Transitions and Instabilities in Imperfect Ion-Selective Membranes

Abstract

Numerical investigation of the underlimiting, limiting, and overlimiting current modes and their transitions in imperfect ion-selective membranes with fluid flow through permitted through the membrane is presented. The system is treated as a three layer composite system of electrolyte-porous membrane-electrolyte where the Nernst–Planck–Poisson–Stokes system of equations is used in the electrolyte, and the Darcy–Brinkman approach is employed in the nanoporous membrane. In order to resolve thin Debye and Darcy layers, quasi-spectral methods are applied using Chebyshev polynomials for their accumulation of zeros and, hence, best resolution in the layers. The boundary between underlimiting and overlimiting current regimes is subject of linear stability analysis, where the transition to overlimiting current is assumed due to the electrokinetic instability of the one-dimensional quiescent state. However, the well-developed overlimiting current is inherently a problem of nonlinear stability and is subject of the direct numerical simulation of the full system of equations. Both high and low fixed charge density membranes (low- and high concentration electrolyte solutions), acting respectively as (nearly) perfect or imperfect membranes, are considered. The perfect membrane is adequately described by a one-layer model while the imperfect membrane has a more sophisticated response. In particular, the direct transition from underlimiting to overlimiting currents, bypassing the limiting currents, is found to be possible for imperfect membranes (high-concentration electrolyte). The transition to the overlimiting currents for the low-concentration electrolyte solutions is monotonic, while for the high-concentration solutions it is oscillatory. Despite the fact that velocities in the porous membrane are much smaller than in the electrolyte region, it is further demonstrated that they can dramatically influence the nature and transition to the overlimiting regimes. A map of the bifurcations, transitions, and regimes is constructed in coordinates of the fixed membrane charge and the Darcy number.

Electrokinetic and Electroconvective Effects in Ternary Electrolyte Near Ion-Selective Microsphere

“…The hydrodynamics inside the particle were neglected, . A similar method of modeling imperfect selective surfaces has been used in solving problems in planar geometry [ 28 ] and proven to be a good approximation for generalizing the model relative to the perfectly selective approach [ 9 , 11 , 29 , 30 , 31 ].…”

“…The parameters and were also fixed, (which roughly corresponds to a potassium chloride solution) and . The value of N was fixed at , which corresponds to a selectivity of more than 90% [ 28 ].…”

The Physical Chemistry and Chemical Physics (PCCP) Section of the International Journal of Molecular Sciences in Its Publications: The First 300 Thematic Articles in the First 3 Years

“…This thematic area is associated with articles [ 12 , 15 , 20 , 21 , 26 , 50 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 ], of which there are a total of 50. In contrast to the areas already discussed above, articles of all four types are presented here ( Table 5 ), although, here, too, the Original constitutes a clear majority over the other 3 types of articles.…”

“…In contrast to the areas already discussed above, articles of all four types are presented here ( Table 5 ), although, here, too, the Original constitutes a clear majority over the other 3 types of articles. The dominant feature of this thematic area was articles devoted to cell membranes, in general, and their electrochemistry, in particular; articles [ 26 , 50 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 92 , 93 , 95 , 99 , 100 ] are devoted to this specific topic. In this connection, it is worth noting that this “membrane topic” turned out to be, generally, the most popular in comparison with all the others presented in the PCCP Section of the IJMS , within the array of 300 articles we are considering.…”

Ion and Molecule Transport in Membrane Systems 2.0

“…A simplified equation system obtained in [ 15 ] describes the power density generated in the system with good accuracy. J. Schiffbauer et al [ 16 ] studied how the presence of hydraulically permeable pores in an ion-selective membrane affects the transitions from underlimiting to overlimiting current and the occurrence of electrokinetic instabilities leading to intensification of electroconvection. The latter is convective transport of solution under the action of an applied electric field.…”