Transport properties of charge-mosaic membranes III. Piezodialysis

A nonequilibrium thermodynamic analysis of piezodialysis is presented. The expressions derived in Part I for the flows as linear functions of the global forces are used to predict the fractional recovery and rate of production of potable water in desalination by piezodialysis. An illustrative calculation is performed for a cylindrical tube (or hollow fiber) made from a hypothetical mosaic membrane whose properties have been calculated from those of Zeo-karb 315 cation exchange membrane. Perfect radial mixing and the absence of concentration polarization are assumed in order to focus attention on the role played by the membrane elements and circulating currents. For a 1 mm thick membrane under an applied pressure difference of 100 atmospheres, the calculation shows an 81% recovery of potable water of 350 ppm from a brackish water feed of 1500 ppm, the rate of production being 23 gpd/ft². A thinner mosaic with a correspondingly reduced pattern size would give a proportionately higher production rate with no loss in recovery, provided that significant polarization could be prevented. This calculation sets upper limits on the performance of a given membrane by assuming that its properties, rather than the hydrodynamic conditions, are rate controlling. The analysis suggests ways of changing membrane properties to improve performance.