Solution of ion channel flow using immersed boundary-lattice boltzmann methods

[[abstract]]Poisson-Nernst-Planck (PNP) model has been extensively used for the study of channel flow under the influence of electrochemical gradients. PNP theory is a continuum description of ion flow where ionic distributions are described in terms of concentrations. Nonionic interparticle interactions are not considered in this theory as in continuum framework, their impact on the solution is minimal. This theory holds true for dilute flows or flows where channel radius is significantly larger than ion radius. However, for ion channel flows, where channel dimensions and ionic radius are of similar magnitude, nonionic interactions, particularly related to the size of the ions (steric effect), play an important role in defining the selectivity of the channel, concentration distribution of ionic species, and current across the channel, etc. To account for the effect of size of ions, several modifications to PNP equations have been proposed. One such approach is the introduction of Lennard-Jones potential to the energy variational formulation of PNP system. This study focuses on understanding the role of steric effect on flow properties. To discretize the system, Lattice Boltzmann method has been used. The system is defined by modified PNP equations where the steric effect is described by Lennard-Jones potential. In addition, boundary conditions for the complex channel geometry have been treated using immersed boundary method