Modeling concentration polarization phenomena for shell-side flow in ultrafiltration process

A correlation for the longitudinal mass flow of a dissolved component in terms of the degree of concentration polarization has been developed. The solution developed is applicable to shell-side flow and is 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 a hexagonal configuration has been carried out. This model permits analysis of the influence of mass flow, bulk concentration, velocity, and channel geometry on the degree of concentration polarization. In addition, it can give the mass flow by using the degree of concentration polarization as an input variable. The solution presented 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. Calculated data are included.