Schematic of electrokinetic focusing experiments. (a) Charged analytes are placed in the right reservoir and a voltage bias is applied. (b) The structure of the pore, electrostatic potential, and electro-osmotically driven fluid flow in dimensionless units, with distance measured in units of the pore radius. For long pores , the concentration and potential fields are approximated as constant within the small hemispherical regions capping the pore (denoted by ±). Field and flux continuity conditions are applied at the hemispherical surfaces. The electro-osmotic flow field in the right chamber will be approximately spherically symmetric (red) if the membrane surface is uniformly charged but will be more lobelike (black) if the membrane flange is uncharged and no-slip boundary conditions are imposed (Refs. 1 and 2).
Salt concentration and electrostatic potential across an unimpeded pore of aspect ratio . (a) The salt density as a function of the axial coordinate for various EOF velocities and salt ratio . (b) The normalized potential for various salt ratios . The flat segments in both plots correspond the hemispherical cap regions in which all quantities are approximated as constant. The errors introduced in the quantities outside the caps with such an approximation are of order .
(a) EOF velocity as a function of effective pore EOF permeability . The response deviates from linear for large and small salt ratios. The deviations are most pronounced for where EOF is into the right reservoir . (b) EOF velocity as a function of salt ratio for various effective pore surface charge densities. For , increasing the salt ratio decreases the effective screening length in the pore, reducing the EOF velocity [cf. Eq. (26)]. When , the salt in the right reservoir is swept into the left reservoir, keeping the screening length approximately throughout the pore and very little dependence on arises. In both plots and .
(a) The electrostatic potential in the right reservoir (normalized by the applied potential ), as a function of salt asymmetry for various pore EOF permeabilities . Here the pore aspect ratio was set to . (b) The magnitude of the potential near the mouth pore as a function of EOF permeability for various salt ratios.
(a) Pore mouth occupation fraction as a function of salt ratio for various EOF permeability and . Note the sharp increase in as a function of for positive surface charges. Parameters used were , , , , , and . For small , larger induces larger , pushing the analyte away. At higher salt , the EOF is mitigated due to the reduction in -potential (or effective surface charge) indicated by Eq. (27). The reduction of EOF to modest values allows the attraction from the term to overcome the repulsive effect of the EOF [cf. Fig. 4(a)], increasing . (b) Occupation fraction as a function of bias voltage at different salt ratios and .
(a) Normalized capture rate as a function of bias voltage. (a) The effect of varying salt ratio . (b) The effect of varying with fixed .
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