Two-phases model for calcium removal from aqueous solution by polymer enhanced ultrafiltration

Water softening has been carried out by polymer enhanced ultrafiltration (PEUF). Poly(acrylic acid–maleic anhydride) sodium salt (PAM-Na), a polyelectrolyte containing COO− groups, attracts Ca2+ and releases Na+ ions. When pH is lowered, H+ replaces the bound Ca2+. Thus, the polyelectrolyte can be regenerated and reused. A model is proposed to explain the observed calcium and sodium rejections at different experimental conditions. The feed solution is considered to be divided into two phases. One phase is occupied by the macro ions and bound counter ions and the other is the remaining solution. The model only needs to determine two equilibrium constants (KNa,H and KCa,Na) which indicate the relative tendencies of Na+ versus H+, and Ca2+ versus Na+ to bind the polymer, respectively. KNa,H value was determined by titration and it is pH dependent. KCa,Na value was calculated from ultrafiltration runs at neutral pH and its value goes well with other ultrafiltration runs when pH is varied.