## Introduction

Reverse osmosis (RO) is a membrane filtration process for removing solvent from a solution by leaving a concentrated solution behind. When a semipermeable membrane separates a dilute solution from a concentrated solution, the solvent crosses from the dilute to the concentrated side of the

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Sustainability Science and Engineering, Volume 2 ISSN 1871-2711, DOI 10.1016/S1871-2711(09)00204-9

membrane in an attempt to equalize concentrations. The flow of solvent can be prevented by applying an opposing hydrostatic pressure to the concentrated solution.

The magnitude of the pressure required to completely impede the flow of solvent is defined as the "osmotic pressure.'' If the applied hydrostatic pressure exceeds the osmotic, flow of solvent will be reversed, that is, solvent will flow from the concentrated to the dilute solution. This phenomenon is referred to as "reverse osmosis.'' Fig. 1 illustrates the concepts of osmosis, osmotic pressure, and RO schematically.

Osmotic pressure (p) is a thermodynamic property of a solution and is related to the mole fraction of the solvent, XBi, as

where R is the universal gas constant [J/(Kmol)], T the temperature (K), and VB the volume of the solvent (m3).

For dilute solutions, the osmotic pressure is found to obey the ideal gas law making Eq. (1) simplify to the van't Hoff equation as

where CAi is the concentration of solute (mol/m3).

Water

Water

Semi permeable membrane

Osmosis

Water flows from low solute concentration to higher solute concentrations

Osmotic Pressure

"Water

"Water

No net flow across the membrane

Hydrostatic Pressure

Watei

Watei

Semi permeable membrane

Osmosis

Water flows from low solute concentration to higher solute concentrations

No net flow across the membrane

E i Reverse Osmosis qui i rium By applying pressure greater

then the osmotic pressure, the pressure required

to stop water flow and water flows from higher reach equilibrium concentration solution to lower

Figure 1 Concept of osmosis, osmotic pressure, and reverse osmosis.

Therefore, the osmotic pressure difference across a membrane, An, is related to the concentration difference, CA2 - C^. The osmotic pressure depends neither on the solute type nor on its molecular size but only on molar concentration as shown in the formula.

In order to use RO as a water purification process, the feedwater is pressurized on one side of a semipermeable membrane. The pressure must be high enough to exceed the osmotic pressure to cause reverse osmotic flow of water. If the membrane is highly permeable to water, but essentially impermeable to dissolved solutes, pure water crosses the membrane and is known as product water. As product water crosses the membrane, the concentration of dissolved impurities increases near the membrane surface, leading to a condition known as concentration polarization. Concentration polarization is associated with the accumulation of solute particles on the membrane surface, resulting in a higher solute concentration at the membrane surface as compared to the bulk solution, which in turn increases the osmotic pressure of the system. A point is reached at which the applied pressure is no longer able to overcome the osmotic pressure and no further flow of product water occurs. Moreover, if the applied pressure is increased in an attempt to gain more product water, the membrane becomes fouled by precipitated salts and other undissolved material from the water. Therefore, there is a limit to the fraction of feedwater, which can be recovered as pure water. RO units are operated in a configuration where only a portion of the feedwater passes through the membrane with the remainder being directed to the drain (cross-flow configuration).

The water flowing to the drain contains concentrated solutes and other insoluble materials, such as bacteria, endotoxin, and particles, and is referred to as the reject stream. The product water to feedwater ratio can range from 10% to 50% for purification of water depending on the characteristics of the incoming water as well as other conditions, such as the membrane material and fouling potential.