Modelisation of transport of neutral solutes through nanofiltration membranes
Although nanofiltration appeared at the end of the 1970s under various names, it was only really recognized as a useful separation process in the 1980s. Nanofiltration membranes are porous media with a mean pore diameter around 1 nanometer. These membranes do not obey the traditional solution-diffusion model given for reverse osmosis or the convection-diffusion model used to describe ultrafiltration. Although the technique has benefited from a fast technological development, the transport mechanisms are still misunderstood and for a particular separation the choice of a nanofiltration membrane remains empirical. The main objective of this work was to understand and to model the transport of neutral solutes through nanofiltration membranes. Neutral solutes were chosen to emphasise geometrical exclusions, to avoid any electrical interactions and to identify the preponderant transport mechanisms through these materials. The experiments were carried out with a laboratory filtration apparatus. The membranes were laid out in a parallel plane osmotic cell, which makes tangential filtration possible. The geometry of the filtration cell involved the choice of two organic membranes supplied as flat sheets: a BQ01 and a MX07 membrane. The filtration area was 86 cm2. The pressure varied from 7 to 30 bars. The temperature was maintained at 20°C whereas tangential velocity in the cell was fixed at 0.45 m×s-1 (the Reynolds number was 3350). As the solutions used were slightly concentrated, the pH remained close to neutral pH. Three sugars were chosen as solutes: glucose, saccharose and raffinose. These molecules have two advantages: they are electrically neutral and they have molecular weights close to the membranes' MWCO, as provided by the manufacturer. First, saccharose was studied on the two membranes with two different concentrations. These experiments showed that the separation of neutral solutes by nanofiltration membranes is due only to a sieving effect. In subsequent experiments a single concentration was used to characterize the retentions of both glucose and raffinose. The results of the filtrations carried out on the three sugars validated the molecular weight cut-off specified by the manufacturer: the MWCO of the BQ01 membrane was estimated to be 1000 Da, and that for the MX07 membrane was 200 estimated as 200 Da. Schematically, the solute transport can be divided into three stages: in the feed, at the feed/membrane interface, and within the membrane material. In the feed, one notes an increase in solute concentration if one approaches the membrane from upstream. This phenomenon, which is general to any selective transport, is called concentration polarization and is described by film theory. This theory stipulates the creation of an antagonistic diffusive flow, from the membrane towards the feed, seeking to restore the concentration balance within the feed solution. The modification of the concentration at the feed/membrane interface leads to the definition of two retention coefficients: a measured value, the observed retention (Robs), and a calculated value, the intrinsic retention (Rm). Steric exclusion based on the size difference between the pore and the solute is set up at the interface. Uncharged solutes can be visualised as rigid spheres and the membranes can be regarded as a bundle of cylindrical, parallel, rigid and right capillaries. Since the elements are rigid and the solutes are subjected to the same geometrical constraints at the entry and at the exit of a pore, the partition coefficients are identical at those two ends. Finally, lying between reverse osmosis and ultrafiltration, transport through nanofiltration membranes is often expressed as the sum of convective and diffusive phenomena. However, the experimental results show that the observed retentions are stable or increase when pressure increases. These observations also highlight the fact that the values of infinite retention are always compatible with values close to 1. These observations corroborate the idea that diffusion is the predominant transport mechanism of neutral species through the studied materials (BQ01, MX07). The transport equation of neutral solutes can then be simplified to its diffusive component. The expression of the intrinsic retention is obtained by using Fick's law, the definition of the retention coefficients and the definition of the partition coefficients: Rm= 1-(1 / 1+Jvα) The geometrical and physicochemical characteristics of the solutes and of the membranes merge into the α parameter. The results found with the theoretical relation were confronted with experimental data derived from film theory (in order to take into account concentration polarization). The simple one-parameter model was successful in correlating the results obtained in this work. The model was also tested with data coming from Combe et al. (1997), who studied filtrations of glucose, saccharose and raffinose in a laminar flow system by ceramic nanofiltration membranes laid out in the shape of tubular module. The results obtained show that the simple model also successfully correlates with the performances of these membranes. With the data obtained in our laboratory as well with the data found in literature, this study shows that a simple one-parameter model, based on the diffusional transport of the solutes within the membrane material, predicts the rejection of neutral solutes by nanofiltration membranes. The simple one-parameter model is able to simulate any filtration carried out by these membranes for different circulation conditions, for diverse geometrical shapes and for various materials.