bath. Accordingly, this is the appropriate Dirichlet boundary condition to impose under normal physiological conditions. This is shown in an idealised manner in Figure \[fbc\].

![If the pore structure at the boundary deforms with the tissue and this boundary is in contact with a fluid bath, the fluid concentration with respect to the current configuration, i.e., $\rho^\mathrm{f}$, remains constant.[]{data-label="fbc"}](concentration.eps){width="7.50cm"}

In the interest of applying boundary conditions (either specification of species flux or concentration) that are physically meaningful, we use the local form of the balance of mass in the current configuration,

$$\frac{\mathrm{d}\rho^\iota}{\mathrm{d}t} = \pi^\iota-
\mathrm{\small{div}}[\bm^\iota] - \rho^\iota
\mathrm{\small{div}}[\bv],\;\forall\,\iota, \label{massbalcurr}$$

where $\rho^\iota(\bx,t),\pi^\iota(\bx,t)$, and $\bm^\iota(\bx,t)$ are the current mass concentration, source and mass flux of species $\iota$ respectively and $\bv(\bx,t)$ is the velocity of the solid phase. They are related to corresponding reference quantities as $\rho^\iota = \left(\mathrm{det} \left(\bF\right)
\right)^{-1} \rho_0^\iota$, $\pi^\iota = \left(\mathrm{det}
\left(\bF\right) \right)^{-1} \Pi^\iota$ and $\bm^\iota =
\left(\mathrm{det} \left(\bF\right) \right)^{-1} \bF \bM^\iota$. The spatial divergence operator is $\mbox{\small{div} [\textbullet]}$, and the left hand-side in Equation (\[massbalcurr\]) is the material time derivative relative to the solid, which may be written explicitly as $\frac{\partial}{\partial t}\vert_X$, implying that the reference position of the solid collagenous skeleton is held fixed.

The kinematics of 