Mass-flux fraction

where

• ${\displaystyle Y_{i}=\rho _{i}/\rho }$ is the mass fraction
• ${\displaystyle v}$ is the mass average velocity of the gaseous mixture
• ${\displaystyle V_{i}}$ is the average velocity with which the species i diffuse relative to ${\displaystyle v}$
• ${\displaystyle \rho _{i}}$ is the density of species i
• ${\displaystyle \rho }$ is the gas density.

It satisfies the identity

${\displaystyle \sum _{i}\epsilon _{i}=1}$,

similar to the mass fraction, but the mass-flux fraction can take both positive and negative values. This variable is used in steady, one-dimensional combustion problems in place of the mass fraction.^[5] For one-dimensional (${\displaystyle x}$ direction) steady flows, the conservation equation for the mass-flux fraction reduces to

${\displaystyle {\frac {d\epsilon _{i}}{dx}}={\frac {w_{i}}{\rho v}}}$,

where ${\displaystyle w_{i}}$ is the mass production rate of species i.

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