Journal of Membrane Science 176 (2000) 55–61 Ultrafiltration flux theory based on viscosity and osmotic effects: application to diafiltration optimisation Greg Foley ∗ , José Garcia School of Biotechnology, Dublin City University, Glasnevin, Dublin 9, Ireland Received 28 June 1999; received in revised form 14 April 2000; accepted 18 April 2000 Abstract The optimisation of diafiltration is examined using the new theory of ultrafiltration based on osmotic pressure and the viscos- ity dependence of the mass transfer coefficient. It is shown that, if the permeate flux is maintained at the limiting value at each bulk macrosolute concentration, the diafiltration time always decreases with increasing concentration. However, the trans- membrane pressure required to reach the limiting flux increases rapidly with concentration, thus putting a practical limit on the concentrations at which an ultrafiltration system can be operated under limiting flux conditions. In contrast, when the osmotic pressure is a polynomial function of the wall concentration and operation at a fixed transmembrane pressure is considered, a finite optimum concentration is found which minimises the diafiltration time. A methodology for computing this optimum concentration is developed. It is shown that the optimum concentration increases with increasing transmembrane pressure but is only weakly dependent on feed velocity and membrane resistance. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Ultrafiltration; Diafiltration; Optimisation; Viscosity; Osmotic pressure 1. Introduction The concentration of macrosolutes by batch ultra- filtration is frequently accompanied by a diafiltration step to remove microsolutes such as salts [1]. A con- tinuous diafiltration cycle involves (i) ultrafiltration to reduce the solution volume from V 0 to V and increase the macrosolute concentration from C b0 to C b , (ii) diafiltration at a constant volume V and a constant macrosolute concentration C b to reduce the microso- lute concentration from C s0 to C sf and (iii) further volume reduction from V to V f to increase the macrosolute concentration from C b to C bf . The work of Ng et al. [2] was the first to predict that there ∗ Corresponding author. Tel.: +353-1-7045395; fax: +353-1-7045412. E-mail address: greg.foley@dcu.ie (G. Foley) should be an optimum macrosolute concentration at which the diafiltration step should be performed to minimise the diafiltration time and hence the total process time. Their theoretical work was supported by experimental data. The aim of the work reported in this paper was to re-examine the diafiltration optimisation problem us- ing new a flux theory [3,4] rather than the gel polari- sation model used in the work of Ng et al. [2]. In the next section, we review the new theory and contrast it with the gel polarisation model. In the following section, we review the basic equations of diafiltration which are used in subsequent calculations. 1.1. Ultrafiltration theory The basic concentration-polarisation model of ultrafiltration can be written [1] as 0376-7388/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII:S0376-7388(00)00429-4