Logarithmic mean solute concentration in the membrane concentration of water in the membrane solute diffusion coefficient diffusivity of the solute in the membrane (m2 s!) diffusivity of the solvent in the membrane (m2 s!) apparent activation energy for solvent transport (kJ kmol!) driving force on component i frictional force between i and j flux of component i Hydraulic permeability friction parameter defined by Equation (36) salt permeability bulk solute concentration at highpressure side (g l!) solute concentration at lowpressure side (g l!) solute concentration at highpressure side of the membrane (at membrane surface) (g l!) mean solute concentration in the membraneĢ 3 3 4 4 4 5 5 5 5 6 7 7 7 8 8 8 9 10 12 13 16 18 18 19 20 #Sumaru head gasket issue verification#Introduction Phenomenological Transport Models Irreversible Thermodynamics-Phenomenological Transport Model IT-Kedem–Spiegler Model Nonporous Transport Models Solution–Diffusion Model Extended Solution–Diffusion Model Solution–Diffusion-Imperfection Model Porous Transport Models Friction Model Finely Porous Model Comparison and Summary of Membrane Transport Models Influence from Operating Conditions on Transport Effect of Pressure Effect of Concentration Effect of Feed Flow Effect of Temperature Effect of pH Experimental Verification of Solute Transport Single-Salt Solutions Mixed-Salt Solutions Organic Solutes and Nonaqueous Solutions Mixed Organic Solutes Membrane Charge Membrane Fouling and Concentration Polarization Phenomena: Limits of Membrane Processes 2.01 Fundamentals in Reverse Osmosis G Jonsson, Technical University of Denmark, Lyngby, Denmark F Macedonio, University of Calabria, Arcavacata di Rende (CS), Italy ª 2010 Elsevier B.V.
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