  Scaling of the behavior of a nanodevice means that the device function
(selectivity, in this work) is a unique function of a scaling parameter that is
an appropriate combination of the device parameters. Although nanopores
facilitate the transport of ions through a membrane of finite length if the
pore is long compared to the pore radius, we deal with an important limiting
case, the infinitely long nanopore (nanotube). While in our previous study
(Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhin
number is an appropriate scaling parameter in the nanotube limit for 1:1
electrolytes, in this work we obtain the Dukhin number from first principles on
the basis of the Poisson-Boltzmann (PB) theory and generalize it to
electrolytes containing multivalent ions as well. We show that grand canonical
Monte Carlo simulations for charged hard spheres in an implicit solvent give
results that are similar to those obtained from the PB theory with deviations
that are the consequences of ionic correlations (including finite size of ions)
beyond the mean-field level of the PB theory. Such a deviation occurs when
charge inversion is present, in 2:2 and 3:1 electrolytes, for example.

Soft Condensed Matter;Mesoscale and Nanoscale Physics;Statistical Mechanics;Chemical Physics