Conservation of Mass for a Reacting Species

To consider the control volume form of the conservation of mass for a species in a reacting mixture volume, we apply Equation (2.14) for the system and make the conversion from Equation (3.12). Here we select/ = pt, the species density. In applying Equation (3.13), v must be the velocity of the species. However, in a mixture, species can move by the process of diffusion even though the bulk of the mixture might be at rest. This requires a more careful distinction between the velocity of the bulk mixture and its individual components. Indeed, the velocity v given in Equation (3.13) is for the bulk mixture. Diffusion velocities, Vi, are defined as relative to this bulk mixture velocity v. Then, the absolute velocity of species i is given as 

In order always to include species i in the system before converting to a control 

Since the chemical reaction may not necessarily be uniformly dispersed over the control volume, it is sometimes useful to represent it in terms of a local reaction rate, m v or the mass production rate of species i per unit volume. Then 

Usually for applications to combustors or room fires, diffusion effects can be ignored at surfaces where transport of fluid occurs, but within diffusion flames these effects are at the heart of its transport mechanism. 

When concentrations are uniform throughout the control and uniform at entering flow paths, Equation (3.20) can be expressed in terms of YL. The mass of species in the control volume can be given as 

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