Water flux (Forward osmosis application)

Description

Forward osmosis (FO) is an osmotic process that, like reverse osmosis (RO), uses a semi-permeable membrane to effect separation of water from dissolved solutes. The driving force for this separation is an osmotic pressure gradient, such that a “draw” solution of high concentration (relative to that of the feed solution), is used to induce a net flow of water through the membrane into the draw solution, thus effectively separating the feed water from its solutes. In contrast, the reverse osmosis process uses hydraulic pressure as the driving force for separation, which serves to counteract the osmotic pressure gradient that would otherwise favor water flux from the permeate to the feed. Hence significantly more energy is required for reverse osmosis compared to forward osmosis.

The equation describing the relationship between osmotic and hydraulic pressures and water (solvent) flux is shiwn here.

Negative values of water flux indicates reverse osmotic flow. The modeling of these relationships is in practice more complex than this equation indicates, with flux depending on the membrane, feed, and draw solution characteristics, as well as the fluid dynamics within the process itself.

Related formulas

Variables

Jwwater flux (dimensionless)
Ahydraulic permeability of the membrane (dimensionless)
Δ_πdifference in osmotic pressures on the two sides of the membrane (dimensionless)
ΔPdifference in hydrostatic pressure (dimensionless)