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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 isan appropriate combination of the device parameters. Although nanoporesfacilitate the transport of ions through a membrane of finite length if thepore is long compared to the pore radius, we deal with an important limitingcase, the infinitely long nanopore (nanotube). While in our previous study(Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhinnumber is an appropriate scaling parameter in the nanotube limit for 1:1electrolytes, in this work we obtain the Dukhin number from first principles onthe basis of the Poisson-Boltzmann (PB) theory and generalize it toelectrolytes containing multivalent ions as well. We show that grand canonicalMonte Carlo simulations for charged hard spheres in an implicit solvent giveresults that are similar to those obtained from the PB theory with deviationsthat are the consequences of ionic correlations (including finite size of ions)beyond the mean-field level of the PB theory. Such a deviation occurs whencharge inversion is present, in 2:2 and 3:1 electrolytes, for example.

The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: extension to multivalent electrolytes