# Solution Diffusion Medel in Membrane Technology

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19-Feb-2017

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SOLUTION-DIFFUSION (SD) MODEL

SOLUTION-DIFFUSION (SD) MODEL- ADIL AGLODIYA -SATISH MOVALIYA

Its one of the earliest models proposed for ROThe model is based on the principle of membrane diffusion through a dense layerThe SD model can be written as: Jw = [(Dwm Cwm Vm /RT)*(P-)] --------------(1) = Aw (P-)--------------------------(2)Where , Dwm = membrane water diffusivity (m2/s) Cwm = membrane water concentration (kg solvent / m3)Vm = molar volume of solventAw = water permeability (constant)

P = P1-P2 is the hydrostatic pressure difference with P1 exerted on feed and P2 on product solution = 1-2 is the difference of osmotic pressure of the feed solution to that of product solutionIn case of dilute organics with negligible osmotic pressure this model fails to predict flux behavior

Above fig a schematic diagram of solvent and solute transport in reverse osmosis process, where c1 and c2 are the feed side and permeate side solute concentration

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For diffusion of solute through membrane the flux equation can be written as: Js= [(Dsm Ks /)*(c1-c2)]--------------------(3) = As (c1-c2)---------------------------------(4)Where,As = Dsm Ks / Js = solute flux (kg solvent / s m2)Dsm = Diffusivity of solute in membrane (m2/s)Ks = distribution coefficientAs = solute permeability constant (m/s)

Under steady state condition, the solute diffusing through the membrane must be equal to the amount of solute leaving the permeate solution Js = (Jw c2)/cw2 ------------------------(5) where, cw2 is the concentration of solvent in permeatestream (kg solvent/m3)

Permeability constants for membrane are determined experimentally for a particular type of membrane.For cellulose acetate membranes, water permeability constants = 110-4 to 510-4 kg solvent/s.m2.atm

For the solute permeability constants As of cellulose acetate membranes, some relative typical values are as follows: NaCl = 4 10-7BaCl2 = 1.6 10-7MgCl2 = 2.2 10-7CaCl2 = 2.4 10-7

SOLUTE REJECTIONThis is defined as the fraction of solute remaining in the feed stream.In RO solute rejection, R is defined as the ratio of concentration difference of the solute across the membrane to the bulk concentration of solute on the feed side.R = (c1-c2)/c1 --------------------------(6)= 1- (c2/c1) ----------------------------(7)Substituting eqn (1) and (3) into eqn (5)[(Dsm Ks /)*(c1-c2)] = [(Dwm Cwm Vm /RT)*(P-)]*(c2/cw2)----------(8)

Above eqn can be solved for c2 and c1, then value can be substitued in eqn (6)

Where B (atm-1)= (Dwm Cwm Vm )/ (Dsm Ks cw2 RT)B must be determine experimentally for each type of membrane.