Electrokinetic energy conversion in micrometer-length nanofluidic channels

In this study, we present a theoretical and numerical investigation of electrokinetic energy conversion in short-length nanofluidic channels, taking into account reservoir resistance and concentration polarization effects. The concentration polarization effect was demonstrated through numerical modeling using the Poisson-Nernst-Planck (PNP) model. In the absence of concentration polarization, the modified Onsager reciprocal relation for the electrokinetic flow through a one-dimensional (1D) nanochannel is derived from both Ohm's law and Kirchhoff's current law while considering the reservoir resistance. Based on this modified Onsager reciprocal relation and the Poisson-Boltzmann (PB) model, a theoretical model for electrokinetic energy conversion is proposed to address the importance of the reservoir resistance effect on electrokinetic energy conversion. The applicability of our proposed model is also verified through numerical modeling of the PNP model. The results calculated from our proposed model are shown to be in good agreement with those from the PNP model when the concentration polarization effect does not occur significantly at the reservoirs. The conversion efficiency and generation power are decreased when the channel resistance is not much larger than the reservoir resistance, especially for a shorter-length nanochannel (e.g., a channel several micrometers in length) with a lower electrolyte concentration and a higher surface charge density. After the concentration polarization effect becomes increased as a larger pressure gradient is applied through an ideal ion-selective nanochannel, the conversion efficiency/generation power is further decreased due to the ion depletion at the inlet reservoir, which increases the electrical resistance of the inlet reservoir or the equivalent electrical resistance of the electrokinetic energy conversion system. The onset pressure difference (or gradient) for a significant concentration polarization is identified both theoretically and numerically. In order to avoid decreases in the conversion efficiency/generation power mentioned above, some key factors such as the length of the nanochannel, the position of electrodes at the reservoirs, and the applied pressure gradient were noticed in this study.