A CFD model for prediction of critical electric potential preventing membrane fouling in oily waste water treatment

Beside several methods of membrane fouling reduction, induction of electric field in system of dielectric materials can also postpone fouling. For the first time, CFD technique is used to develop a model to predict behavior of a sample oil droplet located on the membrane surface affected by dielectrophoresis force in a good agreement with experimental data. Then experimental design is used to study the effects of electric field induction within defined ranges of system variables. In order to quantify droplet behavior, critical voltage is defined as minimum required electric potential to detach droplet from the membrane surface. Contact angle, droplet diameter, interfacial tension, membrane thickness, shear rate, pore diameter and trans-membrane pressure are system variables. Initially, screening experiments with 2-level factorial approach identify first four variables as effective factors. Subsequently, response surface methodology and central composite design were employed for critical voltage modeling and optimization. A quadratic model (R2 = 0.997) is suggested for square root of critical voltage between 1800 and 22,000 V. Optimum or minimum critical voltage is observed at 0.01 N/m interfacial tension, 110° contact angle, 2 µm droplet diameter and 100 µm membrane thickness. The predicted value for optimum critical voltage by a second-order polynomial correlation is 1734 V which deviates about 4% from 1800 V as critical voltage calculated from the CFD model.