Calculation of concentration polarisation in processes of ultrafiltration of non-Newtonian fluids in tubular channel

Abstract

Model for concentration polarisation in ultrafiltration process of non-Newtonian fluid has been developed. The model is applicable for channels with tubular configuration. The proposed solution is based on the following assumptions, (1) flow is to be isothermal, laminar, incompressible and steady-state; (2) fluid properties are independent of applied pressure and time under shear; (3) no slip at the wall; (4) the field of apparent viscosity has non-isotropic configuration (viz. depends on local shear rate), the paper covers pseudoplastic and dilatant time-independent flow; (5) input approximation for concentration profile has parabolic configuration. Balance equations for viscous and diffusion boundary layers are the core of the model. Integrating these equations over the control volume has been carried out. This model permits the analysis of the influence of mass flow, bulk concentration, tangential velocity, transmembrane flux, membrane solute rejection and channel geometry on configuration of concentration polarisation profile. The presented solution can be segmented and built into a complex algorithm of membrane processes. The solution does not contain digital integration. The paper includes developed algorithm, array of calculated data and graphical visualisations of solutions.