Development of a mathematical model to predict different parameters during pharmaceutical wastewater treatment using TiO2 coated membrane

• Effective removal of the pharmaceutical component by heterogeneous photocatalysis.
• Successful immobilization of TiO2 nanoparticles on the membrane surface.
• A mathematical model to measure the substrate concentration in the permeate stream.
• Validation of the developed mathematical model.

The aim of present study is to develop a mathematical model to understand the photomineralization process for an antiseptic drug component, chlorhexidine digluconate using catalytic membrane. Overall process was executed in a photo reactor with immobilized TiO2 nanoparticles on the membrane surface, which gives the better recovery and reuse of the catalyst. To assess the overall process performance, a mathematical model has been developed for prediction of substrate concentration in the permeate stream and the theoretical build-up of the polarized layer in case of a membrane coated with TiO2 nanoparticles. In the developed mathematical model, the governing partial differential equation was solved with the help of initial boundary condition over the concentration boundary layer and Kozeny–Carmen equation. In this model the simultaneous change in the active surface area and the polarized layer thickness with the change in substrate concentration in the boundary layer was incorporated to enhance the accuracy of the model. The resulting non-linear partial differential equation, coupled with other non-linear ordinary differential equation is solved using Runga Kutta fourth order method. Average deviation between theoretical results and the experimental data generated in this study was found to remain within ±5% and precision level was maintained at 0.01%.