Geometries used in the numerical tests, with the set-ups denoted as A (upper) and B (lower). The dashed lines indicate the location of the surface charge. The potential tension is applied between the inlet and outlet regions. Throughout the text, the labels D, d, A, a, and r are expressed in lattice units.
Normalized density of counter-ions (left) and co-ions (right plot) for system A for wide (plots (a) and (b) with d = 40, D = 60, a = 20, and A = 40), medium (plots (c) and (d) with d = 20, D = 60, a = 20, and A = 40), and small (plots (e) and (f) with d = 10, D = 60, a = 20, and A = 40) channels, with ΔV = 10−2.
Comparison of 1D-PNP and 3D-LB longitudinal profiles of the density (upper panels) and the potential (lower panels). The geometries and parameters are as in Fig. 2 .
Normalized density of electrolytes, electrostatic potential, and longitudinal profiles for system A (d = 20, D = 60, a = 40, and A = 40), with ΔV = 0.
Density of electrolytes normalized by the maximum value ((a) and (b)). (c) compares the 1D-PNP and 3D-LB longitudinal profiles of the density (plot (c), upper) and the potential (plot (c), lower) for system A (d = 20, D = 60, a = 20, and A = 140), with ΔV = 10−1.
Longitudinal profiles for system A (d = 20, D = 60, a = 20, and A = 40), system B with (d = 20, D = 60, a = 20, r = 10, and A = 40), and a smoother version labelled B* (d = 20, D = 60, a = 20, r = 30, and A = 0). Data refer to ΔV = 0. Plot (a) reports the counter-ion density, plot (b) the electrostatic potential, and plot (c) the relative difference between the 3D-LB and 1D-PNP profiles. The latter plot includes the case of a channel with homogeneous radius (d = 20, D = 20, a = 20, and A = 40).
Normalized profile of counter-ions and conductance at different Debye lengths as obtained with the 1D-PNP and 3D-LB methods for system A (d = 20, D = 60, a = 20, and A = 40) and ΔV = 10−2. The conductance is normalized by the value G o = e 2 D/a 2 k B T.
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