The secondary phase may or may not have a distinct velocity field i.e. it will at some times follow the continuous phase or at times will have its own velocity field.

**Volume fraction :**

**It is defined as the ratio of volume of dispersed phase to the volume of the medium or the total volume. Mathematically represented by :**

*Volume fraction of a dispersed phase*:

**Similarly, defined as the ratio of volume of continuous phase to the volume of the medium or the total volume. Mathematically represented by**

*Volume fraction of a continuous phase*:where del Vc is the volume of the continuous phase in the volume. By definition the sum of the volume fraction must be unity i.e.

**Densities :**

**Velocities :**

There are generally two terms used to define velocities, the superficial velocity and the phase velocity.

* Superficial Velocities :* It is mostly associated with pipe flow and is the mass flow rate, of the respective phase divided by the pipe area A and material density. So in case of dispersed phase this superficial velocity is given by:

* Phase velocities : *The phase velocity Ud is the actual velocity of the phase. The volume fraction relates the phase velocity with the superficial velocity as follows :

**Mass concentration of dispersed phase :**

It is the ratio of the mass of dispersed phase to that of the continuous phase in a mixture.

**Quality :**

**Phase Loading :**

**Disperse Flows :**

**Dense Flows :**

*Collisions between the particles control the overall flow features.*

**Collision dominated :***Continuous particle to particle contact controls the overall flow features.*

**Contact dominated :****Stokes Number :**

**Significance of Stokes Number :**

##### The Author

## Dr. Ganesh Visavale |
Dr. Ganesh is a leading researcher in computational engineering, sustainable energy and its application in process industry. He has done immence contribution in LearnCAx. Before he joined post-doctoral fellowship at IIT Delhi, he was the general manager at LearnCAx. He was instrumental in conceptualization, development and implementation of online education from CCTech for CAx professional. Ganesh has a number of publications both in international journal and conference proceedings. Before CCTech, he held the position of Associate Scientist in solar thermal division at Sardar Patel Renewable Energy Research Institute, Anand. Ganesh holds Ph.D and M.Chem. Engineering from Department of Chemical Engineering, Institute of Chemical Technology, Mumbai (formerly UDCT Mumbai). |