*4.6. Constitutive Equation*

In this paper, we used a compressible Neo-Hookean model. Though the solid itself was incompressible, due to its porous structure, the entire solid matrix was compressible. The Cauchy stress [19,20] is given by

$$\boldsymbol{\sigma} = -\frac{1}{6} \frac{\ln \boldsymbol{I}}{\boldsymbol{J}} \boldsymbol{G} \boldsymbol{I} (-1 + \frac{3(\boldsymbol{I} + \boldsymbol{n}\_{s,0})}{(-\boldsymbol{I} + \boldsymbol{n}\_{s,0})} + \frac{3 \ln(\boldsymbol{I}) \boldsymbol{I} \boldsymbol{n}\_{s,0}}{(-\boldsymbol{I} + \boldsymbol{n}\_{s,0})^2}) + \frac{\boldsymbol{G}}{\boldsymbol{J}} (\mathbf{F} \cdot \mathbf{F}^T - \boldsymbol{J}^{2/3} \mathbf{I}),\tag{15}$$

where *G* is the shear modulus, and *ns*,<sup>0</sup> represents the initial solid volume fraction. As *J* tends to *ns*,0, the fluid content vanishes and Equation (15) becomes an incompressible law.

When osmotic swelling is included, the total stress reads

$$
\mathfrak{d}\_{tot} = \mathfrak{d} - (\mu^f + \pi)\mathbf{I}.\tag{16}
$$

**Author Contributions:** conceptualization, J.M.H.; methodology, J.D. and E.W.R.; software, J.D. and E.W.R.; validation, J.D.; formal analysis, J.D.; investigation, J.D.; resources, J.J.C.R.; data curation, J.D. and J.J.C.R.; writing—original draft preparation, J.D.; writing—review and editing, J.M.H. and J.D.; supervision, J.M.H. and J.J.C.R.; project administration, the Dutch Technology Foundation STW and J.M.H.; funding acquisition, the Dutch Technology Foundation STW, the technological branch of the Netherlands Organization of Scientific Research NWO and the Ministry of Economic Affairs.

**Funding:** This research was funded by the Dutch Technology Foundation STW, the technological branch of the Netherlands Organization of Scientific Research NWO and the Ministry of Economic Affairs under contract [12538] Interfacial effects in ionized media.

**Acknowledgments:** We acknowledge the financial support from the Dutch Technology Foundation STW, the technological branch of the Netherlands Organization of Scientific Research NWO and the Ministry of Economic Affairs under contract [12538] Interfacial effects in ionized media.

**Conflicts of Interest:** The authors declare no conflict of interest.
