Interface conditions for a polyelectrolyte gel in a salt solution with a thin electrical double layer

Polyelectrolyte gels are electro-active soft materials that are often surrounded by a viscous salt solution. The formation of an electrical double layer (EDL) at the interface between the gel and the solution can give rise to fluid-structure interactions driven by Coulomb forces. However, these interactions are usually neglected in modelling studies due to the difficulty of resolving the EDL, which has a thickness that is orders of magnitude smaller than the characteristic gel size. In this paper, an asymptotically consistent model of a polyelectrolyte gel that is surrounded by a salt solution is derived in the thin-EDL limit. The model consists of bulk equations describing an electrically neutral gel and bath, along with interfacial conditions that capture the electro-mechanical impact of the EDL. A key result is the derivation of a Helmholtz-Smoluchowski slip condition that describes how shear stresses in the EDL lead to a bulk flow in the surrounding salt solution. The impact of this flow on gel-gel friction and swelling-driven instabilities is discussed. The model derived here will lead to a better understanding of how polyelectrolyte gels interact with an external salt solution, which is crucial for applications.