Dialysis is aimed at the removal of charged ionic species in the blood that arise from complications in kidney disease. Although the process for the removal of urea and other unwanted charged species is understood, the effect of this removal on the net sodium concentration in the blood after treatment is not clear. In this report, we focus on formulating a fundamentally-based model to address this question. We consider the formulation near the membrane at the pore scale in order to determine effective jump conditions in ionic concentrations, electric potential and flow rate based on the membrane properties, and in order to determine whether electroneutrality holds within the pore. Secondly, we consider the local blood-cell concentration within one of the fibres and how this varies axially within the dialysis cartridge. Lastly, we consider a simple one-dimensional model of the charged species problem and find that advection transport through the membrane is important for sodium transport, but less pertinent for transport of other cation species
