The main driving forces for transport are pressure, concentration, electrical potential, and temperature, each of which primarily influences the flux of solvent, solute, electrical current, and thermal energy, respectively. In addition to the primary effects, each of the driving forces has a cross-influence on the other fluxes. For instance, the pressure driving force can cause a flux of current, called the streaming current.
In RO systems, the only driving forces of interest are pressure and concentration, which lead to flux of solvent and solute, respectively (Table 1). The cross-influence of solute concentration driving force on solvent flux is represented by the osmotic pressure term in the solvent flux equation. The cross-influence of pressure driving force on solute flux is often small, for high separation membranes, and is therefore neglected.
The solvent flux equation, written here for both volume flux, JV, and molar flux of solvent, NB, indicates that flux is directly proportional to the effective pressure driving force:
Table 1 Driving forces of interest in reverse osmosis
Pressure gradient Concentration gradient
Flux Solvent flow Solvent permeability Osmosis
Diffusion where C is the molar density (kmol/m3), A the pure water permeability coefficient [kmol/(mskPa)], AP the pressure difference across the membrane (kPa), and An the osmotic pressure difference across the membrane (kPa).
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