After a thematic representation about the different modeling approached of multiphase flows in Multiphase Flow Modeling using CFD, we shall now have a look at the mathematical treatments involved behind all these models viz., Eulerian-Lagrangian, Eulerian-Eulerian and Volume of fluid.

Chemical reactions are very common in industry as well as nature. They are used as a crucial tool to enhance and control mixing, heat transfer, material formation and deposition, pollutant release, production processes etc. Any type of reacting flow involves strong coupling between reaction chemistry and flow physics.

"Thermodynamically a phase refers to states of matter which we generally classified as solid, liquid and gaseous". (Clayton T. Crowe; Multiphase Flow Handbook).

Before we enter into any further discussion it is very important to understand what exactly do we mean by phase. From modeling point of view there is a slight modification from the definition. 

The terminologies used in the study of multiphase flows are as follows :

Continuous phase or Primary phase : This is basically the carrier fluid, that is present in bulk.

Dispersed phase or Secondary phaseThis is the discrete phase which is usually in the form of  particles, droplets, or bubbles.

A single phase flow is modelled by governing equations like the continuity equation, momentum equation and the energy equation. These equations are solved at each cell i.e. we divide the entire volume of interest into cells using various discretization schemes such as finite difference, finite element and finite volume schemes. Let us further consider the modeling of a two phase flow.

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