Inversion line

Th is line exhibits a stair idtape that has been found to be typical of many systems, in the central region (e.g., 0.3 early work on the phase inversion temperature with nonionic surfactant systems (84). although the vertical branches were not entirely studied. 

The stair shape of the inversion line may be determined easily by a relatively small number of unidimensional scans. First, mie or two formulation scans located from 40% to 60% water content allow one to locate the (formulation position of) horizontal branch of the inversion line. Then, a few composition f. scans located both below and above the horizontal branch allow one to locate the position of the vertical branches of the inversion line. Whenever there is no previous information on the system, the first composition. scans to be carried out may be located at two or three formulation distance" units from optimum formulation. These distances are evaluated from the correlation for optimum formulation. as discus.scd at the end of previous chapter. This dual-scan technique... 

The horizontal branch of the inversion line has been associated with the so-called transitionar inversion, while the vertical branches correspond to the catastrophic" inversion, a labeling whose origin will become evident later on. 

It is worth remarking that when the inversion line is trespassed across the horizontal branch, the viscosity goes through a minimum, whereas it proceeds through a maximum when any of the vertical branches is crossed. 

It is important to remaiic that in both cases the drop size decreases considerably when approaching the inversion line by augmentation of the internal phase content in any A region (a path indicated as a black arrow). This effect seems to be due to a considerable improvement in stirring efficiency in the viscous high-internal-phase-ratio emulsions located in these zones. So far it is not known whether this fact is absolutely general, but it may be said that it is a quite common circumstance, and this is why Fig. 19 indicates the presence of a small drop size strip in the vicinity of the vertical branches of the inversion line. 

In many maps, the property contours nearly follow the inversion line which exhibits a horizontal brunch and two vertical branches. Actually the horizontal"... 

The vertical branches of the inversion line have been found to depend on most of the other variables chat are susceptible to participate in the balance of breaking and coalescence rates occurring during emulsification. No exhaustive information i.s available at the date hut some trends have been found (83.98). 

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-... 

When a vertical crossing of the inversion line is carried out (white arrows in Fig. 22. left), it is seen that the inversion takes place exactly at the same location, i.e at optimum formulation, whatever the direction of change. Because of these reversibility characteristics, this inversion has been termed "transitional."... 

These regions, known as hysteresis regions, exhibit a triangular shape, so that they vanish at optimum formulation whereas they become wider as formulation departs from optimum. The standard inversion line discussed in the previous... 

The other two branches of the standard inversion line are essentially vertical, and are located typically at 30% water on the negative SAD side of optimum formulation, and at 70% water on the positive side. When the water content is low, the emulsion is always W/0, regardless of the formulation. Similarly, when the oil content is low, an 0/W can be expected, whatever the formulation. In these extreme WOR regions, the phase which is present in larger volume becomes the external phase of the emulsion. It may be said that the composition dominates. However, a closer look at the conductivity value indicates the presence of multiple emulsions in the B" and zones, i.e., where the composition effects dominate over the normal formulation trend. These B" and regions have been called abnormal in opposition to the other ones which are labeled normal because they follow the Bancroft rule and the wedge theory (172). 

Normal A regions and adjacent B and C" normal regions are assoeiated with stable emulsions. In many cases the maximum stability (of both 0/W and W/0 emulsions) is attained in the corresponding A zone near the inversion-line vertieal branch and at some distance from optimum formulation, say 3—4 SAD units (shaded in map). In effect, far away from optimum formulation stability typically drops. The emulsion stability deereases as well when the intemal-... 

Viseosity increases in the normal region in the direction of higher internal-phase ratio (at constant formulation), so that the viscosity maximum is just near the inversion-line vertical branches. On the other hand, the viscosity de-... 

E. Displacement of the Standard Inversion Line Concentration and Stirring Energy Effects... 

Until now, the emulsion was made by stirring a preequilibrated SOW system whose representative point was laid somewhere in the formulation-composition bidimensional map. The line that separated the two types of emulsion on the map was called the standard inversion line. 

The second question deals with what happens when the representative point attains and crosses the standard inversion line Does the emulsion invert at once or is there some delay what become the properties of the emulsion after the inversion takes place ... 

In this section it is assumed that the representative point of an emulsion is displaced on the bidimensional map, typically by modifying either the formulation or the composition, without crossing the standard inversion line so that such changes do not affect the emulsion type. Since each zone of the map is associated with typical emulsion properties, e.g., stability or viscosity, these properties could possibly change during the process. 

The shift in the representative point of an emulsion on the formulation—composition map is now allowed to trespass on the standard inversion line and to move well inside the... 

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... 

The crossing of the vertical branches of the inversion line results in a completely different phenomenon called catastrophic inversion (172,197) because it can be modeled as a cusp catastrophe transition as pointed out by Dickinson (201) and fiirther discussed by others (195—203). 

Figure 13 Inversion line depends upon process conditions.

The SI specification corresponds to flic AB" region of the formulation—composition map, while S2 specification restricts it to the extreme left of the A" zone, near the inversion line. It should be noted that the minimum 70% oil composition could be dangerously near the standard inversion line. 

The S4 specification implies that the point is located in or near the maximum stability region (far from SAD = 0 but not too far away from it, and near the inversion line), including at high temperatures when this variable is taken as a formulation variable (particularly with nonionic surfactants). It also means that the maximum stability region should exhibit a stability value which satisfies the requirement, a featiue not associated with the map characteristics. 

The specification S6 is not really a condition on the drop size to be achieved. It refers rather to finding the best location to produce small drops in the most efficient way, since this is an economic concern. Only two zones are known to satisfy this predicament, which are (1) a strip parallel to the AVA inversion branch at some distance from SAD = 0 and (2) a strip in the A" region near and along the inversion line (see shaded zones in Fig. 9). 

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