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3.1 Flory-Huggins Theory – Prediction of concentration profiles and to explain the sorption selectivity of membranes and real fluid mixtures is done by this method. Activity of the species in the polymer is a function of the volume fraction of the species, the molar volumes of the components and the Florry-Huggins interaction parameters. Originally, this method was developed for the binary mixtures, further it was extended to ternary systems with non- crosslinked polymer membranes. Flory- Huggins thermodynamics equation is represented as follows (13):
Where x and are the mole fraction and volume fractions respectively and X’s are the adjustable parameters.
The binary Flory-Huggins interaction parameter Xi,j describes the interaction between two liquid solvents can be expressed as*…show more content…*

gE can vanish as either x1 or x2 becomes zero. The activity coefficients derived from this equation are: ln ϒ1 = - ln (x1 + 12x2 ) + x2( ) ln ϒ2 = - ln (x2 + 21x1 ) – x1( ) There are two adjustable parameters in Wilson’s equation; 12 = exp ( ) 21 = exp ( ) Disadvantages of Wilson equations There are two basic disadvantages of Wilson’s equations: The equations derived for activity coefficients above are not useful for those systems where the logarithms of the activity coefficients, when plotted against x, exhibit maxima or minima. The second and more serious disadvantage of Wilson’s equation is its inability to predict limited miscibility. Applications: Should be used only for liquid systems which are completely miscible or also for the limited regions of partially miscible systems where only one liquid phase is present. 8 3.2.2 NRTL equation The NRTL equation for Gibbs energy is (18) = x1x2 ( ) Where = = = exp (- α12 τ12) G21 = exp (- α12 τ21) The activity coefficient in NRTL equation is estimated as follows: ln ϒ1 = x22 [ τ21( )2 + ] ln ϒ2 = x12 [ τ12( )2 + ]

gE can vanish as either x1 or x2 becomes zero. The activity coefficients derived from this equation are: ln ϒ1 = - ln (x1 + 12x2 ) + x2( ) ln ϒ2 = - ln (x2 + 21x1 ) – x1( ) There are two adjustable parameters in Wilson’s equation; 12 = exp ( ) 21 = exp ( ) Disadvantages of Wilson equations There are two basic disadvantages of Wilson’s equations: The equations derived for activity coefficients above are not useful for those systems where the logarithms of the activity coefficients, when plotted against x, exhibit maxima or minima. The second and more serious disadvantage of Wilson’s equation is its inability to predict limited miscibility. Applications: Should be used only for liquid systems which are completely miscible or also for the limited regions of partially miscible systems where only one liquid phase is present. 8 3.2.2 NRTL equation The NRTL equation for Gibbs energy is (18) = x1x2 ( ) Where = = = exp (- α12 τ12) G21 = exp (- α12 τ21) The activity coefficient in NRTL equation is estimated as follows: ln ϒ1 = x22 [ τ21( )2 + ] ln ϒ2 = x12 [ τ12( )2 + ]

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