Mixing and chemical reactions a tutorial

Abstract

The objective of this paper is to complement previous reviews focusing on somewhat more classical aspects of mixing in the content of chemical reaction engineering and to provide additional fluid mechanical perspective by highlighting recent developments. Coverage is restricted to frameworks capable of accommodating a visual and physical description of fluid flow and associated spatial inhomogeneities that might ultimately lead to predictions in a variety of situations, in both laminar and turbulent flows. It is argued that the treatment of laminar or viscous mixing is in good shape. This has been spurred by theoretical developments based on chaos theory and increased computational resources, as well as by advances in fluid mechanics and a host of new experimental results; in this case a body of theory fulfills the double role of producing basic understanding leading to prediction. By contrast, the picture in turbulent mixing is still less sharply defined and no accepted paradigm fulfills both the role of understanding and engineering prediction. Typical flows undergo transitions and are, in general, far from homogeneous, involving coexistence of regions of active and poor mixing; current statistical approaches are not fully equipped to deal with these situations. The difficulty lies in the case of moderate and fast reactions. If reactions are diffusion controlled, chemistry is controlled by the smallest scales. Important processes occur within striations, and straightforward averaging, in general, does not work; coarse graining results in loss of interface and computing the rate of reaction cannot be accomplished without some sort of subgrid model based on the physics of the problem. A lamellar model provides a simple picture that frequently leads to accurate predictions and indicates when mixing effects are important. Noteworthy among recent developments are the observations of lamellar structures at Kolmogorov scales in highly turbulent flows and the establishment of the kinematical connection between chaos and mixing. Remarkably, the smallest scales in turbulent flows and chaotic flows appear to be described by identical statistics. Illustrations are provided throughout.