(490e) Detecting Molecules with an Electrokinetic Instability in Membrane Microfluidics

A unique electrokinetic microvortex instability occurs on one side of a perm-selective membrane, where ions have been depleted, and the resulting electro-convective ion transport triggers the onset of the Overlimiting Current (OR) region from the classical Limiting Current (LC) region first studied by Levich. Earlier work by Rubinstein and Zaltzman and from our group (Annual Rev of Fluid Mech 2012) showed that finite differential resistance in the LC region occurs if the extended polarized (Debye) layer becomes significant compared to the diffusion length of the ion depleted region. We have used this principle, plus the observation that the hydrophilic perm selective membrane is fouling resistant and the ion depletion action in the LC region enhances electrostatic interaction, we have invented a membrane sensor for high sensitivity (pM-nM) and large dynamic range quantification of charged molecules (nucleic acids and endotoxins) and for weakly charged molecules (proteins) with charged nanoparticle reporters (Annual Rev of Analytical Chem 2014; ACS Applied Materials and Interfaces 2020; JCP 2021). These electrokinetic point membrane sensors can be inserted into microlfuidic biochips and provide voltage signals much larger than conventional electrochemical sensors. They are also much more selective, as redox Faradaic reaction is not involved--the molecules and reporters are gating the ion current.

Our extensive measurements show the charge impurity triggered LC and OC share some universal features that are distinct from naturally excited electroconvective instabilities. With numerical simulation, scaling theory and experimentation, we report here the mechanisms underlying these features and offer scaling theories, backed by numerics, to collapse the relevant data. The ion depletion action in the LC region produces a near-ion free neighborhood with a large (100 nm) Debye screening length that enhances the range of the electric field from the charged impurities. It also enhances the resulting electroosmosis along the membrane surface, due to an extended polarized (Debye) layer, to drive micro-vortices with a linear dimension corresponding to the charge spacing. The OR transition occurs when the Peclet number of the vortices exceeds a critical value and we use this scaling theory to collapse the measured transition voltage, which scales as 1/2 power of the impurity surface concentration. For a periodic impurity array, the vortices undergo successive asymmetric coalescence bifurcation such that the smaller vortices near the surface are half or 1/3 the size of the primary vortex at the onset. These intense smaller vortices enhances counterion flux into the membrane and effectively reduce the diffusion length by half or 1/3. The result for an ideally selective membrane is that differential resistance in the OR is twice or three times lower that in the LR. Both the OR onset voltage and the differential resistance ratio scalings are consistent with measured data at small spacing (high concentration).

For charge separation much larger than the natural electro-convective length scale, the charge spacing no longer selects the vortex size or length scale. Instead, we use Guoy-Chapman theory to estimate the threshold voltage the charged impurities impose on the counterion current. We show that the transition voltage scales as logarithm of the impurity concentration and are able to collapse the experimental data in this limit. The asymmetric vortex bifurcation still occurs to produce a differential resistance that is 2 or 3 times lower than that in the LR. This logarithm scaling offers the large dynamic range and low detection limit necessary for a universal molecular sensor.