Improved Extended Nernst Plank nanofiltration modeling via inclusion of pore size, electrostatic interactions, and compound shape and orientation

Abstract

Nanofiltration (NF) membrane rejection models are often simplified by ignoring some compound physical characteristics to ease computational complexity. Yet these simplifications can reduce model flexibility in addressing all compounds and conditions. Herein, the Extended Nernst Plank model of NF rejection is improved upon by combining compound charge, geometry, and rotation, along with pore size distribution. The NF rejection of ionic alkyl chain compounds (C2 to C14) at various pH is experimentally determined and modeled. Rejections of the ionic compounds via an NFG membrane ranged from 49.8 % to 80.6 % for benzyldimethyldodecylammonium chloride, 23.6 % to 38.6 % for 1-methyl-3-octylimidazolium chloride, 32.5 % to 37.6 % for 1-ethyl-3-methylimidazolium chloride, 52.5 % for sodium dodecyl sulfate, 34.7 % to 63.5 % for sodium octyl sulfate, and was only measurable at 28.5 % for sodium ethyl sulfate. The rejections of an additional eight membranes and 81 compounds reported in the literature were also modeled. Overall the improved model predicted rejections with lower percent differences (i.e., 0.96 % to 144 % for the model herein) compared to simplified models presented in the literature (e.g., 5.0 % to 154 %). The improved model will be useful for simulations of NF membrane rejection where pore size distributions and size and charge of compounds cannot be ignored.