## 5.1. Multiphase Notation

In addition to the notation given here, review the list of symbols. For details, see List of Symbols.

Different phases of fluids are denoted using lowercase Greek letters , , , and so on. In general, a quantity subscribed with , , , and so on, refers to the value of the quantity for that particular phase. For example, the volume fraction of is denoted . Thus, the volume occupied by phase in a small volume around a point of volume fraction is given by:

| (5–1)

The total number of phases is . The volume fraction of each phase is denoted , where .

It is important to distinguish between the material density and the effective density of a fluid . The material density, , is the density of the fluid if it is the only phase present, that is, the mass of per unit volume of . The effective density is then defined as:

| (5–2)

This is the actual mass per unit volume of phase , given that phase only occupies a fraction of the volume, that is, the mass of per unit volume of the bulk fluid.

The mixture density is given by:

| (5–3)

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