Microscopic Theories of the Rheology of Stable Colloidal Dispersions

Lionberger, Robert; Russel, William B.

doi:10.1002/9780470141700.ch3

Cited by 31 publications

(39 citation statements)

References 91 publications

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“…For both large and small separations analytical expressions for these functions exist [48] and are supplemented by tabulated numerical data for intermediate ranges [150]. At higher volume fractions approximations are required to obtain the hydrodynamic functions and a number of schemes have been developed which aim to incorporate the effects of many-body hydrodynamics [28,50,100,151,152]. In the absence of hydrodynamic interactions A = B = 0 and G = H = 1 leading to considerable simplification.…”

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

“…Although exact expressions relating the stress tensor to to the flow distorted microstructure are known formally, the situtation is complicated by the appearance of unknown conditionally averaged hydodynamic functions in the expressions. However, reliable approximations for these functions are available and enable the stress to be evaluated directly from g(r) [28]. For the simpler case of a system interacting via a pair potential and in the absence of hydrodynamic interactions, the stress tensor may be completely determined by a simple integral over the pair correlation function [155] …”

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

“…Indeed, it is the absence of time-dependent data from the pair Smoluchowski approach which has served to obscure the relationship between these two methods, despite the fact that they are formally equivalent. The only available Smoluchowski-based time-dependent calculations were performed using the Lionberger-Russel theory [28,190,192] for small amplitude oscillatory shear flow. As pointed out in subsection 6.3.4, the available results for the volume fraction dependence of G ′ (ω) and G ′′ (ω) within the LR theory reveal underlying problems resulting from the approximations employed (i.e.…”

Section: Temporal Locality Vs Memory Functionsmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.

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Section: Pair Smoluchowski Equationmentioning

confidence: 99%

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

Section: Temporal Locality Vs Memory Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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“…[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). Essentially, most of these works introduce particle correlations by taking into account hydrodynamic interactions and provide a conceptual framework that explains how the microstructure of the systems modifies the behavior of the viscosity as a function of the volume fraction.…”

Section: Introductionmentioning

confidence: 99%

The rheology of concentrated suspensions of arbitrarily-shaped particles

Santamaría‐Holek¹,

Mendoza²

2010

Journal of Colloid and Interface Science

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We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the intrinsic viscosity is known in the dilute limit and the particles are not too elongated. The procedure allows to construct a continuum-medium model in which correlations between the particles are introduced through an effective volume fraction. We have tested the procedure using spheres, ellipsoids, cylinders, dumbells, and other complex shapes. In the case of hard spherical particles, our expression improves considerably previous models like the widely used Krieger-Dougherty relation. The final expressions obtained for the viscosity scale with the effective volume fraction and show remarkable agreement with experiments and numerical simulations at a large variety of situations.

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“…RðfÞ ¼ 2:8123 Â 10 6 ð1ÀfÞ À9:7 Pa s m À2 , ð60Þ and the suspension consistency k and index n are mated with theoretical predictions of the dilute suspension rheology at the low shear limit (Lionberger and Russel, 2000) k 2 ðfÞ ¼ m 1þ…”

Section: Application To Gravity Thickener Operationmentioning

confidence: 99%