$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

The sliding-biphasic-solute implementation for sliding interfaces can deal with biphasic-solute contact surfaces (including biphasic-solute-on-biphasic-solute, biphasic-solute-on-biphasic, biphasic-solute-on-elastic, biphasic-solute-on-rigid) and the sliding-multiphasic contact interface can similarly deal with multiphasic contact surfaces. These contact interfaces allow for the possibility to track fluid and solute flow across the contact interface [12]. In other words, fluid and solute can flow from one side of the contact interface to the other. To use this feature, the user must define additional contact parameters, namely:

<pressure_penalty>1.0</pressure_penalty>
<concentration_penalty>1.0</concentration_penalty>
<ambient_pressure>0</ambient_pressure>
<ambient_concentration>0</ambient_concentration> (for sliding-biphasic-solute)

or

<ambient_concentration sol="id">0</ambient_concentration> (for sliding-multiphasic)

In the same way that the penalty parameter controls the contact tractions, these penalty parameters control the penalty values that are used to calculate the Lagrange multipliers for the pressure and concentration constraints. If the laugon flag is set, the augmented Lagrangian method is used to enforce the pressure and concentration constraints. And if the auto_penalty flag is defined, an initial guess for the pressure and concentration penalty is calculated automatically using the following formulas: $$\varepsilon_{p}=\frac{k\cdot A}{V}\,,\quad\varepsilon_{c}=\frac{d\cdot A}{V}\,,$$ where $A$ is the element's area, $V$ is the element's volume, $k$ is a measure of the fluid permeability which is defined as one third of the trace of the material's initial permeability tensor, and $d$ is a measure of the solute diffusivity which is defined as one third of the trace of the material's initial diffusivity tensor.

<ambient_pressure lc="2">1.0</ambient_pressure>
<ambient_concentration lc="3">1.0</ambient_concentration>

When performing biphasic-solute-on-rigid or multiphasic-on-rigid contact, a two-pass analysis should not be used; the rigid surface should be the secondary surface.