Membrane Transport Characteristics of Ultrafine Capillaries

Gross, R. J.; Osterle, J. F.

doi:10.1063/1.1669814

Cited by 346 publications

(279 citation statements)

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“…Charged capillary nanopores and nanotubes are essential in many natural and technological systems, as part of porous membranes separating two aqueous electrolytes [1][2][3][4][5][6][7][8][9][10][11][12][13]. Membranes containing charged nanopores can be used for water desalination, selective ion removal, and electrokinetic energy conversion.…”

Section: Introductionmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

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Section: Introductionmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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“…The radial variation of potential and ion concentrations in the pore as well as the impact of electroosmotic flow on ion transfer are taken into account in the space-charge (SC) model, which was originally developed in [20]. Detailed comparison between results obtained from SC and TMS models [21] showed a good agreement for pores with small radius (less than 2 nm) and low surface charge density.…”

Section: Introductionmentioning

confidence: 71%

“…Figure 3 shows the dependence of residuals R for continuity equation (18) or (25) and negative ion transport equation (20) or (27) on the number of iterations n. One can see that the use of Slotboom variables allows to decrease the required number of iterations by 2-3 times in comparison with the use of Primitive variables. The Coupled method allows to decrease this number further by 5 times.…”

Section: Numerical Implementationmentioning

confidence: 97%

Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density

Ryzhkov

Минаков

2016

Journal of Membrane Science

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Abstract. The pressure-driven ion transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one-dimensional Nernst-Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. A simplified model for the case of constant surface potential is also proposed. The second approach is based on two-dimensional Nernst-Planck, Poisson, and Navier-Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter-ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co-ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one-and two-dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, electrolyte concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low.

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“…We have performed a comparison of convergence between formulations in Primitive variables (3)- (5) and Slotboom variables (10)- (12). It was found that the use of Slotboom variables allows to decrease the required number of iterations by 2 times.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…The radial variation of potential and ion concentrations in the pore as well as the impact of electroosmotic flow on ion transfer are taken into account in the space-charge (SC) model, which was originally developed in [12]. Experimental verification of this model was performed by comparing the theoretical predictions for streaming potential, pore conductivity, and diffusion potential with the measured data [13].…”

Section: Introductionmentioning

confidence: 99%