4(%3)3 - Ecole nationale supérieure de chimie de Montpellier

Flux (L.h- 1 .m -2 )14012010080604020P=4 barP=3.5 barP=3 barP=2.5 barP=1.5 barP=0.8 barP=0.6 barP=0.2 barP=0.07 barP=0.04 bar00 2 4 6 8 10 12Time (hr)Figure – 2.10: Evolution of water flux with respect to time for the dynamic membrane at different pressure values.Since the flux values tend to merge towards near zero values hence to have a significantmeasurable value for longer durations and for a better representation of the dynamics of the membrane,the quantity “fluid flow resistance” (R) was preferred instead of flux. The merit of using this quantity isthat unlike flux, the value of resistance increases with time reaching infinity hence providing moremeaningful and measurable values at all time period. Nonetheless, flux values are still needed tocalculate the resistance values.To obtain resistance values from flux, the membrane can be considered as a porousnanomaterial with cylindrical pores of constant diameter along length at a particular instant, for whichthe relationship between the empty tower velocity U and the pressure drop can be expressed usingDarcy’s law: = = ……….. Eq. (2.1)where Q represents the fluid flow rate through the section A and R is the fluid flow resistance of The empty tower velocity U is equivalent to the flux ofthe membrane, which is a measurable quantity.55