquaviva

2015, Classical and Quantum Gravity

We consider a Friedmann-Robertson-Walker spacetime filled with both vis-cous radiation and nonviscous dust. The former has a bulk viscosity that is proportional to an arbitrary power of the energy density, i.e. , v z r µ n and viscous... more

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