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When the Debye length is on the order of or larger than the height of a nanofluidic channel containing surface charge, a unipolar solution of counterions is generated to maintain electrical neutrality. A pressure-gradient-driven flow under such conditions can be used for ion separation, which forms the basis for electrochemomechanical energy conversion. The current−potential (I−φ) characteristics of such a battery were calculated using continuum dynamics. When the bulk concentration is large and the channel does not become a unipolar solution of counterions, both the current and potential become small. On the other hand, when bulk concentration is so much smaller, the mass diffusion becomes the rate-controlling step and the potential drops rapidly in the high current density region. When the Debye length of the solution is about half of the channel height, the efficiency is maximized.
Daiguji et al. (Tue,) studied this question.