Simulation of an ultrafiltration process of bovine serum albumin in hollow-fiber membranes

This work presents a numerical simulation of an ultrafiltration process of bovine serum albumin in solution, using hollow-fiber membranes. Such membranes are constituted of tiny polymer cylinders disposed in a tube-and-shell arrangement. The concentrate flows through the interior of the fibers and the pure solvent is recovered in the shell, assuming perfect solute rejection. In modeling the process, the flow of concentrate inside the fibers was considered to be laminar, with constant density, viscosity and solute diffusivity. Axial diffusion and angular effects were ignored. The model combines the effect of concentration polarization and adsorption, which are the two main limiting phenomena in ultrafiltration processes. The pressure on the shell side was considered constant and inside the fibers a linear pressure profile, dependent on the axial position, was adopted. The solution of the problem was achieved with the method of orthogonal collocation, with adequate choice of the weight function in the radial direction. In the axial direction, a finite-difference method was used. The numerical results were compared with experimental data available in the literature.