Membranes - Principles of Chemical Separations with Environmental Applications - page 237

Electrodialysis (ED)
Removal of heavy metals, nitrates, and cyanides from water streams.
Desalination of brackish water.
Processing of rinse waters in the electroplating industry.

9.5 Basic parameters and separation mechanisms

The mass transport across the membrane is caused by one or more driving forces. A
gradient in chemical or electrical potential is the usual basis for these driving forces.
Pressure or concentration differences are the most common driving forces. The total flux
( N i ) of a species is related to the driving force ( P or C )by

Q
l

N i = ( P ) . (9.1)

The driving force is ( P - ) when there is an osmotic pressure difference ( )

across the membrane. Q is the permeability and Q l is the permeance. Permeance is used

when the actual membrane thickness is unknown. The separation factor

/

α ij is calculated

as the ratio of permeabilities or permeances.
Liquid separations, which typically involve filtration, use a term called rejection ( R ).
This term, with values between 0 and 1, measures the degree of rejection (lack of per-
meation) for a given solute. It is defined as:

C p
C f ,

R = 1 − (9.2)

where C p = permeate concentration

C f = feed concentration.

A value of 1 implies complete rejection.
For membrane separation processes, the mass-separating agent is the membrane itself.
Energy is supplied to provide the driving force for permeation through the membrane. The
mechanisms by which membranes separate different gas-phase components are outlined
in Section 9.7. For liquid-phase separations, filtration is based on size. Larger particles are
prevented from permeating while smaller components (typically solvents such as water)
permeate. This mechanism is similar to molecular sieving and is equivalent if the degree
of rejection is 1 (complete rejection). For pervaporation, a phase change is involved in
liquid-phase separations.

9.6 Dense membranes

Dense membrane materials are usually polymers. They are usually classified as rubbery
(amorphous) (above their glass transition temperature, T g ) or glassy (crystalline) (below
T g ). As a polymer is cooled below T g , it does not immediately become a completely