From critical phase transition to critical flux via critical osmotic pressure and critical Peclet number
Résumé
Critical flux is now a ten years old concept in membrane processes which is used in numerous application fields. Commonly, the critical flux separates operating conditions leading to irreversible fouling to others allowing to work with no (or very low) fouling. The presentation will give a summary of physical causes for critical flux, will propose a way to depict membrane transfer phenomena from these causes, and then will detail consequences on critical fouling conditions both in cross-flow and in dead-end filtration. Physical causes can be seen through a phase diagram for a colloidal suspension where it appears an irreversible phase transition between a dispersed phase and an aggregated phase when increasing volume fraction. This transition, which can be explained when considering multi-body particles interactions, seems to be the physical causes for a phase change on the membrane surface corresponding to irreversible fouling layers : the term “critical” has here then its physical significance. A way to depict consequences of this phase transition on membrane transfer phenomena is proposed through the use of colloidal osmotic pressure, 0. Colloid osmotic pressure allows describing the phase transition (which is related to a maximum of 0 versus volume fraction curve) as well as transfer phenomena through a collective diffusion (which is related to the derivative of 0 with volume fraction). Consequences on fouling can be deduced from classical mass balance based on the colloidal osmotic pressure by defining critical Péclet numbers both for cross-flow and dead-end filtration. These critical Pe number allows then to define a critical flux in cross flow filtration and a critical filtered volume in dead-end filtration leading to the formation of an irreversible fouling on the membrane surface. Examples of applications of this theory will be developed in cross-flow and dead end filtration.