The most common class of Multiphase Flows are two-phase flows, and these include the following:

Gas-liquid flows. This is probably the most important form of multiphase flow, and is found widely in a whole range of industrial applications. These include pipeline systems for the transport of oil-gas mixtures, evaporators, boilers, condensers, submerged combustion systems, sewerage treatment plants, air-conditioning and refrigeration plants, and cryogenic plants. Gas-liquid systems are also important in the meteorology and in other natural phenomena.

Gas-solid flows. Flows of solids suspended in gases are important in pneumatic conveying and in pulverised fuel combustion. Fluidised beds may also be regarded as a form of gas-solid flow. In such beds, the solid remains within the fixed container while the gas passes through. However, within the bed itself, both the gas and the solid are undergoing complex motions.

Liquid-liquid flows. Examples of the application of this kind of flow are the flow of oil-water mixtures in pipelines and in liquid-liquid solvent extraction mass transfer systems. Solvent extraction equipment includes packed columns, pulsed columns, stirred contactors and pipeline contactors.

Liquid-solid flows. The most important application of this type of flow is in the hydraulic conveying of solid materials. Liquid-solid suspensions also occur in crystallisation systems, in china clay extraction and in hydro-cyclones.

Each of the above classes of two-phase flow are dealt with in separate articles to which the reader is referred. In what follows below, a brief overview is given on the design parameters of two-phase flow systems and of the various modelling methods which may be employed.

The more important design parameters for two-phase flow systems include the following:

Pressure drop Pressure losses occur in two-phase flow systems due to friction, acceleration and gravitational effects. If a fixed flow is required, then the pressure drop determines the power input of the pumping system. Here, examples are the design of pumps for the pipeline transport of slurries, or for pumping of oil-water mixtures. If the available pressure drop is fixed, the relationship between velocity and pressure drop needs to be invoked in order to predict the flow rate. An example of this latter application is in the prediction of the circulation rate in natural circulation boiler systems. A detailed discussion of this area is given in the section on Pressure Drop, Two-Phase.

Heat transfer coefficient Heat transfer coefficients in two-phase systems are obviously important in determining the size of heat exchangers in such systems. Examples here are thermo-syphon reboilers in distillation plant and condensers in power plant. Further details in these two areas are given in the articles on Forced Convection Boiling, Pool Boiling and Condensation.

Mass transfer coefficient This is important in the design of separation equipment and also in predicting the situation of combined heat and mass transfer such as in the condensation of vapor mixtures. Further information is given in the articles on Mass Transfer and Mass Transfer Coefficient. Mass transfer in falling film systems is described in the article on Falling Film Mass Transfer.

Mean phase content (e) This quantity represents the fraction by volume or by cross-sectional area of a particular phase. In gas-liquid flows, the gas mean phase content e_{G} is often referred to as the Void Fraction and the liquid phase fraction e_{L} the *liquid holdup*. In systems containing a solid phase, the mean solid phase content (8s) is referred to as the *solid hold-up*. Mean phase content can be important in governing the inventory of a particular phase within a system, particularly when that phase is toxic or valuable. Mean phase content also governs the *gravitational pressure gradient*.

Flux limitations Limitations in mass and heat fluxes are important in the design of two-phase flow systems. Examples of mass flux limitations include Critical Flow (which tends to occur at lower velocities in multiphase system than those found in single-phase systems), Flooding and Flow Reversal in counter-current flow systems (for example in a reflux condenser), and minimum fluidisation velocities in Fluidised Beds. Heat flux limitations are important in boiling, where exceeding the burnout or critical heat flux can lead to poor system performance or physical damage due to excessive increases in the channel wall temperature (see articles on Burnout, Forced Convection and Burnout in Pool Boiling).

A wide range of models have been developed for two-phase flow systems. These include:

Homogeneous model. In the *homogeneous model*, the two phases are assumed to be travelling at the same velocity in the channel and the flow is treated as being analogous to a single phase flow (see article on Multiphase Flow).

Separated flow models. Here, the two fluids are considered to be travelling at different velocities and overall conservation equations are written taking this into account (see article on Multiphase Flow).

Multi-fluid model. Here, separate conservation equations are. written for each phase, these equations containing terms describing the interaction between the phases (see article on Conservation Equations, Two-Phase).

Drift flux model. Here, the flow is described in terms of a *distribution parameter* and an averaged local velocity difference between the phases (see article on Drift Flux Model).

Computational fluid dynamic (CFD) models. In contrast to the above models, the Computational fluid dynamic, CFD, models usually involve two or three dimensions, and attempt to describe the full flow field (see article on Computational Fluid Dynamics).

The choice of the modelling approach will depend on the availability of data (the more complex the models, the more detailed information is required to feed into it!) and on the accuracy required.

Heat & Mass Transfer, and Fluids Engineering