# Nonlinear rheological behavior of a concentrated spherical silica suspension

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DOI: 10.1007/BF00368994

- Cite this article as:
- Watanabe, H., Yao, ML., Yamagishi, A. et al. Rheola Acta (1996) 35: 433. doi:10.1007/BF00368994

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## Abstract

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^{*} obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus *G*(*t*) was obtained for small step strain γ(≤0.2) while the nonlinear relaxation modulus *G*(*t*, γ) characterizing strong stress damping behavior was obtained for large γ(>0.2). *G*(*t*, γ) obeyed the time-strain separability at long time scales, and the damping function *h*(γ) (−*G*(*t*, γ)/*G*(*t*)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity η(γ) for small shear rates γ(< τ ^{−1}; τ = linear viscoelastic relaxation time) and shear-thickening for larger γ (>τ^{−1}). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, η + (*t*, γ) and η_{−} (*t*, γ). In the shear-thinning regime, the γ and τ dependence of η_{+}(*t*,γ) and η_{−}(*t*,γ) as well as the γ dependence of η(γ) were well described by a BKZ-type constitutive equation using the *G*(*t*) and *h*(γ) data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.