Technical Report: Solid Pyrolysis

[Sabinbhattarai21]

Dear Team,
I am confused about term ρ_(s,α) in given below. In technical report, it is mentioned that mass per unit volume of component α as it is shown in Eq. (7.34). Does that volume indicate volume of the component α or volume of the particle or volume of the finite volume?
If it is the volume of the component α, then how the Eq. (2.27) can be derived

[drjfloyd]

Eq. 7.27 is just a definition for the term ${\rho_{s,\alpha}}$.

The density in Eq 7.34 is taken at a point in space. It would be computed as masss contained in a differential volume around the point x.

[Sabinbhattarai21]

Does ρ_(s,α) indicate in Eq. (7.27) and Eq. (7.34) have the same meaning? Is density in both is computed as mass (of alpha) contained in a differential volume around the point x?

[drjfloyd]

They are the same. 7.27 is defining the term that is being used in 7.34

[bshoto]

Considering the first comment by Jason, eq. (7.27) and the fact that Y_alpha denotes the mass fraction of solid component alpha, then rho_s indicates the total mass of solid within that differential volume and rho_{s,alpha} indicates the mass of solid component alpha within that differential volume.