Ion Concentration Polarization by Bifurcated Current Path

Ion concentration polarization (ICP) is a fundamental electrokinetic process that occurs near a perm-selective membrane under dc bias. Overall process highly depends on the current transportation mechanisms such as electro-convection, surface conduction and diffusioosmosis and the fundamental characteristics can be significantly altered by external parameters, once the permselectivity was fixed. In this work, a new ICP device with a bifurcated current path as for the enhancement of the surface conduction was fabricated using a polymeric nanoporous material. It was protruded to the middle of a microchannel, while the material was exactly aligned at the interface between two microchannels in a conventional ICP device. Rigorous experiments revealed out that the propagation of ICP layer was initiated from the different locations of the protruded membrane according to the dominant current path which was determined by a bulk electrolyte concentration. Since the enhancement of surface conduction maintained the stability of ICP process, a strong electrokinetic flow associated with the amplified electric field inside ICP layer was significantly suppressed over the protruded membrane even at condensed limit. As a practical example of utilizing the protruded device, we successfully demonstrated a non-destructive micro/nanofluidic preconcentrator of fragile cellular species (i.e. red blood cells).

straight microchannel with the geometries of 15 m depth, 200 m width, and 15 mm length (SI Figure 1(a)). The second one had a patterned nanoporous membrane at the bottom of the first device with ~1 m height of Nafion nanoporous membrane (SI Figure 1(b)). The conductance of the second device would be the sum of microchannel and nanoporous membrane since the nanoporous membrane was paralleled with the microchannel.
The microchannel was filled and flushed with target concentration electrolytes for ~2.5 hours so that the impurities inside the microchannel to be eliminated and the nanoporous membrane to become equilibrium state. The voltage was stepped from -0.1 V to +0.1 V at the rate of 0.05 V / 60 s, where time current transients were saturated. The conductance of each devices with different electrolyte concentrations were determined by obtaining the fitting curve's slope (ionic current vs. applied voltage). Each measurements was repeated at least 5 times with 5 devices for reliability. The ionic conductance of the first device, which only had a microchannel part, was proportional to the bulk concentration (SI Figure 1(c)), while the ionic conductance of the second device, which had a parallel connection of the microchannel and the nanoporous membrane, formed a plateau below a threshold concentration (SI Figure 1(d)). The ionic conductance (G) was defined as where F is the Faraday constant, A is the cross-sectional area, L is the length of the current path, i is the electrophoretic mobility of i-th charge carrier and Ni is the concentration of i-th charge carrier. In an electrohydrodynamic system, the Ni is the Donnan concentration on the cross-section.
The Donnan concentration was represented by for cation and for anion, respectively 1 . In the above, c0 is the bulk concentration and Nw is the surface charge concentration which was defined as where Am is the cross-sectional area of microchannel. On the other hand, the surface charge concentration of the nanoporous membrane was non-negligible compared with the bulk concentration due to the electrical double layer overlap so that the ionic conductance of the nanoporous membrane (Nafion) was where An is the cross-sectional area and Nn is the surface charge concentration of the Nafion. Using the circuit theory, the ionic conductance in the case of SI Figure 1 The appearance of plateau is attributed to electric double layer (EDL) overlap phenomenon which becomes severe as the bulk concentration decreases. Since the fixed amount of counter-ions existed inside the nanoporous membrane with the severe EDL overlap, the ionic conductance of the nanoporous membrane was independent from the bulk concentration 5 .
The ionic conductance of the nanoporous membrane and the electrolyte were separated from each another using the measured conductance of two devices. Then these data was recalculated for the device with protruded membrane since the device had different dimensions. The recalculated data was shown in Figure 1(d) in main text.

Descriptions for transport phenomena of ionic species inside nanoporous membrane
From the theory of the Donnan equilibrium 1 , the concentrations of cation and anion in nanoporous membrane were expressed as  