From “black box” to a real description of overall mass transport through membrane and boundary layers

E. Nagy, Márta Vitai

Research output: Contribution to journalArticle


The “black box” model defines the enhancement, E the polarization modulus, C*/C o and the intrinsic enhancement, E o 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, E o or C*/C o ) 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.

Original languageEnglish
Article number18
Issue number2
Publication statusPublished - Feb 1 2019



  • Dense membrane
  • Diffusive plus convective flow
  • Enhancement
  • Polarization modulus
  • Porous membrane
  • Solution-diffusion model
  • Two-layer transport
  • “black box” model

ASJC Scopus subject areas

  • Chemical Engineering (miscellaneous)
  • Process Chemistry and Technology
  • Filtration and Separation

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