Viscosity of colloidal suspensions

Abstract

Simple expressions are given for the Newtonian viscosity N ( ) as well as the viscoelastic behavior of the viscosity ( , ) of neutral monodisperse hard-sphere colloidal suspensions as a function of volume fraction and frequency over the entire fluid range, i.e., for volume fractions 0Ͻ Ͻ0.55. These expressions are based on an approximate theory that considers the viscosity as composed as the sum of two relevant physical processes: ( , )ϭ ϱ ( )ϩ cd ( , ), where ϱ ( )ϭ 0 ( ) is the infinite frequency ͑or very short time͒ viscosity, with 0 the solvent viscosity, ( ) the equilibrium hard-sphere radial distribution function at contact, and cd ( , ) the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the Péclet time scale P , the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity N ( )ϭ ( , ϭ0) agrees very well with the extensive experiments of van der Werff et al., ͓Phys. Rev. A 39, 795 ͑1989͒; J. Rheol. 33, 421 ͑1989͔͒ and others. Also, the asymptotic behavior for large is of the form ϱ ( )ϩ 0 A( )( P ) Ϫ1/2 , in agreement with these experiments, but the theoretical coefficient A( ) differs by a constant factor 2/ ( ) from the exact coefficient, computed from the Green-Kubo formula for ( , ). This still enables us to predict for practical purposes the viscoelastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.

The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens

“…7. Normalised e!ective Newtonian viscosity of a suspension of hard spheres ( / ), according to Verberg et al (1997) the process (Einstein 1906(Einstein , 1911; van der Wer! & de Kruif 1989; Jones et al 1992).…”

Response to “Comment on ‘The viscoelastic response of Brownian suspensions’ ” [J. Chem. Phys. 114, 3339 (2001)]

“…͑13͒ of Ref. 3. Having done so, the result they obtain for the Brownian contribution to the viscosity, B , can be expressed as a Padé approximation,…”

“…Despite its simplicity, it forms the basis for theories which predict a viscoelastic response that is in remarkably good agreement with experiment. 2,3 This would suggest that the model is quite adequate, thus providing a convenient means for predicting, either theoretically or numerically, the long time properties of suspensions. However, in order to obtain analytic results for the simple model further simplifications are required.…”

“…͑1͒ to the diffusion coefficient characterizing the motion of the particles in our model system, D in . In their paper, 3 Verberg et al do not specifically interpret the diffusion coefficient appearing in the Smoluchowski equation as the short time diffusion coefficient until, in Sec. VI, they consider the high frequency viscoelastic response.…”

“…In our paper, we made a comparison with the modecoupling theory of Verberg et al 3 Their approach basically involves substituting a wave vector, k, and volume fraction, , dependent ''cage'' diffusion coefficient, D c (k,), into the two particle Smoluchowski equation, valid at low densities. The cage diffusion coefficient they approximate by analogy with the hard sphere fluid.…”