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

According to the law of mass action for forward reactions, $$\begin{equation} \hat{\zeta}=k\left(\theta,\mathbf{F},\rho_{r}^{\sigma}\right)\prod\limits _{\alpha}\left(c^{\alpha}\right)^{\nu_{R}^{\alpha}}\,.\label{eq525} \end{equation}$$ A constitutive relation for the specific reaction rate $k\left(\theta,\mathbf{F},\rho_{r}^{\sigma}\right)$ must also be provided.