### Abstract

A model of the electrostatic and molecular interactions of a charged colloid particle with a charged membrane surface in an electrolyte solution has been developed. In Derjaguin's approximation, the force between a spherical colloid particle and a cylindrical membrane pore (with a rounded inlet) is calculated taking into account both electrostatic and van der Waals interactions. The force and energy are strongly dependent on the zeta-potential of both the particle and the membrane pore, the electrolyte concentration, and geometrical parameters. Conditions are found for which a potential barrier exists at the pore entrance. This barrier prevents a particle from entering the pore and, hence, gives an equilibrium position of the particle above the membrane surface. Therefore, there is a possibility in this case of removing the particle by a tangential flow, preventing pore blocking. The model was verified using a Finite Element Method (FEM) analysis developed earlier for colloidal interactions by two co-authors. It has been found that the accuracies of analytical formulae obtained for the interaction energy and force are within 10 and 20%, respectively, for practical application ranges of physico-chemical and geometrical parameters. Two major advantages of the model proposed compared to FEM calculations are: (1) the possibility of non-centerline calculations (when a particle is not moving along the axis of a membrane pore) without a three-dimensional solution; and (2) speed of calculations using the analytical formulae is much higher. Using a simplified expression for hydrodynamic force, critical values of pressure gradients across the membrane pore have been calculated analytically.

Original language | English |
---|---|

Pages (from-to) | 35-72 |

Number of pages | 38 |

Journal | Advances in Colloid and Interface Science |

Volume | 81 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jun 1999 |

### Fingerprint

### ASJC Scopus subject areas

- Surfaces and Interfaces
- Physical and Theoretical Chemistry
- Colloid and Surface Chemistry

### Cite this

*Advances in Colloid and Interface Science*,

*81*(1), 35-72. https://doi.org/10.1016/S0001-8686(99)00004-4