A broad range of scientific and engineering problems involve multiple scales. Thus, there is a growing interest in developing systematic modelling and simulation approaches for multi-scale problems. It is, in fact, very well assessed that a multi-scale approach provides an improved accuracy of simulations predictions, which are attained in an absolutely fundamental way and without resorting to experimental data or to adjustable parameters.  The aim of the present paper was the formulation/solution of multi-scale models aimed at characterizing, from a fundamental point of view, the mutual interactions existing between macromolecules, like proteins or water contaminants, and a porous support, like a membrane. In particular, an improved multi-scale model aimed at rigorously describing membrane fouling in ultrafiltration was formulated.  The local charges on either protein or contaminants molecule contact surface or the polymer fragments representing the considered membrane surface were calculated through an accurate Quantum Mechanics (QM) method. A polymeric surface model was also defined through a simulated Molecular Dynamics (MD) procedure and the surface charges were calculated by the same QM theory level. The so-obtained local charges were exploited to achieve a detailed knowledge about macromolecule and polymer behavior at nanoscopic scale and to get some fundamental parameters that allowed a smooth transition to a larger scale. It is worth noting that such a result was achieved by applying rigorous Quantum and Molecular Mechanics calculation and had not to be considered as a modeling hypothesis, as it was previously done in the majority of the already-available articles. An overall additional resistance, as due to both the deposited first layer on the surface and to layers constituting the cake was computed. An alternative approach, based on Monte Carlo (MC) simulations, was exploited to estimate such an overall resistance; the predictions obtained by either force balance approach or MC simulations were then compared.  The final transition to the macroscopic scale was achieved by formulating an unsteady-state mass transfer model aimed at describing a typical dead-end UF process.  It is worth noting that such work points to a double utility. On the one hand, a method for the simulation and optimization of wastewater treatment is obtained, and on the other hand, an approach for the development of methods for the recovery of contaminants in water is developed.

Multiscale modeling approach to describe waste-water membrane treatment technologies

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