2.5. Evaluation of concentration polarization by osmolarity calculation
The effect of CP caused by the permeate fluxwas evaluated by calculating the osmolarity on the membrane surface from the difference of the permeate flux with the feed solution and pure-water permeability. The osmotic pressure on the membrane surface, πm, can be calculated using the Morse equation: πm = CmRT, in which Cm, R, and T are the osmolarity on the membrane surface, gas constant, and temperature, respectively. The permeate flux with the feed solution, J, can be described as J = L(P − πm), in which L and P are the pure-water permeability and TMP respectively [19]. From these equations, the osmolarity on the membrane surface is calculated as Cm = (P − J / L) / RT. The values of J and L were measured by using the same apparatus as shown in Fig. 1.