The more recent studies are illustrated in Figure 1 [Arirachakaran et al. (1989)]. As suggested by this figure the nature of liquid-liquid flows is highly complex, with full stratification occurring at low velocities and full dispersion at velocities. This makes prediction of these flows a real challenge.
Given the complexities of the flow, there has been a concentration of work on either fully-separated (stratified, and to a lesser extent, annular) flows on the one hand and fully-dispersed flows on the other. In the latter type of flow conditions under which there is an inversion between the continuous and the disperse phases is of great interest. Below the hydrodynamics of two-phase liquid flows and phase inversion are briefly discussed.
This type of flow occurs when two liquids are in laminar flow. The parallel flow of two immiscible fluids in a two-dimensional channel is a classical problem discussed by Bird et al. (1960). Since the flows are laminar in both phases separated flows can be treated theoretically and solutions are in good agreement with experimental observations. In the case of flow in cylindrical tubes analytical solutions are not possible. However numerical solutions are being obtained that can be extended to turbulent flow by using suitable turbulence models. As the flow rates of the phases are increased, waves appear at the interface that, upon turbulence intensification, lead to dispersed flow.
With increased turbulence breakage of one phase into the other takes place, as shown in Figure 1. As dispersion is formed flow behavior becomes dependent on dispersion viscosity. Water in oil dispersions behave as Newtonian fluid up to 10% by volume water. Above this fraction they show significant pseudoplastic behavior; as mass flow increases, viscosity decreases. It has been found that the smaller the drop size is, the higher the viscosity.
Models for fully-dispersed flows are discussed by Arirachakaran et al. (1989), who found good agreement between predicted and observed results in the fully-dispersed region provided the correct viscosity is used. There is some evidence that the presence of droplets can sometimes suppress the turbulence of the continuous phase.
In liquid-liquid systems, it is of crucial importance to know the conditions governing phase inversion. This is defined as the point at which the continuous phase becomes the dispersed one and vice versa. Thus, an inversion point would represent a change from an oil-in-water to a water-in-oil dispersion. The condition that triggers this change is the increase of dispersed phase hold-up. This is accompanied by an increase in dispersion viscosity. It has been observed that viscosity of the mixture reaches a peak near the inversion point, with the mixed viscosity often being much higher than that of the more viscous phase. As the hydrodynamic conditions of pipe flow and continuous (or batch) stirred tanks are different, conditions governing phase inversion in these two cases are not the same.
Phase inversion of dispersions in stirred tanks systems has received substantially more attention than that in pipe systems. Typical data for phase inversion in stirred vessels are illustrated in Figure 2. Conditions for phase inversion depend on the physical properties of the system and on hydrodynamic conditions. Therefore, for a given tank configuration and a given system the inversion point will depend on phase hold-up and stirring speed, as shown in Figure 2. The graph shows an upper and lower band for phase inversion, rather than a single line. This means there is hysteresis. Thus on increasing stirrer speed to create inversion, a lower stirrer speed on lower volume fraction of the specified phase is required for reversion of the inversion process. In addition, the inversion band is not the same when starting from an oil-dispersed system or a water-dispersed one. It should be noted that if mass transfer is taking place, the conditions for phase inversion will most certainly change due to the presence of solute at the interface.
Figure 2. Inversion curves for binary immiscible liquid-liquid systems. Source: McClarey and Mansouri (1978).
There is considerable controversy about the effect of wettability of the containing vessel (and also of the agitator) on phase inversion, but there are no general conclusions on this respect, although it has been suggested that wettability may only be significant at low stirring rates.
In pipe systems, the mechanisms of mixing leading to inversion are much more complex and, from the point of view of the experimentalist, uncontrolled. There is little information in the literature about phase inversion in pipes. Unlike the case of stirring speed, there seems to be no effect of mixture velocity or droplet size on phase inversion. Phase fraction and temperature, on the other hand, seem to be the key parameters.
Arirachakaran, S., Oglesby, K. D., Malinowsky, M. S., Shoham, O., and Brill, J. P. (1989) An analysis of oil/water flow phenomena in horizontal pipes. Paper presented at SPE Production Operation Symposium. (SPE 18836) March, Oklahoma City.
Bird, R. B., Stewart, W. S., and Lightfoot, E. N. (1960) Transport phenomena. John Wiley and Sons.
Godfrey, J. and Hanson, C. (1982) Liquid-liquid systems, in Handbook of multiphase systems. (ed. Hetsroni, G.). McGraw-Hill Book Company.
McClarey, M. J. and Ali Mansouri, G. (1978) Factors affecting the phase inversion of dispersed immiscible Liquid-liquid mixtures. A.I.Ch.E. Symp. Series 74. 173:134−139.