Critical behavior of the non-Newtonian shear viscosity of colloidal systems

Abstract

The anomalous behavior of the ͑zero frequency͒ shear viscosity of colloidal systems on approach of the gas-liquid critical point is analyzed. As a result of hydrodynamic interactions, the anomalous behavior is found to be qualitatively different from that of molecular systems. On the basis of the asymptotic solution of the Smoluchowski equation for the shear rate dependent pair-correlation function, an expression for the non-Newtonian zero frequency viscosity of a near-critical suspension is derived. The viscosity depends on two dimensionless groups: on Ϫ1 d via a cutoff function and on ϰ␥ 4 via the structurefactor ͑ is the correlation length in the equilibrium system, d is the core diameter, and ␥ is the shear rate͒. The transition from weak to strong shear occurs at Ϸ1. The anomalous behavior of both the zero shear viscosity and the non-Newtonian characteristics is formally due to the fact that close to the critical point, where is large, a very small shear rate ␥ is sufficient to make a large number. The critical exponent for the zero shear viscosity is found to be equal to that of the correlation length. This exponent is much larger than for molecular systems, which is known to be very small ͑Ϸ0.03͒. The exponential behavior sets in at /dϷ3.

Strong Critical Enhancement of the Shear Viscosity of Colloidal Systems

“…This value agrees with some of the theories that have been developed in the past to describe anomalous behavior beyond the mean-field region [1-4]. Mean-field anomalous behavior of the shear viscosity of atomic and molecular systems is probably nonexistent.In a recent publication, one of the present authors (J. K. G. D.) predicted quite a different critical behavior of the shear viscosity for colloidal systems [5]. In addition to direct interactions, also present in molecular systems, there is another type of interaction particular to colloidal systems.…”

“…In a recent publication, one of the present authors (J. K. G. D.) predicted quite a different critical behavior of the shear viscosity for colloidal systems [5]. In addition to direct interactions, also present in molecular systems, there is another type of interaction particular to colloidal systems.…”

“…These so-called hydrodynamic interactions are the result of scattering of the shear flow field by the Brownian particles, which scattered flow field affects other Brownian particles in their motion. Such interactions are long ranged and are responsible for the much stronger divergence of the shear viscosity as compared to molecular systems.The theoretical prediction for the critical divergence of the shear viscosity h for Brownian systems is [5] hwhere h B is the viscosity in the absence of long ranged critical correlations, the so-called background viscosity, and h A is the additive anomalous contribution, which is proportional to the correlation length j in the unsheared suspension:h A~j .(2) In this Letter we present experimental results on both the divergence of the correlation length and the viscosity of a colloid polymer mixture. Without polymer the colloidal particles behave as hard spheres.…”

“…The theoretical prediction for the critical divergence of the shear viscosity h for Brownian systems is [5] h…”