Mathematical modelling of electrokinetic phenomona in soft nanopores

In and around porous systems with at least one characteristic dimension below 100 nm, solid/liquid interfaces play a key role in surface-charge-governed transport, separation processes and energy storage devices. Nanopores with well-defined geometry and chemical characteristics have emerged as valuable tools to unravel interactions between external and induced electric fields and the underlying transport, in the presence of embedded charges. In this thesis, theoretical and numerical investigations of electrokinetic effects in soft cylindrical nanochannels with uniformly distributed surface charges are carried out within continuum mean-field approximations. The aim is to provide a theoretical framework through which one can access a comprehensive understanding of the coupling between electrokinetic transport, double-layer charging and wall deformations in nanochannels embedded in soft polymeric membranes. In the first part of the thesis, numerical calculations using the coupled continuum mean-field equations are conducted to quantify ion and fluid transport in a finite, cylindrical and rigid nanochannel connected to cylindrical electrolytic reservoirs. Results of these calculations, verified by experiments, serve as a guide for theoretical investigations in later components of the thesis. Subsequently, the transport of protons and water in a long, negatively charged channel is studied from a theoretical point of view. A theoretical model is developed that describes nonlinear coupling between wall deformation and water and proton flows in a charged, eformable nanochannel whose viscoelasticity is governed by the linear Kelvin-Voigt model. In addition to focusing on transport phenomena in an open nanochannel, we direct attention to the equilibrium structure of the electric double layers. This was achieved by considering a physical situation where the charged channel is finite and sealed at both ends by metal electrodes under external voltage bias. Size-modified mean-field equations were used to account for finite ion sizes, subject to a self-consistent electroneutrality condition which demands that the net amount of charge on both electrode surfaces balances. Equilibrium ion distributions and differential capacitance curves are presented and analysed. Motivated by electroactuators, the last part of the thesis added deformations of the channel walls to the closed-channel system modelling.