Jarrod Schiffbauer

Universal low-frequency asymptotes of dynamic conic nanopore rectification: An ionic nanofluidic inductor

We report the first nanofluidic inductor (L) to complement the known nanofluidic capacitors (C), resistors (R), and diodes for ion currents. Under negative bias, the nanopore behaves like a parallel RC circuit at low frequencies; however, under positive bias, the asymptotic dynamics is that of a serial RL circuit. This new ionic circuit element can lead to nanofluidic RLC or diode-inductor oscillator circuits and new intrapore biosensing/rapid sequencing strategies. A universal theory, with explicit estimates for the capacitance and inductance at opposite biases, is derived to collapse the rectified dynamics of all conic nanopores to facilitate design of this new nanofluidic circuit.

Ion current rectification in funnel-shaped nanochannels: Hysteresis and inversion effects.

Ion current rectification inversion is observed in a funnel-shaped nanochannel above a threshold voltage roughly corresponding to the under-limiting to over-limiting current transition. Previous experimental studies have examined rectification at either low-voltages (under-limiting current region) for conical nanopores/funnel-shaped nanochannels or at high-voltages (over-limiting region) for straight nanochannels with asymmetric entrances or asymmetric interfacing microchannels. The observed rectification inversion occurs because the system resistance is shifted, beyond a threshold voltage, from being controlled by intra-channel ion concentration-polarization to that controlled by external concentration-polarization. Additionally, strong hysteresis effects, due to residual concentration-polarization, manifest themselves through the dependence of the transient current rectification on voltage scan rate.

Modes of electrokinetic instability for imperfect electric membranes

The direct transition to overlimiting current bypassing the stage of limiting currents is considered for imperfect membranes. Instability of the quiescent steady-state one-dimensional solution, which is the result of a balance of diffusion and electromigration, is investigated on the basis of the full Nernst-Planck-Poisson-Stokes system and a simplified quasielectroneutral system. A three-layer geometry, electrolyte-porous membrane-electrolyte, is considered. The usual assumption of a constant electrochemical potential along the membrane surface is removed from consideration. The effect of bulk and surface effects on the instability and transition to the overlimiting currents is evaluated for a different membrane selectivity. It becomes clear that for sufficiently small fixed charge concentration (large ion concentration in the electrolyte), the monotonic instability is replaced by an oscillatory one. The dependence of instability on the membrane porosity is found to be weak.

Confinement effects on electroconvective instability

We present an analysis of hydrodynamic effects in systems involving ion transport from an aqueous electrolyte to an ion‐selective surface. These systems are described by the Poisson–Nernst–Planck and Navier–Stokes equations. Historically, such systems were modeled by one‐dimensional geometries with spatial coordinate in the direction of transport and normal to the ion‐selective surface. Rubinstein and Zaltzman [JFM 579, 173–226 (2007)] showed that when such systems are unbounded in the transverse directions, a hydrodynamic instability can occur. This instability, referred to as electroconvective instability, leads to advective mixing, which results in overlimiting transport rates significantly beyond what is predicted from one‐dimensional models. In this study, we present an analysis of electroconvection in confined systems, considering a broad range of applications including microfluidic systems and porous media. Our analysis reveals that full confinement in the transverse directions significantly suppresses electroconvection and overlimiting current. However, when at least one transverse direction allows for flow escape, such as in thin but wide channels or in porous media, the onset of instability is only weakly affected by confinement. We will also present a review of relevant literature and discuss how the present study resolves the contradictory contrasts between the results of recent work on this topic.

Robust ion current oscillations under a steady electric field: An ion channel analog.

We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorells nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous 1/f power spectrum.