Instability mechanism description

Agarwal GP, Hudson JL, Jackson R. Fluid mechanical description of fluidized beds. Experimental investigation of convective instabilities in bounded beds. Ind Eng Chem Fundam 19 59-66, 1980. 

Ruspini et al. (2014) and Ruspini (2013) has given detailed descriptions of the physical phenomena and processes associated with each of the several types of instability. The following is taken, by permission (with sUght changes in the display of a few of the words), from the Table of Contents of his PhD dissertation (Ruspini, 2013), Two-Phase Flow Instability Mechanisms. 

In this entry, the basic concept of stress is introduced and its relation to earthquake mechanisms is explained (for description of focal mechanisms, see entry Earthquake Mechanism Description and Inversion ). Mohr s circle diagram and simple failure criteria are described and used for defining the fault instability, principal faults and principal focal mechanisms. Methods of determining stress from observed earthquake mechanisms are reported and their robustness is... 

The theories of elastic and viscoelastic materials can be obtained as particular cases of the theory of materials with memory. This theory enables the description of many important mechanical phenomena, such as elastic instability and phenomena accompanying wave propagation. The applicability of the methods of the third approach is, on the other hand, limited to linear problems. It does not seem likely that further generalization to nonlinear problems is possible within the framework of the assumptions of this approach. The results obtained concern problems of linear viscoelasticity. 

Although equation 33 gives a physical description of the mechanism of the instability that leads to microstructure formation during solidification, it is not rigorous because it does not consider the effects of the rates of heat and species transport on the evolution of the disturbance. Because of this deficiency, equation 33 cannot be used as a basis for further analysis of microstructure formation. This deficiency is shown clearly by the inability of equation 33 to predict the spatial wavelength of the microstructure formed along the interface. 

The overbearing successes of linear instability theory impeded development in other important areas of (i) receptivity and (ii) many other mechanisms of transition, e.g. bypass transition and spatio-temporal growth of disturbances seen in flows where linear theories apply. In chapter 2, we have dealt with a unified description of instability and receptivity- which has not been dealt systematically before. This should be considered a first for this monograph. 

Equation (13-12) and (13-13) plus a small noise term—which introduces small imperfections into the macrolattice—complete the description of the the model. Because of the periodic nature of the elastic stress [Eq. (13-9)] in large-strain shearing, instabilities occur that allow layers to slip with respect to each other, and the strain y, then varies from layer to layer. Thus flow occurs by yielding a mechanism similar to that discussed in Section 1.5.3. 

Before the model discussed above was published, tha-e were three other suggestions of how to model spatiotemporal dynamics in electrochemical systems. The first attempt at a theoretical description of electrochemical pattern formation came from Jome. His model is based on a chemical instability in the reaction mechanism and only takes into account the concentrations of the reacting species as dependent variables, not the potential. This, of course, means that the model is not applicable to any of the systems exhibiting an electrical instability. This includes the examples treated by Jome, namely, anion reduction reactions or cation reduction in the presence of SCN . Meanwhile, both oscillators are unanimously classified as NDR oscillators [see Section n.2.(ii)] and hence their spatiotemporal description requires a different approach. 

In this chapter we develop the stability criteria for both pure substances and for mixtures. Since we have three kinds of equilibria, we have three kinds of stabilities thermal stability, mechanical stability, and diffusional stability. If the proposed state of a single phase violates any of these criteria, then the phase might spontaneously split into two or more phases. Therefore, violations of stability criteria contribute to the wealth of phase behavior observed in Nature. In this chapter we introduce some of the phase behavior that results from instabilities, but the subject is an extensive one, so the descriptions of observable phase behavior are continued in the next chapter. 

Abstract This chapter deals with capillary instability of straight free liquid jets moving in air. It begins with linear stability theory for small perturbations of Newtonian liquid jets and discusses the unstable modes, characteristic growth rates, temporal and spatial instabilities and their underlying physical mechanisms. The linear theory also provides an estimate of the main droplet size emerging from capillary breakup. Formation of satellite modes is treated in the framework of either asymptotic methods or direct numerical simulations. Then, such additional effects like thermocapiUarity, or swirl are taken into account. In addition, quasi-one-dimensional approach for description of capillary breakup is introduced and illustrated in detail for Newtonian and rheologically complex liquid jets (pseudoplastic, dilatant, and viscoelastic polymeric liquids). 

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