Viscosity

In General > s.a. dark energy; fluids; Kinetic Theory; Stokes' Law; Transport.
* Idea: Viscosity is a fluid's resistance to gradual deformation by shear stress or tensile stress; It measures how local disturbances in the system are transmitted to the rest of the system through interactions, and depends on the strength of the interactions between its constituents; If those interactions are strong, neighboring parts of the fluid more readily transmit the disturbances through the system; Thus low shear viscosities, as in a perfect fluid, indicate significant interaction strength, while no interactions, as in an ideal gas, correspond to an infinite viscosity.
* Coefficient of viscosity: The constant of proportionality between the stress and the derivatives of the velocity in a fluid (when the velocity gradient is not too large, in terms of the mean free path), $P^~_{ij} = \eta\,\partial u^{\,j}/\partial x^i\;.$

* Temperature dependence: Molecular theory tells us that the viscosity of a gas tends to increase with temperature, that of a liquid tends to decrease; However, at low temperature a gas condenses to a liquid and then can become a solid, so viscosity increases with decreasing temperature and one expects to find a minimum at some intermediate temperature; The same behavior is expected in QCD.
@ General references: Desloge AJP(62)dec [coefficient of viscosity for a gas]; Viscardy cm/06/SHPMP [history]; letter PT(10)oct.
@ Related topics: news pn(08)may [shear thinning – as in ketchup]; Behroozi et al AJP(10)nov [measurement from the attenuation of capillary waves].

In Specific Systems > s.a. phenomenology of gravity [gravitational viscosity].
* Extreme viscosity: Vigorously stirring a suspension of micrometer-sized particles, such as cornstarch in water, can make the flowing fluid so viscous it behaves like a solid (shear thickening); Experiments indicate that the reason is increased friction between the particles forced into contact.
@ General references: Enss et al AP(11) [unitary Fermi gas]; Torrieri PRD(12) [ideal relativistic quantum fluid]; Lin et al PRL(15) [shear thickening]; Niethammer & Schubert a1903 [suspensions, Einstein's formula].
@ In cosmology: Disconzi et al PRD(15) + news tel(15)jul [and big rip].

Viscosity Bound
* Idea: We do not know of any fluid in nature that violates the bound $$\eta/s \ge \hbar/4\pi k^~_{\rm B}$$ (and see temperature dependence above).
* Kovtun-Starinets-Son bound: The conjecture, based on gauge-gravity duality, that there is a universal bound for the shear-viscosity-to-entropy-density ratio, given by $$\eta/s \ge \hbar/4\pi k^~_{\rm B}$$, at least for black holes in theories with a holographic interpretation; In general relativity, results by Thorne & Price on the membrane paradigm imply that for Kerr black holes $$\eta/s = \hbar/4\pi k^~_{\rm B}$$, and measurements on quark-gluon plasmas assumed to be modelled by the dual theories on the brane give results close to $$\hbar/4\pi k^~_{\rm B}$$; But the bound was shown to be violated in Gauss-Bonnet gravity, where $$\eta/s = \hbar/4\pi k^~_{\rm B}\, (1-8\lambda)$$ in the IR limit (λ is the Gauss-Bonnet coupling constant), and for black holes in $$f(R)$$ gravity results show that $$\eta/s = f'(R)\,\hbar/4\pi k^~_{\rm B}$$.
@ References: Kovtun et al PRL(05)ht/04 [proposal]; Cherman et al JHEP(08)-a0708 [re viability of conjecture]; Fouxon et al PRD(08)-a0710 [and generalized second law]; Brigante et al PRL(08)-a0802 [in Gauss-Bonnet gravity, and inconsistency from microcausality violation], PRD(08); Hod NPB(09)-a0907 [from thermodynamics], GRG(09)-a0905-GRF; Brustein & Medved PLB(10)-a0908 [proof]; Pal PRD(10)-a0910 [at finite coupling]; Schäfer Phy(09) [rev]; Shu PLB(10) [in Lovelock gravity]; Jakovac PRD(10) [of shear-viscosity to entropy-density ratio]; Johnson & Steinberg PT(10)may; Chirco et al PRD(10)-a1005 [from entanglement entropy in Rindler spacetime]; Kovtun et al PRD(11)-a1104 [absolute lower limit]; Cremonini MPLB(11)-a1108 [rev]; Rebhan & Steineder PRL(12) [violation in a strongly coupled anisotropic plasma]; Trachenko & Brazhkin a1912 [from fundamental physical constants].