## General Concepts of Multiphase Flow

**Basic Parameters of Multiphase Flow:**

The flow pattern of multiphase flow can be determined by the relations of following characteristic times:

(1) The flow characteristic time t/.

where L is the character length of the flow domain and vr is the reference velocity of the flow.

(2) The particle response time tr, which is the measure of the dynamic response of particles.

where dp is the particle diameter, pp is the particle material density, and H is the fluid viscosity. The subscript/* indicates the particle phase.

(3) The mean particle response time tri.

where Rep is particle Reynolds number

(4) The fluctuation time TT of fluid flow:

where / is the fluid turbulence length, and u' is the fluctuation velocity of the flow. And k is the turbulent kinetic energy of the flow and s is the turbulent energy dispassion rate.

(5) The particle collision time tp;

which is like tT, is expressed by using the particle characters.

The flow patterns of multiphase flow can be determined according to the relation between the foregoing characteristic measures in the following extreme conditions.

**Density and Volume Fraction:**

Relations between deferent density determinations of multiphase flow are as follows:'

where P™ is the density of mixture, Pf is the fluid bulk density, Pk->PP are the particle bulk densities, and Pp is the particle material density. And nu is the particle number in the unit volume.