Effects of sizes of charged species on the flocculation of biocolloids: Absorption of cations in membrane layer

Abstract

The rate of flocculation of suspended biocolloidal particles each covered with an ion-penetrable charged membrane immersed in an electrolyte solution is investigated theoretically. We take into account the effects of sizes of charged species, including cations, anions, and functional groups in the membrane layer, where the absorption of cations by the functional groups leads to the variations in fixed charge density of the membrane phase of a biocolloid. The simulated results reveal that the sizes of cations, anions, and fixed groups have negative effect on the rate of biocolloidal flocculation for an originally negatively charged membrane (ONCM), and the classical point-charge model overestimates this rate. The discrepancy between an ONCM and an originally uncharged membrane (OUCM) for the time required for flocculation increases with the number of functional groups involved in the absorption or chelation of mobile cations. The rate of flocculation produced by an OUCM is faster than that by an ONCM under the same conditions. For an ONCM, the stronger the effect of the cationic absorption by the functional groups, the faster the rate of flocculation, and the reverse is true for an OUCM. Comparing with an OUCM, the effects of membrane thickness, concentration of functional groups, ionic strength of the bulk liquid and relative permittivity of the solution on the variations of flocculation time ratio are more considerable for an ONCM. A thicker membrane, a lower concentration of functional groups, a higher ionic strength of the bulk liquid and a larger relative permittivity of the solution cause a faster rate of flocculation.