Membrane and Desalination Technologies - TCE Moodle Website

Desalination of Seawater by Reverse Osmosis 561
Fig. 13.1. Schematic of
reverse osmotic
equilibrium (a) and
reverse osmosis (RO)
membrane (b).
Here, P is the osmotic pressure (force/length 2 ), CS is the summation of molarities of all
dissolved ions (moles/length 3 ), R is the ideal gas constant (force-length/mass-temperature),
and T is the absolute temperature (K). The magnitude of the osmotic pressure, even in very
dilute solution, is very large.
For instance, with a solute of 0.01 M at room temperature (298 K), the osmotic pressure
would be
P ¼ CSRT ¼
0:010 mol
1L
0:0821 L atm
mol K
Solvent
Solvent
Osmotic
pressure
298 K ¼ 0:24 atm:
This pressure is sufficient to support a column of water 8.1-ft high.
For applications of the RO of seawater, an approximate expression is (88):
Pressure
Solution
Low MW solute
High MW solute
Large molecular
materials
P ¼ 1:12 T X mi; (2Þ
where P is in psia, T is in K, and P mi is the summation of molarities of all dissolved ions
and nonionic species in the solution (M).
RO membrane has an anisotropic (also called asymmetric) structure: it consists of an
extremely thin skin layer (100–500-nm thick) with very fine microporous texture (1) and on
the top of it a much thicker, spongy, supporting sublayer with much larger pore size. In the
case of cellulose acetate (CA) RO membranes of the Loeb–Sourirajan type (2), for example,
the pores of the skin layer have been estimated, based on results of titrated water diffusion
experiments, to be less than 0.8 nm (8 A ˚ ) in diameter (3), and the pore size of the substructure
is in the range of 100–400 nm (4).
a
b
Osmotic pressure Π
High density solution