Part I: Prediction of the charged dialysis process performance using a deterministic model

A deterministic model was developed to describe the charged state of the dialysis process. It provides a conceptual insight into such a process with highly interconnected parameters. A corrective term was developed and added to the generalized Maxwell–Stefan (MS) equation to explain the transfer behavior of the charged particles through a charged membrane in the dialysis process. Transfer of sodium do-decyl sulphate (SDS) micelles through a charged conductive membrane was experimentally investigated as a case study. In the first step, the general structure of the added corrective term was determined using full factorial experimental design for three levels of electrical charge, feed phase concentration, and concentration gradient. In the next step, the experimental data are used to fully determine the corrective term and quantify its coefficients. A comparison was made between the experimental data, the predicted results by the proposed equation and the predicted results by the MS equation. The proposed equation shows a high capability to predict the dialysis process performance for both the charged and the neutral state of the dialysis process. Moreover, the same is true for the competitive batch dialysis processes. Furthermore, the proposed model conceptually describes the recently published results [Godini et al., Desalination, 2010. in press], showing that at different concentration and concentration gradient, the mass transfer mechanisms are different. Although some coefficients values in the proposed equation are specialized to the current case study, the general structure of the proposed corrective term is valid for other similar systems as well.

Research Highlights
► Generalized Maxwell–Stefan equation was extended to explain the charged dialysis process performance.
► The proposed model enables to catch the different mass transfer mechanisms in charged dialysis process.
► A model based control for competitive dialysis process can be provided using the proposed approach.