Dynamic inversion

In summary, it is clear from the above-discussed aspects that it was possible by multinuclear NMR (oxygen-17, nitrogen-15, carbon-13, and technetium-99) to successfully study the very slow cyanide exchange and the slow intermolecular oxygen exchange in these oxocy-ano complexes and correlate them both with the proton-transfer kinetics. Furthermore, the interdependence between the proton transfer and the actual dynamic inversion of the metal center was clearly demonstrated. 

N. Zambrano, E. Tyrode, I. Mira, L. Marquez, M.-P. Rodriguez, and J.L. Salager Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 1. Effect of the Water-to-Oil Ratio Rate of Change on the Dynamic Inversion Frontier. Ind. Eng. Chem. Res. 42, 50 (2003). 

VIII. The Control of Dynamics-Inverse Scattering Duality... 

VIII. THE CONTROL OF DYNAMICS-INVERSE SCATTERING DUALITY... 

This chapter deals with emulsion properties, i.c.. type, drop. si c. siahility. and viscoMty. It shows how to estimate or measure them in practice and how thev arc related to formulation. conipu.sition. and other variables. The current kiiow how is presented in a comprehensive way so that the emulsion maker can use it to attain some suitable propeily. The ea.se of emulsion made from preequtli-bruted surfactant-oil-Water systems is treated first. Then follows a discu.ssion on how to modify emulsions to seek specific properties, which leads to the introduction t)f the dynamic inversion phenomena, discussed from the practitioner s point of view. 

Up to now the inversion line has been the limit between emulsion types when emulsihcalion is carried out from a preequiljbrated system according to the so-called standard procedure. In practice the emulsion inversion could also be the situation in which a change in formulation or composition triggers a switch in emulsion type. This kind of inversion is generally called dynamic inversion since it takes place as a consequence of the change. Depending on the circumstances it may be favorable or quite detrimental, and should be either harnessed or avoided. 

Dynamic inversion is studied by producing a change that moves the point that represents the formulation and composition of an emulsion on the map from one side of the inversion line to the other side. In practice the system is first equilibrated and then emulsified, to produce the initial emulsion. Then its formulation or composition is altered continuously or by small increments, while a low-... 

Figure 22 indicates the typical patterns found in dynamic inversion. The arrows indicate the direction and path of change while their respective heads indicate the inversion point along a formulation (white) or composition (black) shift. Depending on which branch is crossed, one of two possible inversion types is encountered. 

The two different ways of crossing the inversion line are associated with quite different behaviors. The first one, which is known as transitional inversion, is produced by changing formulation at a constant water-to-oil ratio, i.e., along a vertical path in the bidimensional map. Such a crossing takes place in the A region in the central zone of the map. The experimental evidence indicates that, in this kind of dynamic process, the inversion takes place at the very moment the standard inversion line is crossed, i.e., essentially at SAD = 0, whatever the direction of change [from A to A or vice versa as indicated with white arrows in Fig. 12 (left)]. The horizontal branches of the standard and dynamic inversion lines are thus identical. The term... 

Figure 12 Emulsion formulation or composition evolution up to dynamic inversion occurrence.

The newly inverted emulsion properties often match the properties of standard emulsions made in the same (new) location, sometimes with extra features such as extremely small drop size formed during the inversion. In fact, industrial plants that produce extremely fine emulsions use a dynamic inversion process even more complex than the one described here, which promotes the surfactant mass transfer from one of the phases to the other in order to trigger a spontaneous emulsification (209, 210). 

Path 2 makes use of the delay in the dynamic inversion when the oil content is increased. The initial formulation (black circle in Fig. 15) is taken far fi om optimum, and near the standard inversion line, say at 70-75% oil. The system is then stirred at low shear and oil is added to reach an 80% oil content or even more (black square). 

F Silva, A Pena, M Minana-Perez, JL Salager. Dynamic inversion hysteresis of emulsions containing anionic surfactants. Colloids Surfaces A Physico-chemical Eng Aspects 132 221—227, 1998. 

A Pena, JL Salager. Effect of stirring energy upon the dynamic inversion hysteresis of emulsions. Colloids Surfeces, in press. 

Dynamic inversion (DI) control methodology is a member of feedback linearization control techniques and is applied to different types of aircraft applications (Reiner et al., 1995). In this technique the existing deficient or undesirable dynamics in the system are nullified and replaced by designer specified desirable d5mamics (Reiner et al., 1995 Ali and Padhi, 2009). This tuning of system dynamics is accomplished by a careful algebraic selection of afeedback function. Itis for this reason that the DI methodology is also called the feedback linearization technique. Details of feedback linearization and DI can be found in Marquez (2003). 

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