Reluctance of a neutral nanoparticle to enter a charged pore

We consider the translocation of a neutral (uncharged) nanoparticle through a pore in a thin membrane with constant surface charge density. If the concomitant Debye screening layer is sufficiently thin, the resulting forces experienced by the particle on its way through the pore are negligible. But when the Debye length becomes comparable to the pore diameter, the particle encounters a quite significant potential barrier while approaching and entering the pore, and symmetrically upon exiting the pore. The main reason is an increasing pressure, which acts on the particle when it intrudes into the counter ion cloud of the Debye screening layer. In case the polarizability of the particle is different (usually smaller) than that of the ambient fluid, a second, much smaller contribution to the potential barrier is due to self-energy effects. Our numerical treatment of the problem is complemented by analytical approximations for sufficiently long cylindrical particles and pores, which agree very well with the numerics.