Basics of Multiphase Systems

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A multiphase system is one characterized by the simultaneous presence of several phases, the two-phase system being the simplest case. The term two-component is sometimes used to describe flows in which the phases consist of different chemical substances. For example, steam-water flows are two-phase, while air-water flows are two-component. Some two-component flows (mostly liquid-liquid) technically consist of a single phase but are identified as two-phase flows in which the term “phase” is applied to each of the components. Since the same mathematics describes two-phase and two-component flows, the two expressions will be treated as synonymous. This book deals with a variety of multiphase systems, in which the phases passing through the system may be solid, liquid or gas, or a combination of these three.

The analysis of multiphase systems can include consideration of multiphase flow and multiphase heat and mass transfer. When all of the phases in a multiphase system exist at the same temperature, multiphase flow is the only concern, however, when the temperatures of the individual phases are different, interphase heat transfer also occurs. If different phases of the same pure substance are present in a multiphase system, interphase heat will result in a change of phase, which is always accompanied by interphase mass transfer. The combination of heat with mass transfer during phase change makes multiphase systems distinctly more challenging than simpler systems.

Based on the phases that are involved in the system, phase change problems can be classified as: (1) solid-liquid phase change (melting and solidification), (2) solid-vapor phase change (sublimation and deposition), and (3) liquid-vapor phase change (boiling/evaporation and condensation). Melting and sublimation are also referred to as fluidification because both liquid and vapor are regarded as fluids.

Phase change problems can also be classified on the basis of the system’s geometric configurations and the structures of the interfaces separating different phases. From the geometric configuration of the system, one can classify multiphase problems as (1) external phase change problems in which one phase extends to infinity, and (2) internal phase change problems in which the different phases are confined to a limited space. Examples belonging to the former class include melting and solidification in semi-infinite regions, pool boiling, and film condensation. Some examples belonging to the latter class are melting and solidification in finite slabs, forced convective boiling, and condensation in channels. Another method for classifying multiphase systems considers the structure of the interfaces. Multiphase systems can be classified as (1) separated phase, (2) mixed phase, and (3) dispersed phase, as summarized in the table below. The separated phase case has two immiscible phases separated by a clearly-defined geometrically-simple interface (Cases A through E). Such systems can be further classified according to whether phase change occurs on a plane surface or inside a channel. Phase change occurring on a plane surface can include combinations of different phases, as indicated in the table. Liquid-gas jet flow may involve a liquid jet in a gas phase or a gas jet in a liquid phase, while phase change in a channel includes liquid-vapor annular flow as well as melting and solidification occurring at a single temperature. At the other extreme of interfacial complexity are the dispersed phases (cases L through N), including bubbly flow – discrete gaseous bubbles in a continuous fluid; droplet flow – discrete fluid droplet in a continuous liquid-vapor (gas) system; and solid-particle flow – discrete particles in a liquid or gas carrier. Change in an interfacial structure from separated phase to dispersed phase can occur gradually; as a result, there are mixed phases (Cases F through K) in which both separated and dispersed phases coexist. For a liquid- vapor annular flow with a vapor core surrounded by a liquid film, thin film evaporation occurs when heat is applied to the external surface of the tube – Case C of the separated-phase type. If the wall temperature is increased to a sufficient level, vapor bubbles can be generated in the liquid layer, so the system transforms to case G of the mixed-phase type: bubbly annular flow. If the wall temperature is further increased, the flow changes to a liquid-vapor droplet form – Case M of the dispersed-flow type.

Classification of multiphase systems

Type Case Typical regimes Geometry Configuration Examples
A Phase change
on plane
(a) Liquid layer in vapor
(b) Vapor layer in liquid
(c) Solid layer in liquid
(d) Liquid layer in solid
(e) Solid layer in vapor
(a) Film condensation
(b) Film boiling
(c) Solidification
(d) Melting
(e) Sublimation and
B Liquid-gas
jet flow
(a) Liquid jet in gas
(b) Gas jet in liquid
(a) Atomization
(b) Jet condenser
C Liquid-vapor
annular flow
(a) Liquid core and vapor film
(b) Vapor core and liquid film
(a) Film boiling
(b) Film condensation or evaporation
D Melting at a
single melting
Solid core and liquid
annular layer
Melting of ice in a duct
E Solidification
at a single
melting point
Liquid core and solid
annular layer
Freezing water in a duct
F Slug or plug
Large vapor bubbles in a
continuous liquid
Pulsating heat pipes
G Bubbly annular
Vapor bubbles in liquid film
with vapor core
Film evaporation with wall
H Droplet
annular flow
Vapor core with liquid
droplets and annular liquid
Steam generator in boiler
I Bubbly droplet
annular flow
Vapor bubbles in liquid
film with vapor core
Boiling nuclear reactor
J Melting over a
Solid and mushy zone in
Melting of binary solid
K Solidification
over a
Liquid core with layer of
solid and mushy zone
Freezing of binary
L Liquid-vapor
(gas) bubbly
Discrete vapor bubbles in a
(a) Chemical reactors
(b) Absorbers
(c) Evaporators
(d) Separating devices
M Liquid-vapor
(gas) droplet
Discrete liquid droplets in a
(a) Spray cooling
(b) Atomizers
(c) Combustors
N Particulate
(a) Solid particles in liquid (Slurry Flow)
(b) Discrete solid particles in gas
(c) Fluidized beds
(a) Melting, solidification
of PCM suspension in
(b) Combustion of solid
(c) Fluidized bed reactors

Characteristic features may be associated with the behavior of each of the three possible phases comprising the multiphase systems of the table. The solid phase can be regarded as incompressible because the density of the solid phase can be treated as constant for most cases. In cases where no fluidification or solidification occurs, the solid phase has a non-deformable interface with the fluid phase, or phases, flowing over it. The flow characteristics depend strongly on the size of the individual solid elements and on the motion of the associated fluids. When melting and solidification are involved, the volume and shape of the solid can change with time. For melting and solidification occurring at a single melting point, the liquid phase is continuous, while the solid phase is discontinuous in a mushy zone formed by melting or solidification of a binary substance. The solid phase is also discontinuous in cases of particulate flow, because the solid particles are dispersed in either liquid or gas phases.

In multiphase systems containing a liquid phase, the liquid can be the continuous phase, containing dispersed elements of solids (particles), gases (bubbles), or other liquids (drops). The liquid can also be discontinuous, for example, in the form of drops suspended in a gas or in another liquid such as in liquid-vapor droplet flow. A liquid also differs from a solid because its interface with other fluids (gases or other liquids) is readily deformable. The vapor (gas) phase in a multiphase system can be continuous, as in film evaporation or condensation, or as in liquid-vapor annular flow. It can also be discontinuous, as in liquid-vapor bubbly flow. Compared with the liquid phase, a vapor (gas) is highly compressible because its density is a strong function of the temperature and pressure. Notwithstanding this behavior, many multiphase flows containing vapor (gases) can be treated as essentially incompressible, especially if the pressure is reasonably high and the Mach number for the gas phase is low, say less than 0.3.

A multiphase system with separated phases can be considered as a field that is divided into single-phase regions with interfaces between the phases. The governing equations for a multiphase system with separated phases can be written using the standard local instantaneous differential balance for each single-phase region, with appropriate jump conditions to match the solution of these differential equations at the interfaces. This method, which is referred to as the interface tracking method, involves solving the single-phase equations in each separate phase. By contrast, explicit tracking of the interfaces in mixed-phase and dispersed-phases is more complex and sometimes even impossible. In this case, spatial averaging of the governing equations is performed over each phase or simultaneously over the phases within a multiphase control volume.


Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

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