$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

Solutes are denoted generically by $\alpha=\iota$ . In chemistry solute content is often represented in units of molar concentration (moles per fluid volume). It follows that solute molar concentration $c^{\iota}$ and molar supply $\hat{c}^{\iota}$ are related to $\rho^{\iota}$ and $\hat{\rho}^{\iota}$ via $$\begin{equation} c^{\iota}=\frac{\rho^{\iota}}{\left(1-\varphi^{s}\right)M^{\iota}},\quad\hat{c}^{\iota}=\frac{\hat{\rho}^{\iota}}{\left(1-\varphi^{s}\right)M^{\iota}}\,.\label{eq159} \end{equation}$$ The molar flux of constituent $\iota$ relative to the solid is given by $$\begin{equation} \mathbf{j}^{\iota}=\left(1-\varphi^{s}\right)c^{\iota}\left(\mathbf{v}^{\iota}-\mathbf{v}^{s}\right)\,,\label{eq160} \end{equation}$$ where it may be noted that $\mathbf{m}^{\iota}=M^{\iota}\mathbf{j}^{\iota}$ . Combining these relations with (2.10-4)-(2.10-5) produces the desired form of the mass balance for the solutes, $$\begin{equation} \frac{1}{J}\frac{D^{s}\left[J\left(1-\varphi^{s}\right)c^{\iota}\right]}{Dt}+\mbox{div}\mathbf{j}^{\iota}=\left(1-\varphi^{s}\right)\hat{c}^{\iota}\,.\label{eq161} \end{equation}$$ This form is suitable for implementation in a finite element analysis where the mesh is defined on the solid matrix.