Note on the thermodynamic state of laminar flow and on the viscosity of liquids

Fluids in a steady state of laminar flow (shear) are not in their thermodynamic equilibrium states. They have more energy and (or) less entropy than their corresponding static states.Phenomenological considerations suggest that in the case of 'ideal' liquids, shear states involve dilational energy increases, while in the case of ideal gases shear states involve entropy decreases associated with distortions of momentum fluxes.It is shown that the viscosities of some liquids (metals, hydrocarbons, water, etc.) can be described approximately by the equation[Formula: see text]where η is the viscosity, β the compressibility, D the coefficient of self-diffusion, M the molecular weight, ρ the density, and N v Avogadro's number. F measures the strain or effective dilation necessary for a 'layer' to flow over an adjacent 'layer'. Ideally F should be about 0.06 but varies from about 0.05 for metals to 0.14 for water.Equation [a] implies that liquids in a state of laminar flow are somewhat dilated compared with the static state at the same temperature and pressure. The density change as a function of the velocity gradient u′ is given by[Formula: see text]