Calculation of ionic flocculation concentrations for biological membranes bearing ionizable groups

The flocculation concentrations in the DLVO theory of colloid stability have previously been calculated under conditions of constant plate potential or constant plate charge. These boundary conditions are not appropriate in the case of biological membranes bearing ionizable surface groups. In this case the surfaces undergo charge regulation as they approach each other and both the surface charge and potential vary. In this paper a numerical method is used to calculate the ionic flocculation concentrations for the two membranes undergoing surface charge regulation. It is shown that the flocculation concentration lies between that for constant charge and that for constant potential. Flocculation concentrations are calculated as a function of the surface density of ionizable groups and are shown to be dependent on both the pKa of the surface groups and the bulk pH of the solution.