Abstract
AbstractThe effect of natural convection on polarization and flow patterns in liquid phase convective diffusion in a vertical duct with semipermeable membrane walls has been investigated theoretically. It is found that at low flow rates, gravitational fields can play a significant role in distorting the velocity profiles and thereby they affect the transition from laminar to turbulent flow. Natural convection also significantly affects mass transfer rates and therefore the extent of polarization at low flow rates. Results are presented for both momentum and mass transfer in upward and downward flows for different wall Peclet numbers. The hydrodynamic stability of the system also has been investigated and critical values of the buoyancy parameters are reported. Also, these results enable one to estimate when natural convection may create errors in membrane testing systems.The analysis and results are of practical interest in reverse osmosis and other membrane separation processes. The more productive the system, the more likely it will be that buoyancy effects are important.
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