Effective one-dimensional model for counter-ion flow through a viscoelastic, charged nanochannel

In this work, we present a theoretical model for nonlinear deformational properties of the wall of a charged, viscoelastic nanochannel under the influence of water and ion flow. The nanochannel viscoelasticity is described by the Kelvin-Voigt model. Using continuum theories for mass and momentum conservation of the solid-liquid coupled system, we derive a set of 1-D nonlinear partial differential equations for the dynamics of the system. By means of linear perturbations and numerical calculations, the propagation properties of the fluid governed by these evolution equations are analysed in detail. Finally, we discuss one key application of this study: the dynamic response of polymeric membrane nanopores to the flow of water and protons in polymer electrolye membrane (PEM) fuel cells.