Basic Concepts and Mixing Mechanisms

2 Mixing Equipment and Operations of Multicomponent and Multiphase Systems, 354 

Mixing principles are relevant to many disciplines what makes mixing polymeric materials unique is their exceptionally high viscosity. There are numerous texts (1-5) that are entirely devoted to the complex problem of mixing of polymers and plastics, and we refer the reader to them for further reading. 

In this chapter we will discuss the mixing operations and machines, present an overview of the principles of mixing mechanisms, review characterization tools of mixtures, and outline mathematical tools and models for analyzing mixing processes. 

1 BASIC CONCEPTS AND MIXING MECHANISMS Definitions of Mixtures and Mixing Mechanisms 

We start our discussion with two fundamental concepts mixture and mixing. The former defines the nature of the state of the materials we are concerned with, while the latter, concerns the mechanism by which we manipulate a property of the former. Mixture is defined (4) as the state formed by a complex of two or more ingredients which do not bear a fixed proportion to one another and which, however commingled, are conceived as retaining a separate existence.  

---

Considerable progress has been made during the past decade toward a better insight into the basic concepts and mechanism involved in metallic dissolution and corrosion. More emphasis has been placed on the "fundamental particles (metallic ions, electrons, and electron acceptors) and on the use of current-voltage characteristics. The wide recognition of dissolution and corrosion as electrode processes, and the idea of a polyelectrode exhibiting a mixed potential, have augmented the use of electrochemical techniques in the study and interpretation of corrosion phenomena. There is even some evidence that the phenomenon of passivity may soon be clarified. 

Much of what is summarized here is presented in more detail in the excellent article on mixed-mode cracking in layered materials by Hutchinson and Suo [55]. In that reference, the authors consider not only interfacial fracture, but also cracking within coatings and cracking in substrates below coatings. Only interfacial cracking (delamination) will be considered in detail here. Before proceeding however, we will first discuss some basic concepts of fracture mechanics. 

Terminology associated with mixture classification is mired in controversy (Egermann, 1980 Thiel, 1982 Nienow et al., 1985 Hersey, 1975). Previously accepted terms have come under scrutiny as our understanding of mixing mechanisms has improved over the years. There is a serious lack of homogeneity and consistency in the terms used in the literature. An effort is made here to present basic concepts and various viewpoints on mixture classification. 

The basic concept of diffusion refers to the net transport of material within a single phase in the absence of mixing (by mechanical means or by convection). Both experiment and theory have shown that diffusion can result from pressure gradients (pressure diffusion), temperature gradients (thermal diffusion), external force fields (forced diffusion), and concentration gradients. Only the last type is considered in this book that is, the discussion is limited to diffusion caused by the concentration difference between two points in a stagnant solution. This process, called molecular diffusion, is described by Pick s laws. His first law relates the flux of a chemical to the concentration gradient ... 

As follows from the previous chapters, a complex interface Metal/MIEC/Electrolyte (MIEC = mixed ion-electron conductor) appears in many processes related to the electrochemistry of polyvalent metals. The model of MIEC in terms of the concept of polyfunctional conductor (PFC) can be a useful approach to deal with the mechanisms of the processes in such systems. The qualitative classification of EPS has been given based on this approach. Further on, we are going to demonstrate that this concept is useful for quantitative (or at least, semi-quantitative) modelling of macrokinetics (dynamics) of the processes in highly non-equilibrium systems. Before doing this, it is worthwhile to outline some basic ideas related to the MIEC. These considerations will also show some restrictions and approximations that are commonly applied in electrochemical practice and which are no longer valid in such kind of systems. 

---