### Abstract

The mass transport mechanisms during cross-flow ultrafiltration (UF) are mathematically expressed using the two-dimensional convective diffusion equation where the axial diffusion term is neglected for an axial Peclet number much greater than the transverse Peclet number. A numerical scheme is presented to solve the steady-state two-dimensional convective diffusion equation for the case of known uniform permeate flux. However, in the actual cross-flow UF process, the permeate flux along the axial direction is unknown and usually decreases with axial distance. Therefore, an iterative algorithm is developed to predict the steady-state permeate flux based on the assumption that the concentration at membrane surface cannot exceed a certain limiting value. Using the numerical model with an effective diffusion coefficient, which is considered to be the sum of molecular diffusion and shear-induced hydrodynamic diffusion coefficients, the effects of particle size, feed concentration, and axial velocity on the steady-state permeate flux were investigated.

Original language | English (US) |
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Pages (from-to) | 241-251 |

Number of pages | 11 |

Journal | Desalination |

Volume | 109 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1997 |

### Keywords

- Concentration polarization
- Cross-flow ultrafiltration
- Flux decline
- Molecular diffusion
- Shear-induced hydrodynamic diffusion

### ASJC Scopus subject areas

- Chemistry(all)
- Chemical Engineering(all)
- Materials Science(all)
- Water Science and Technology
- Mechanical Engineering