Predicting the performance of direct contact membrane distillation (DCMD): Mathematical determination of appropriate tortuosity based on porosity

Direct contact membrane distillation (DCMD) is a promising novel membrane technology for management of waste streams from food manufacturing operations, and for concentration of value-added components from the waste streams. Due to the complexity of technology, the development of prediction models to describe mass transfer during DCMD presents a significant contribution. The overall objective of this investigation was to propose models for prediction of membrane tortuosity based on measured porosity, and to confirm the models by experimental measurements of water flux for DCMD applications. Three types of commercial membranes with porosities ranging from 69.8% to 87.9% were investigated. Eleven (11) different models for prediction of tortuosity from porosity were identified from published literature and evaluated. Statistical comparisons of predicted and experimental water flux were conducted using root-mean-square-error, accuracy factor, and bias factor to identify the models providing the closest agreement between predicted and experiment outcomes. The statistical comparisons indicated that models based on the fractal theory provide the closest agreement between predicted and experimental water flux for DCMD applications. In addition, the proposed model provided best agreement between predicted and experimental temperatures. The simulations of water flux were used to evaluate the influence of membrane surface area on water flux, and capabilities of the tortuosity models. As the width and length of membrane were increased, the differences in water flux predicted by proposed model, as compared to the traditional model, increased significantly. These outcomes confirm the importance using appropriate models for prediction of tortuosity for DCMD applications.