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

摘要

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 (~) and shear rate (~) through the temperature value (9*) that is energetically equivalent to the medium vibrations imp1ied~ Viscosity also turns out to depend on the Debye temperature 9D (see (p~ 9/9~) and an equivalent Gruneisen parameter (p), defined with respect to viscosity variations. Increasing p in pseudoplastic and dilatant media, respectively, increases and decreases i~, which always increases with increasing p. 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 (NaCI)concentrations.olymethylmethacrvlate (PMMA) suspensions in dioctylphthalate (DOP). and for a molecularl~ tam liquid film of octarnethylciclotetrasiloxane (OMCTS). Best fit coefficients for ~ and ~ ha’.e ~ constrained to the Debye temperature and the effective low-shear viscosit’ ~ xrd~ a~dependences upon the suspezKled vo~unie frmnon gd’). 6D=90(dul. and ~ ~ agreement with experiinensal ~a is satisfattimy in all cases here caL ksuggested that the viscous chwta~ of a Iq.iid ~ be kaer~ied in wm~s of nw Brownian diffusion and phonon wave mohim.