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2 - Theory of Colloidal Suspension Structure, Dynamics, and Rheology

Published online by Cambridge University Press:  07 April 2021

By
Gerhard Nägele ,
Jan K. G. Dhont  and
Thomas Voigtmann
Edited by
Norman J. Wagner  and
Jan Mewis
Norman J. Wagner
Affiliation:
University of Delaware
Jan Mewis
Affiliation:
KU Leuven, Belgium
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Summary

Chapter 2 introduces the statistical physics description of the rheology of concentrated colloidal suspensions at low Reynolds number. While the solvent is a Newtonian fluid, the suspension exhibits viscoelasticity and non-Newtonian rheology. After explaining the hydrodynamic interactions between Brownian particles mediated by the intervening solvent flow, two theoretical methods for describing the suspension rheology are discussed. In the Langevin Equation method, stochastic particle trajectories are considered under the influence of direct and hydrodynamic interactions, and solvent-induced fluctuating forces. This method is fundamental to simulation schemes where the macroscopic suspension stress is calculated from time-averaging the microscopic stress over representative trajectories. The main focus is on the second so-called generalized Smoluchowski equation (GSmE) method invoking a many-particles diffusion-advection equation for the configurational probability density of Brownian particles in shear flow. Based on the GSmE, real-space and Fourier-space schemes are discussed for calculating rheological properties including the shear stress relaxation function and steady state and dynamic viscosities. Starting from exact Green-Kubo relations for the shear stress relaxation function, the linear mode coupling theory (MCT) and its non-linear extension, termed Integration Through Transients (ITT), are introduced as versatile Fourier-space schemes. They allow for studying the rheology of concentrated suspensions close to glass and gel transitions.

Keywords

rheologycolloidssuspensionstheorystatistical mechanicsreview
Type
Chapter
Information
Theory and Applications of Colloidal Suspension Rheology , pp. 44 - 119
Publisher: Cambridge University Press
Print publication year: 2021

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