L. Vera et al., Dimensionless numbers for the steady-state flux of cross-flow microfiltration and ultrafiltration with gas sparging, CHEM ENG SC, 55(17), 2000, pp. 3419-3428
The steady-state flux, observed for gas-sparged microfiltration or ultrafil
tration through inorganic composite membranes, could be expressed using two
dimensionless numbers. The generalised shear stress number N-S', with intr
oduction 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-how 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, obt
ained 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 parti
cle deposition or polarisation limited the mass transport. A negative slope
and a positive intersection with the N-S'-axis means that the induced resi
stance can completely be eliminated with gas sparging. A straight line of n
egative slope followed by a plateau means that an irreversible fouling is s
uperimposed to a reversible phenomenon in the hydrodynamic conditions of th
e run. A positive slope means that the flux reaches a plateau when cross-fl
ow is increased. Gas sparging allows then decreasing the slope and reaching
negative values. (C) 2000 Elsevier Science Ltd. All rights reserved.