Figure 1

Representation of a nanostructured channel filter as modelled in the present letter. The nominal shape of the channel is supposed to be cylindrical with length L, and the figure shows only the differential slice with axial coordinate from x to x + dx. The radiuses r₀ and ρ₀ correspond to the average dimensions of the bare channel and impurities. The effective radiuses r_e and ρ_e vary as trapped impurities cover the inner wall, via their dependences on, respectively, the areal density n of trapped impurities and on the areal density z_e of effective charge of the inner wall. This z_e reflects that exposed charges in a nanostructured surface attract the impurities in the fluid and also constitute binding anchors for those impurities. It is expected to diminish as impurities cover the surface, for which we assume the simple z_e(n) dependence given by Equation 1 of the main text.