Sangkyun Koo

Analysis of fractal aggregates in a colloidal suspension of carbon black from its sedimentation and viscosity behavior

Colloidal aggregates in a suspension of carbon black particles are characterized by fractal dimension and their shear dependence. Carbon black particles of 100 nm in diameter are dispersed in Newtonian ethylene glycol with particle volume fraction ϕ ranging from 0.01 to 0.1. Microstructure of the aggregates is estimated by hydrodynamic transport properties such as average settling velocity and shear viscosity. Scaling analysis is conducted to correlate the hydrodynamic transport properties and the fractal dimension df. The fractal dimension is estimated to be 2.21 from the scaling relation between the settling velocity and the particle volume fraction for ϕ = 0.01-0.05. The shear viscosity results show shear-thinning behavior of the colloidal suspension. The intrinsic viscosity for the colloidal aggregates is obtained from the data of shear viscosity versus particle concentration. A scaling relation between the intrinsic viscosity and the shear rate gives df = 1.93 at m = 1/3, where m is the exponent defined by a scaling relation between aggregate radius Rg and shear rate S, Rg ∝S−m. Another scaling relation using yield stress data presents df = 1.94, which is nearly equivalent to 1.93 from that by the intrinsic viscosity but quite lower than that from the settling velocity. This discrepancy of the fractal dimension can be attributed to growth or restructuring of the colloidal aggregates by the hydrodynamic stress during long-time settling process.

Prediction of shear viscosity of a zinc oxide suspension with colloidal aggregation

We deal with scaling relations based on fractal theory and rheological properties of a colloidal suspension to determine a structure parameter of colloidal aggregates and thereby predict shear viscosity of the colloidal suspension using an effective-medium model. The parameter denoted by β is m(3-df), where m indicates shear rate (D) dependence of aggregate size R, i.e.R∝D−m, and df is the fractal dimension for the aggregate. A scaling relation between yield stress and particle volume fraction φ is applied to a set of experimental data for colloidal suspensions consisting of 0.13 μm zinc oxide and hydroxyethyl acrylate at φ = 0.01-0.055 to determine β. Another scaling relation between intrinsic viscosity and shear rate is used at lower φ than the relation for the yield stress. It is found that the estimations of β from the two relations are in a good agreement. The parameter β is utilized in establishing rheological models to predict shear viscosity of aggregated suspension as a function of φ and D. An effective-medium (EM) model is employed to take hydrodynamic interaction between aggregates into account. Particle concentration dependence of the suspension viscosity which is given in terms of volume fraction of aggregates φa instead of φ is incorporated to the EM model. It is found that the EM model combined with Quemada’s equation is quite successful in predicting shear viscosity of aggregated suspension.

Large-scale calculation of hydrodynamic transport properties for random suspensions of hard-sphere particles

A numerical method based on fast multipole summation scheme is used to calculate hydrodynamic interactions in random suspensions of non-colloidal hard-sphere particles. The calculation is carried out for suspensions of 1,024 particles randomly placed in periodic unit cell to determine hydrodynamic transport properties such as permeability of a viscous flow through porous medium, effective viscosity of suspension, and sedimentation velocity of the suspended particles. The particle volume fraction ø ranges from 0.01 to 0.25. Effect of particle number N on the transport properties was examined through the numerical calculations with N=64-1,024. It is shown that sedimentation velocity increases with N approaching an estimate for infinite N, and the finite N effect is negligible in effective viscosity and permeability problems. The present scheme is quite useful for obtaining a statistically-averaged quantity for random suspensions. As an example, ensemble-averaged velocity when position of one particle is fixed is numerically obtained in sedimentation problem. The numerical results are shown to be in excellent agreement with theoretical prediction.

Rheological analysis of particle aggregation in a colloidal suspension of carbon black particles

We examine scaling theories to estimate microstructural parameters of fractal aggregates in a colloidal suspension. The scaling theories are based on fractal theories and rheological properties of the colloidal suspension. Rheological measurement in oscillatory and steady shear modes is performed for colloidal suspensions of 56 nm carbon black particles in Newtonian ethylene glycol at the particle volume fractions φ ranging from 0.005 to 0.05. Elastic modulus G’ of the colloidal suspension at φ = 0.02-0.05 in the state of colloidal gel is used to estimate fractal dimension df of the aggregates. Steady-shear measurement gives yield stress τy as a function of φ. Shear dependence of the aggregate radius R is given by a power-law scaling, i.e., R∝S−m, where S is the shear rate. The power-law exponent m is estimated from df and a scaling relation between τy and φ. The estimation gives df = 2.14 and m = 0.33. The parameters df and m which can be determined by either direct measurement or theoretical calculation are used to establish a microrheological model for predicting shear viscosity of aggregated suspension as a function of φ and S. Both the concentration dependence and the shear dependence of aggregates are combined to obtain an expression for the shear viscosity. Hydrodynamic interaction effect among the aggregates is roughly considered in calculating average shear stress on the aggregate. It is found that this consideration critically contributes to behavior similarity with experimental result. It is shown that the predictions by the model reasonably agree with the experimental result.