Geometrical Influence on Particle Transport in Cross-Flow Ultrafiltration: Cylindrical and Flat Sheet Membranes.

Cross-flow membrane ultrafiltration (UF) is used for the enrichment and purification of small colloidal particles and proteins. We explore the influence of different membrane geometries on the particle transport in, and the efficiency of, inside-out cross-flow UF. For this purpose, we generalize the accurate and numerically efficient modified boundary layer approximation (mBLA) method, developed in recent work by us for a hollow cylindrical membrane, to parallel flat sheet geometries with one or two solvent-permeable membrane sheets. Considering a reference dispersion of Brownian hard spheres where accurate expressions for its transport properties are available, the generalized mBLA method is used to analyze how particle transport and global UF process indicators are affected by varying operating parameters and the membrane geometry. We show that global process indicators including the mean permeate flux, the solvent recovery indicator, and the concentration factor are strongly dependent on the membrane geometry. A key finding is that irrespective of the many input parameters characterizing an UF experiment and its membrane geometry, the process indicators are determined by three independent dimensionless variables only. This finding can be very useful in the design, optimization, and scale-up of UF processes.