Semiclassical law for the apparent viscosity of non-Newtonian fluids: An analogy between thixotropy of fluids and sintering of solids

Abstract

A theory is presented to describe the apparent viscosity of thixotropic fluids as a function of the rate of shear. It represents the extension of a semiclassical approach that was previously formulated to deal with matter densification phenomena in solids starting from the state equation of the medium. In this context, the Debye expression for the Helmholtz free energy has been provided with a density of vibrational modes that accounts for atomic and microstructural changes occurring at the frequency scale of momentum transport (see diffusion). Working out the steady-state condition with respect to time gives an equation relating reduced apparent viscosity (η̃) and shear rate (γ̃) through the temperature value (θ*) that is energetically equivalent to the medium vibrations implied. Viscosity also turns out to depend on the Debye temperature θD (see φ∼θ*/θD) and an equivalent Gruneisen parameter (μ), defined with respect to viscosity variations. Increasing φ in pseudoplastic and dilatant media, respectively, increases and decreases η̃, which always increases with increasing μ. The analogy between dilatancy/sintering and pseudoplasticity/desintering is suggested, and a correspondence between matter and momentum transports is traced on the basis of the phononic spectrum properties. Application to experimental measurements are presented and discussed for aqueous monodispersions of polystyrene (PS) latex particles, aqueous glycerol solutions of partially hydrolyzed polyacrylamide (PHPAA) at different sodium chloride (NaCl) concentrations, polymethylmethacrylate (PMMA) suspensions in dioctylphthalate (DOP), and for a molecularly thin liquid film of octamethylciclotetrasiloxane (OMCTS). Best fit coefficients for φ and μ have been constrained to the Debye temperature and the effective low-shear viscosity (η0) according to their dependences upon the suspended volume fraction (φ), θD=θD(φ), and η0=η0(φ), and the agreement with experimental data is quite satisfactory in all cases here examined. It is then suggested that the viscous character of a liquid can be described in terms of a coupling between Brownian diffusion and phonon wave motion.