The barycentric mass flux of component i is j m , i = ρ ρ ( u i − − ⟨ ⟨ u ⟩ ⟩ ) , where ⟨ ⟨ u ⟩ ⟩ is the average mass velocity of all the components in the mixture, given by ⟨ ⟨ u ⟩ ⟩ = 1 ρ ρ ∑ ∑ i ρ ρ i u i = 1 ρ ρ ∑ ∑ i j m , i where