Viscosity of Colloidal Suspensions

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $\phi$ and frequency $\omega$ over the entire fluid range, i.e., for volume fractions $0 < \phi < 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $\eta (\phi,\omega) = \eta_{\infty}(\phi) + \eta_{cd}(\phi,\omega)$, where $\eta_{\infty}(\phi) = \eta_0 \chi(\phi)$ is the infinite frequency (or very short time) viscosity, with $\eta_0$ the solvent viscosity, $\chi(\phi)$ the equilibrium hard sphere radial distribution function at contact, and $\eta_{cd}(\phi,\omega)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'{e}clet time scale $\tau_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $\eta_N(\phi) = \eta(\phi,\omega = 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $\omega$ is of the form $\eta_{\infty}(\phi) + A(\phi)(\omega \tau_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(\phi)$ differs by a constant factor $2/\chi(\phi)$ from the exact coefficient, computed from the Green-Kubo formula for $\eta(\phi,\omega)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.Comment: 51 page

Transport in a highly asymmetric binary fluid mixture

We present molecular dynamics calculations of the thermal conductivity and viscosities of a model colloidal suspension with colloidal particles roughly one order of magnitude larger than the suspending liquid molecules. The results are compared with estimates based on the Enskog transport theory and effective medium theories (EMT) for thermal and viscous transport. We find, in particular, that EMT remains well applicable for predicting both the shear viscosity and thermal conductivity of such suspensions when the colloidal particles have a ``typical'' mass, i.e. much larger than the liquid molecules. Very light colloidal particles on the other hand yield higher thermal conductivities, in disagreement with EMT. We also discuss the consequences of these results to some proposed mechanisms for thermal conduction in nanocolloidal suspensions.Comment: 13 pages, 6 figures, to appear in Physical Review E (2007

Mesoscopic two-phase model for describing apparent slip in micro-channel flows

The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactins. The weakly-inhomogeneous limit of this model is solved analytically. The present mesoscopic approach permits to access much larger scales than molecular dynamics, and comparable with those attained by continuum methods. However, at variance with the continuum approach, the existence of a gas layer near the wall does not need to be postulated a priori, but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is therefore argued that a mesoscopic Lattice Boltzmann approach with non-ideal fluid-fluid and fluid-wall interactions might achieve an optimal compromise between physical realism and computational efficiency for the study of channel micro-flows.Comment: 5 pages, 3 figure

Nonlinear viscoelasticity of metastable complex fluids

Many metastable complex fluids such as colloidal glasses and gels show distinct nonlinear viscoelasticity with increasing oscillatory-strain amplitude; the storage modulus decreases monotonically as the strain amplitude increases whereas the loss modulus has a distinct peak before it decreases at larger strains. We present a qualitative argument to explain this ubiquitous behavior and use mode coupling theory (MCT) to confirm it. We compare theoretical predictions to the measured nonlinear viscoelasticity in a dense hard sphere colloidal suspensions; reasonable agreement is obtained. The argument given here can be used to obtain new information about linear viscoelasticity of metastable complex fluids from nonlinear strain measurements.Comment: 7 pages, 3 figures, accepted for publication in Europhys. Let

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur

Thixotropy in macroscopic suspensions of spheres

An experimental study of the viscosity of a macroscopic suspension, i.e. a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density-matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown for the first time that a macroscopic suspension shows thixotropic viscosity, i.e. shear-thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10000 times larger than the viscous time scale and about 1000 times smaller than the thermodynamic time scale. The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern

The Physics of the Colloidal Glass Transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. This kinetic arrest is the colloidal glass transition. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including tremendous increases in viscosity and relaxation times, dynamical heterogeneity, and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.Comment: 56 pages, 18 figures, Revie