Modelling concentration polarization phenomena for membrane channel with cylindrical geometry in an ultrafiltration process

A correlation for longitudinal mass flow of dissolved component against degree of concentration polarization has been developed. The developed solution is applicable to tube-side flow and based on the assumptions that the flow is to be isothermal, laminar, incompressible and steady state. Balance equations for viscous and diffusion boundary layers are the core of the model. Integration of these equations over the control volume of the cylindrical configuration has been carried out. This model permits the analysis of the influence of mass flow, bulk concentration, and velocity on the degree of concentration polarization. It can also give mass flow using the degree of concentration polarization as an input variable. The presented solution can be segmented and built into a complicated algorithm of a membrane-based process. The solution does not contain digital integration and permits simulation and analysis of the influence of various factors. The calculated data are included.