Density functional theory of colloidal systems for water/oil separation

  Roi Bar-On  
The interdisciplinary graduate program of applied mathematics

Oil-polluted water has a high global environmental impact that makes water/oil (w/o) separation of interest. Many industries, such as mining, textiles, foods, petrochemicals, and metal/steel industries, produce massive volumes of oily wastewater. Although water and oil are immiscible, they might create emulsions that make their separation more complected, energy demanding and expansive. We have modeled the near-equilibrium thermodynamics of w/o emulsion separation problem using the density functional theory (DFT) while considering surface forces between sub-micron particles (DLVO theory). Using the mentioned model, we have calculated the w/o droplets spatial density in a half-space system involving a hydrophilic or a hydrophobic surface (to our desire).

Our tool to analyze w/o emulsions is the classical DFT who addresses the difficulty of describing thermodynamic equilibrium states of many-particle systems with nonuniform density. We have used the simplest approach to DFT which is the squared-gradient approximation (SGA) that dates back to van der Waals and has been re-invented and exploited in many different circumstances, most notably by Landau in the context of phase transitions and by Cahn and Hilliard for the description of interfaces. A characteristic element in DFT is the direct correlation function (DCF) which takes into account the different positions of particles and their mutual interaction. More specifically, it describes the effective interaction between two particles in the presence of a number of surrounding particles. Combining the DFT ideal and non-ideal components allows to approach non-trivial systems and improve the thermodynamics understanding of emulsion separation.