Membrane Permselectivity

The permselectivity of cation and anion exchange membranes is defined by:

Table 1 Definition of symbols used in mathematical equations Table 1 Continued

Symbol

Definition

Symbol

Definition

Ap AC

p Don

Az a

^min

m Cco cm

D dz

Edes

I i ilim

Electrochemical potential Chemical potential Electrical potential

Stoichiometric coefficient which determines into how many ions a salt will dissociate in the solution Permselectivity of a membrane Current utilization Thickness of a cell

Resistance of ion exchange membranes Potential difference between solutions separated by a membrane assuming electrochemical equilibrium Difference in salinity of feed and product water Donnan potential

Energy required for production of the dilute Average activity coefficients of salt in the membrane

Amount of salt in moles transferred from a feed to a concentrate solution

Hydrodynamic pressure loss through the stack Equivalent conductivity

Average activity coefficients of salt in the electrolyte solution

Thickness of the boundary layer

Activity

Effective area

Minimum membrane area required for a certain plant capacity

Concentration differences between feed and diluate Co-ion concentration in the membrane Concentration fixed ions in the membrane Co-ion concentration in the electrolyte solution Diffusion coefficient

Directional coordinate perpendicular to the membrane surface

Energy required for desalination

Pumping energy

Faraday constant

Total electrical current

Current density

Limiting current density

Flux of component / (individual ions)

Constant referring to efficiency of pumps

Mobility of ions in the membrane

Number of cell pairs in a stack

Volumetric flow of the product

Gas constant

Electric resistance

Temperature

Transference number

Time

Transport number of component i (ions)

Linear flow velocity of solution in electrodialysis cells

Voltage drop across the electrodialysis stack Volume

Electrochemical valence

Superscripts

'and " Two phases separated by the membrane b Boundary layer ba Concentrate bulk solution bc Concentrate bulk solution bd Diluate solution in the bulk diff Ion diffusion l Current leakage through the manifold m Membrane ma Anion membrane mc Cation membrane md Diluate solution at the membrane surface mig Ion migration ms Membrane selectivity

0 Feed p Product solution s Solution sc Concentrate solution sd Diluate concentration se Electrode rinse solution sf Feed solution sp Product solution w Water transport through the membranes

Subscripts a Anion c Cation cou Counterion

1 Ion s Salt w Water

The permselectivity of an ion exchange membrane relates the transport of electric charges by counter-ions to the total transport of electric charges through the membrane. An ideal permselective cation exchange membrane would transmit positively charged ions only, i.e. for tmc = 1, ^mc = 1. The permselectivity approaches zero when the transference number within the membrane is identical to that in the electrolyte solution. For the anion exchange membrane the corresponding relationship holds.

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