Abstract
A capacitive mixing engine is developed which follows four stages of operation analogous to those of a Carnot cycle. This work establishes and evaluates control schemes for cell voltage and current as functions of time to maintain cycling stages where a constant number of ions property (dependent on both cell charge and concentration) can be maintained. The cycle is examined and compared for three different models of the electrochemical double layer in the cell, each of which function best at a different set of concentration ranges: The Gouy Chapman Stern (GCS) model for high concentrations, the modified Donnan (mD) model for low concentrations, and the improved modified Donnan (imD) model to account for both ranges. The cycle baseline condition operates between high concentration seawater (600 mM) mixed with heavily diluted brackish water (20 mM). Under this voltage range, the imD functions best at capturing the appropriate range of concentrations, but future connections with experimental studies will be necessary to assure that the constant parameters used for fitting in the model are valid. In this mode of operation, cell voltage and current were found to follow linear/exponential trends, but the high concentration range required very long running times on the order of thousands of hours, approaching the infinitely slow cycle limits previously developed. Before more rigorous studies can be considered, a design space exploration should aim to decrease operating time to more reasonable values. This study suggested high flow rates (> 1 L/min) will be effective while keeping current lower (< 1 A) to minimize irreversibilities. While the transient cycle does not truly extract the maximum energy of mixing predicted theoretically, it reaches 75% for baseline conditions studied, and approaches 100% as minimum concentration approaches zero.
