Dimensionless numbers for the steady-state flux of cross-flow microfiltration and ultrafiltration with gas sparging

Abstract

The steady-state flux, observed for gas-sparged microfiltration or ultrafiltration through inorganic composite membranes, could be expressed using two dimensionless numbers. The generalised shear stress number N S ′, with introduction of an equivalent fluid density, compares the shear stress against the membrane wall to the driving pressure, while the resistance number N f compares the convective cross-flow transport to the driven transport through a layer, whose resistance is the sum of all the resistances induced by the different processes which limit the mass transport. Experimental data, obtained in ultrafiltration of dextran solutions and microfiltration of ferric hydroxide suspensions and secondary treated wastewater, were re-calculated in terms of these dimensionless groups. Straight lines were plotted; their slope is a decreasing function of the gas–liquid velocity ratio when particle deposition or polarisation limited the mass transport. A negative slope and a positive intersection with the N S ′-axis means that the induced resistance can completely be eliminated with gas sparging. A straight line of negative slope followed by a plateau means that an irreversible fouling is superimposed to a reversible phenomenon in the hydrodynamic conditions of the run. A positive slope means that the flux reaches a plateau when cross-flow is increased. Gas sparging allows then decreasing the slope and reaching negative values.