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A mathematical model of diafiltration with variable volume is presented in this study. The characteristics of the process were examined, both with constant flux and variable flux. In the case of variable flux, the equations for the flux were taken from the literature, based on different theories. The time dependence of the macro solute concentration, the amount of out-wash liquid, the out-wash degree of the micro solute were studied. The results show that the accomplishment of a high concentration of macro solutes, required more time and out-wash liquid. In order to remove small amounts of micro solutes larger amounts of out-wash liquid must be used. For high degrees of out-washing, the velocity of the process increases and the amount of out-wash liquid decreases. It was observed that the rejection coefficient decreased with macro solute penetration through the membrane causing decrease of the process velocity.

A model with simultaneous ultrafiltration and diafiltration, which includes the rejection coefficients, is presented in this study. Adding a diafiltration solution at a constant, lower rate than the filtrate rate results in a constant decrease of the solution volume in the tank. This enables the simultaneous attainment of the desired macrosolute concentration and microsulute dilution. The proposed model, based on incomplete macrosolute rejection and incomplete mi-crosolute permeation through a membrane, as well as constant permeate flux, is compared to the classical constant volume, diafiltration process. The obtained results show that less diafiltration volume is necessary with this process. Simultaneously, the duration of the process, for higher purification requirements, is shorter in this case.