phenomenologically: The fluid stress depends on fluid concentration (see Equation (\[Pf\])), and fluid stress gradient-driven flux appears as a concentration gradient-driven flux.

The saturation dependence of Fickean diffusion is modelled by using the measure of saturation introduced in Section \[satswel\]. We rewrite the chemical potential as

$$\begin{aligned}
\mu^\mathrm{f} &=&  
e^\mathrm{f} - \theta\eta^\mathrm{f},\nonumber\\
\eta^\mathrm{f} &\to& 0, \quad \mbox{as}\, \tilde{v}^\mathrm{f} +
\tilde{v}^\mathrm{c} \to 1.
\label{fickeanmobility}\end{aligned}$$

It is again important to note that under physiological conditions, soft tissues are fully saturated by fluid, and it is appropriate to set $\mu^\mathrm{f} = e^\mathrm{f}$.

### Transport of solute species {#solutespecies}

The dissolved solute species, denoted by s, undergo long range transport primarily by being advected by the fluid. In addition to this, they undergo diffusive transport relative to the fluid. This motivates an additional velocity split of the form $\bV^s=\widetilde{\bV^\mathrm{s}}+\bV^\mathrm{f}$, where $\widetilde{\bV^\mathrm{s}}$ denotes the velocity of the solute relative to the fluid. The constitutive relation for the corresponding flux, denoted by $\widetilde{\bM^s}$, has the following form, similar to Equation (\[fluidflux\]) defined for the fluid flux.

$$\widetilde{\bM^\mathrm{s}} = \bD^\mathrm{s}\left(
- \rho^\mathrm{s}_0\mathrm{\small{GRAD}}\left[e^\mathrm{s} -
 \theta\eta^\mathrm{s}\right]\right),
\label{soluteflux}$$

where $\bD^\mathrm{s}$ is the positive semi-definite mobility of the solute relative to the fluid, and again, isothermal conditions are assumed to approximate 