Mass Balance
The mass balance equation states that the total variation of mass, m, in a domain, V, is caused by the mass entering or exiting its surrounding boundary, and mass sources or sinks inside the domain
(3-292)
The time variation of the mass in the domain given in the reference configuration can be expressed as follows
where ρ0 is the density in the undeformed configuration. It is related to the current density through the volume ratio
After using the divergence theorem for the source term, Equation 3-292 reads
The flux vector Γ contains the Fickian diffusion plus external fluxes