Modelling of permeability loss in membrane filtration: Re-examination of fundamental fouling equations and their link to critical flux

A re-evaluation of the flux decline relationships in the appendix of the 1995 critical flux paper has failed to establish that one may have a critical flux in the presence of fouling that is represented by the complete pore blocking (n = 2) mode. It remains valid to contemplate the possibility of a critical flux for the n = 1 and n = 0 (cake) modes. This re-evaluation was undertaken for the situation where the removal terms can be considered to be linearly dependent upon shear stress (and no other hydrodynamic parameters). The integral method for the evaluation of inter alia the switch from one mode of fouling to another was introduced and is an available tool if the suggested hydrodynamic dependency is valid. An alternative hydrodynamic dependency (proportional to shear stress and inversely proportional to flux) was also explored, especially with regard to steady-state fluxes. For n = 1 and n = 0, a square root dependency of final flux upon shear stress was found. Experimental investigation of the validity of the alternative is desirable. From a theoretical point of view, it is noted that for the alternative a critical flux is again incompatible with the n = 2 mode of fouling. (C) 2011 Elsevier B.V. All rights reserved.