Mass transfer of differently sized organic solutes at spacer covered and permeable nanofiltration wall

• Cross-flow velocity significantly affects removal of organics.
• Sherwood relation correctly estimates mass transfer at small solute fluxes.
• At high solute fluxes Schmidt number needs correction.
• Correction correlation is proposed for Schmidt number.

Concentration polarization (CP) phenomena may significantly affect water permeability and removal of organics solutes in cross-flow nanofiltration (NF) making it an important optimization parameter. Most of the models predict CP using mass transfer coefficients that may be estimated using model Sherwood (Sh) relations of a general form, Sh = a*RebScc. In many cases Sh relations are able to predict mass transfer coefficients remarkably well; however, such relations are in general valid only for non-permeable walls. Sh relations were experimentally validated using a binary solution of single solute and water where Schmidt numbers (Sc) were varied by changing the temperature or density of the solution, at a constant or varied Reynolds number (Re). This study evaluated Sh relations from different angle and used ten organic solutes of different diffusivity at a constant concentration and viscosity of solutions, covering a range of Sc from 850 to 2022. The aim of this study was to evaluate the Sh relation in predicting the mass transfer of differently sized organic solutes in rectangular channel, at spacer covered and permeable NF wall of defined porosity. Comparison of experimental Sh, obtained using the velocity variation method, and model Sh showed that model Sh relation correctly predicts mass transfer of organics when particular solute flux through the NF permeable wall is sufficiently low. A correction correlation is proposed for coefficient c on Sc in model Sh relation, where c approaches the model Sh value, 0.42, with the increase in size of the solutes. In addition, data presented show that the removal of organic solutes from the water may be significantly improved, up to 280%, by changing the hydrodynamics in the channel.

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