One dimensional theory of electrokinetic transport in deformable nanochannels

In this work, we present a theoretical study of nonlinear coupling between wall deformation and water and ion flows in a charged, deformable nanochannel. The classical treatment of the mass and momentum conservation of the solid-liquid coupled system is based on the Stokes-Poisson–Nernst–Planck equations. For elastic but non-viscous walls undergoing small deformation, analytically solvable diferential equations were obtained in one dimension. Quantitative response of the walls’ relaxation dynamics and the channel’s electrokinetic transport was investigated at different charging regimes. Within the framework of nonequilibrium thermodynamics, compact formulae in terms of Onsager's phenomenological coefficients were derived for the electrokinetic transport parameters and energy conversion efficiency. Furthermore, an extension of the model is presented for electroactuator modelling which operates through a coupling of electrical and mechanical interactions for closed nanochannels. Numerical methods and results are presented, highlighting the significance of the fluid and charge redistribution on elastic deformations of the nanochannel.