A. General description of liquid-liquid flows: Flow patterns

Flows of mixtures of two immiscible liquids are encountered frequently in the design of industrial processes and equipment. The two liquids are almost exclusively an aqueous phase (water) and an organic (oil) phase. Gas-liquid systems actually represent a very particular extreme of two-fluid systems characterized by low-density ratio and low viscosity ratio. In liquid-liquid systems the density contrast between the phases is low. However, the oil phase may be lighter or heavier than the aqueous phase. Hence, the viscosity ratio between the lighter and heavier liquids ranges between more than a million to less than 10^–6. Oils and oil-water emulsions may show a Newtonian or non-Newtonian rheological behavior (Sherman, 1968 and Schramm, 1992). Therefore, the various concepts and results experienced in gas-liquid two-phase flows cannot be readily translated to liquid-liquid systems.

(a) Flow patterns in horizontal tubes

Diverse flow patterns were observed in liquid-liquid systems (Russell and Charles, 1959; Russell et al., 1959; Charles et al., 1961a; Charles et al., 1961b; Guzhov and Medvedev, 1971; Guzhov et al., 1973; Guzhov et al., 1974; Soot, 1971; Malinowsky, 1975; Laflin and Oglesby, 1976; Oglesby, 1979; Scott, 1985; Arirachakaran et al., 1989; Cox, 1986; Valle and Utvik, 1997; Valle and Kvandal, 1995; Trallero, 1995; Angeli, 1996; Tabeling et al., 1991; Nädler, 1995; Mewes et al., 1997; Andreini et al., 1997; Hapanowicz et al., 1997). These may be classified into four basic prototypes:

1. Stratified layers with either smooth or wavy interface.
   
   
2. Large slugs, elongated or spherical, of one liquid in the other.
   
   
3. A dispersion of relatively fine drops of one liquid in the other.
   
   
4. Annular flow, where one of the liquids forms the core and the other liquid flows in the annulus.