## Abstract

A discrete multilayer model for the deposition of solutes inside membrane pores during ultrafiltration is proposed. The model takes into account the time-dependent steric exclusion of solutes at the pore inlet and the difference between the deposition coefficients for the first and higher layers caused by the action of the double-layer electrostatic repulsion forces between suspended and deposited solutes. The governing differential equations are solved numerically for 2- and 3-layer deposition on the pore wall. Also, a much simpler approximate solution with an error less than 10% is obtained for the main practical scenario by the generalized variable-parameter averaging method. Permeability, rejection, and selectivity-permeability tradeoff curves are calculated and compared for the monolayer coverage (Langmuir adsorption), 2-layer, and 3- layer cases at different values of higher-to-first layer deposition coefficient and initial pore radius. It is shown that the value of the deposition coefficient for the higher deposited layers of solutes can dramatically affect the performance of the membrane. For the monolayer coverage case, simple algebraic equations for finding the rejection coefficient and its minimum are derived. They imply that the rejection coefficient can follow three scenarios: monotonically decreasing, monotonically increasing, or having a minimum. A set of derived equations for determining the initial, minimum, and steady-state values of the rejection coefficient and permeate flux is suggested to use along with an experimental selectivity-permeability tradeoff curve to find the unknown physicochemical and geometrical parameters needed to describe the ultrafiltration process of interest, optimize its process parameters, and change the process of membrane manufacturing in order to obtain a more efficient membrane.

Original language | English (US) |
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Pages (from-to) | 382-396 |

Number of pages | 15 |

Journal | Theoretical Foundations of Chemical Engineering |

Volume | 48 |

Issue number | 4 |

DOIs | |

State | Published - Jul 2014 |

## All Science Journal Classification (ASJC) codes

- General Chemistry
- General Chemical Engineering

## Keywords

- membrane permeability
- membrane selectivity
- multilayer deposition
- pore constriction model
- steric exclusion
- ultrafiltration