Microscale model definition

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... 

Microfluidics is also a cross-disciplinary subject that uses the methods and principles of microelectronics to construct very small analogs or models of such macroscopic fluidic elements as wind tunnels, valves, or fluidic amplifiers. The natural question that comes to mind is at what dimensional scale does fluid motion depart from the extremely well understood and well established laws of fluid dynamics There is no definitive answer to that question yet since the study of fluid motion in microscale and nanoscale structures is still at an early stage. 

Continuum models are used almost exclusively in this book and are adequate down to the microscale. They fail on the nanoscale where it becomes necessary to directly address the particulate nature of matter. On the nanoscale, the diffusion times and Reynolds numbers shown in Table 16.1 become rather meaningless. Instead, the models must address the behavior of individual molecules. Thus, an alternative definition of the nanoscale is the scale at which continuum models must be replaced by molecular models. 

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