Calculation of flow and solute deposition through threedimensional reconstructed model of microporous membranes

The morphology of a typical microfiltration membrane is a random, irregular, three-dimensional, and interconnected network. In this study, a realistic model of microporous membrane was obtained using Confocal Scanning Laser Microscopy (CSLM). CSLM allows accurate and non-destructive membrane sectioning in a plane perpendicular to the optical axis of the microscope. Microporous membranes made of mixed ester (cellulose nitrate/ cellulose acetate) with 1.2 µm pore size were investigated. Optical sections of the MF membrane mounted in immersion oil were recorded on all the membrane depth. The numerical permeabilities were obtained by solving the Stokes equation for this three-dimensional media and were compared to experimental results. Finally, the simulation of solute transport through the microporous membrane was discussed by considering convection-diffusion equations.

Fig. 1. Confocal Scanning Laser Microscopy images of (a) the membrane mounted in immersion oil at z = 0 µm depth, (b) binarized image z = 0 µm, (c) three-dimensional reconstruction from the optical sections taken at 1 µm intervals from 0 µm to 10 µm (quarter of images). The pore space is in black. Also, it may result from heterogeneities on scales larger than the experimental image size, which cannot be accounted for in the present analysis. 4.3. Solute transport Two parameters were needed for the simulation: the diffusion coefficient, D and the reaction coefficient, Ks. For bovine serum albumin, the diffusion coefficient was taken equal to 4·10–11 m2.s–1 [8]. The reaction coefficient was evaluated as described Various approximations have been proposed, to capture membrane form and structure in terms of mathematical models. For the purpose of simulation of solvent and solute transport, pores are usually represented as a bundle of cylindrical nonintersecting capillaries of uniform radius and length. The optical sectioning capability of CSLM is a tool of choice to give a realistic model of microporous membranes. The main drawback of CSLM for microporous membrane characterization is its low resolution (≈0.4 µm). Therefore, only microporous membranes with large pores (typically greater than 0.2 µm) can be observed [4]. In order to evaluate our methodology, experimental permeabilitites were compared to numerical results. It is important to note that this comparison does not involve any hidden parameter and every quantity is measured or calculated. The experimental and calculated permeabilities were found in rather good agreement. Two parameters are needed for the simulation of solute or particle transport: the diffusion coefficient and the local deposition rate constant, determined by classical fouling experiments. Two important assumptions are made for the purpose of simulation. First, it is assumed that there is no particle accumulation (cake formation) at the membrane surface, a phenomenon which is currently observed especially when the solute diameter is larger than the membrane pore size. This phenomenon could be taken into account, i.e. by characterizing the filtration cake by means of Confocal Scanning Laser Microscopy and calculating the solvent transport through the filtration cake. The second assumption is that the reaction between the solute and the membrane is of first-order, which also may be not verified. Additional work will have to be made to consider more complicated reactions.