Poisson-Nernst-Planck (PNP) theory is based on the continuum description of ion flow and has been extensively used for its study across a channel under electro-chemical gradients. PNP theory, however, does not include non-ionic interactions and thus is insufficient to describe flows where these interactions become important, ion channel flow being one such case. Over the years, several improvements have been made to PNP in order to counter its limitations. Kurnikova et al.[1] used density functional theory(DFT) while Eisenberg and Nonner[2] developed a simplified model for ions in the bulk region and inside the channel lter. Liu et al.[3] pioneered in energy variational (EnVar) approach which was later on adopted by Eisenberg et al.[4]. Here we are following the methodology of Eisenberg. In this approach, inter-particle collisions are addressed by the introduction of Lennard-Jones potential. These interactions play an important role in defining the selectivity of the channel, concentration distribution of ionic species and current across the channel etc.

This study is focused on understanding the relationship between the steric effect and selectivity of the channel. The system is discretized using lattice boltzmann method (LBM). A generalized 3D geometry is being considered for the channel, thus, we are including immersed boundary method (IBM) for an appropriate treatment of the boundary conditions. Additionally, we are using multiple GPUs to reduce the execution time which is aptly aided by high parallelizability of LBM.