Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids

Abstract

Starting from relativistic quantum field theories, Kovtun et al. (2005) have quite recently proposed a lower bound η/s ≥ /(4πk B ), where η is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient η and a thermodynamic quantity s. Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity η(T ) for the four heaviest alkalis is known to scale onto an 'almost universal' curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.

On the ratio of the shear viscosity to the density of entropy of the rare gases and H2,N2,

“…Therefore we can only state that on account of the existing thermophysical data the minimum of j is located near the critical point. Nevertheless this observation is supported by some global considerations [14], several theoretical arguments concerning helium gas [18] as well as experimental values on D 2 given in different data sources [36]. Especially j m % 8:4 Â 10 À12 Ks found at the critical point of D 2 seems to be quite reasonable in view of our present results displayed in Fig.…”

“…A few of them like He, N 2 , and H 2 O have been casually studied [1,13,12]. A general but more refined analysis was given by March and co-workers [14] who additionally considered NH 3 and dense alkali metals [15], too. They found that also for ordinary systems the inequality j P j 0 holds and the minimum value j m is observed at or very near the critical point.…”

Basic theory and some applications concerning the ratio of shear viscosity to entropy density in dense fluids

“…Because of the continuing fundamental interest in this ratio, the present Letter begins by summarising recent fundamental theoretical predictions beyond those referred to in [1]. Then, following this, we shall consider a model equation of state going back to a proposal by Chapman and March [4], which we shall bring into contact with [1] in relation to results presented there for the number density versus temperature T under isobaric conditions for the dense fluids H 2 O and NH 3 .…”

“…In a recent study, the present authors have discussed, with examples of monatomic insulating liquids like argon, and metallic fluids, in particular the alkali metals [1] and the proposed lower bound for the ratio /s [2,3]. Here, denotes the shear viscosity, while s is the entropy density.…”

“…Then, following this, we shall consider a model equation of state going back to a proposal by Chapman and March [4], which we shall bring into contact with [1] in relation to results presented there for the number density versus temperature T under isobaric conditions for the dense fluids H 2 O and NH 3 .…”