### 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 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Advances in Colloid and Interface Science*,

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

**Model of the interaction between a charged particle and a pore in a charged membrane surface.** / Richard Bowen, W.; Filippov, Anatoly N.; Sharif, Adel O.; Starov, Victor M.

Research output: Contribution to journal › Article

*Advances in Colloid and Interface Science*, vol. 81, no. 1, pp. 35-72. https://doi.org/10.1016/S0001-8686(99)00004-4

}

TY - JOUR

T1 - Model of the interaction between a charged particle and a pore in a charged membrane surface

AU - Richard Bowen, W.

AU - Filippov, Anatoly N.

AU - Sharif, Adel O.

AU - Starov, Victor M.

PY - 1999/6/1

Y1 - 1999/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0344210455&partnerID=8YFLogxK

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U2 - 10.1016/S0001-8686(99)00004-4

DO - 10.1016/S0001-8686(99)00004-4

M3 - Article

VL - 81

SP - 35

EP - 72

JO - Advances in Colloid and Interface Science

JF - Advances in Colloid and Interface Science

SN - 0001-8686

IS - 1

ER -