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rainwater harvesting, among others [1]. For removal of toxic ions, common methods that are used are adsorption of toxic ions on certain media, such as activated alumina, ion exchange in ion exchange resins, and flocculation and subsequent precipitation and filtration of toxic ions using floc- culation agents, such as bleaching powder [32]. While these methods are effective at removing these agents at the small scale, effectiveness has been a problem at the larger scale. Furthermore, major problems with these systems are continuous oper- ation due to the frequent need for maintenance and replacement of used filters and resins. In developed countries, the methods for desalination discussed above are also sometimes used, but are often very inefficient. 1.2 Water Desalination Thermodynamics An important metric for evaluating desalination processes is the comparison between the energy consumption required by the desalination process and the minimum ther- modynamic limit required to achieve the separation. From a thermodynamic perspec- tive, this limit can be calculated by imagining a reversible demixing process between the initial state (the feed solution) and the final state (the fresh water solution and the brine solution). Since the Gibbs free energy is a state function, we can simply look at the Gibbs free energy of mixing (which is equal but opposite to the Gibbs free energy of demixing) to calculate the energy difference. The Gibbs free energy of mixing per mole of total solution is defined as [117] −∆Gmix = RT [Σxi ln (γixi)] − r [Σxi ln (γixi)] − (1 − r) [Σxi ln (γixi)] mixed f resh brine (1.1) where xi is the mole fraction of component i, γi is the activity coefficient, R is the gas constant, T is the temperature, and r is the water recovery (ratio of the flow rate of fresh water to the total inlet flow rate). However, for the purposes of easily comparing energy requirements with the thermodynamic limit, we need to the 29PDF Image | Shock Electrodialysis for Water Purification and Electrostatic Correlations
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