Pressure-sensitive ion conduction in a conical channel: optimal pressure and geometry

Using both analytic and numerical analyses of the Poisson-Nernst-Planck equations we theoretically investigate the electric conductivity of a conical channel, which in accordance with recent experiments exhibits a strong non-linear pressure dependence. This mechanosensitive diodic behavior stems from the pressure-sensitive build-up or depletion of salt in the pore. From our analytic results we find that the optimal geometry for this diodic behavior strongly depends on the flow rate, the ideal ratio of tip-to-base-radii being equal to 0.22 at zero flow. With increased flow this optimal ratio becomes smaller and simultaneously the diodic performance becomes weaker. Consequently an optimal diode is obtained at zero-flow, which is realized by applying a pressure drop that is proportional to the applied potential and to the inverse square of the tip radius thereby countering electro-osmotic flow. When the applied pressure deviates from this ideal pressure drop the diodic performance falls sharply, explaining the dramatic mechanosensitivity observed in experiments.