Fluid-particle flow microscale model

There are three chapters in this volume, two of which address the microscale. Ploehn and Russel address the Interactions Between Colloidal Particles and Soluble Polymers, which is motivated by advances in statistical mechanics and scaling theories, as well as by the importance of numerous polymeric flocculants, dispersants, surfactants, and thickeners. How do polymers thicken ketchup Adler, Nadim, and Brenner address Rheological Models of Suspensions, a closely related subject through fluid mechanics, statistical physics, and continuum theory. Their work is also inspired by industrial processes such as paint, pulp and paper, and concrete and by natural systems such as blood flow and the transportation of sediment in oceans and rivers. Why did doctors in the Middle Ages induce bleeding in their patients in order to thin their blood ... 

The remaining chapters in this book are organized as follows. Chapter 2 provides a brief introduction to the mesoscale description of polydisperse systems. There, the mathematical definition of a number-density function (NDF) formulated in terms of different choices for the internal coordinates is described, followed by an introduction to population-balance equations (PBE) in their various forms. Chapter 2 concludes with a short discussion on the differences between the moment-transport equations associated with the PBE and those arising due to ensemble averaging in turbulence theory. This difference is very important, and the reader should keep in mind that at the mesoscale level the microscale turbulence appears in the form of correlations for fluid drag, mass transfer, etc., and thus the mesoscale models can have non-turbulent solutions even when the microscale flow is turbulent (i.e. turbulent wakes behind individual particles). Thus, when dealing with turbulence models for mesoscale flows, a separate ensemble-averaging procedure must be applied to the moment-transport equations of the PBE (or to the PBE itself). In this book, we are primarily... 

If we interpret this question as asking whether models exist for the general class of complex/non-Newtonian fluids that are known to provide accurate descriptions of material behavior under general flow conditions, the current answer is that such models do not exist. Currently successful theories are either restricted to very specific, simple flows, especially generalizations of simple shear flow, for which rheological data can be used to develop empirical models, or to very dilute solutions or suspensions for which the microscale dynamics is dominated by the motion deformation of single, isolated macromolecules or particles/drops.24... 

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