From "Black Box" to a Real Description of Overall Mass Transport through Membrane and Boundary Layers

The "black box" model defines the enhancement, the polarization modulus, and the intrinsic enhancement, without knowing the transport mechanism in the membrane. This study expresses the above-mentioned characteristic parameters, simultaneously taking into account the mass transport expressions developed for both the polarization and the membrane layers. Two membrane models are studied here, namely a solution-diffusion model characterizing solute transport through a dense membrane and a solution-diffusion plus convection model characterizing transport through a porous membrane due to transmembrane pressure difference. It is shown that the characteristic parameters of the "black box" model (E, or ) can be expressed as a function of the transport parameters and independently from each other using two-layer models. Thus, membrane performance could be predicted by means of the transport parameters. Several figures show how enhancement and the polarization modulus varied as a function of the membrane Peclet number and the solubility coefficient. Enhancement strongly increased up to its maximum value when H > 1, in the case of transport through a porous membrane, whereas its change remained before unity in the case of a dense membrane. When the value of H < 1, the value of E gradually decreased with increasing values of the membrane Peclet number.