### Abstract

The application of membrane separation processes, such as microfiltration and ultrafiltration, is one of the most important developments in chemical engineering in recent years. The paper presents a quantification of both electrostatic and hydrodynamic effects to identify conditions for the operation of such processes with much greater efficiency. In particular, the hydrodynamic and electrostatic forces on a charged spherical particle as a function of distance of approach and entry to a charged cylindrical pore in a charged planar surface have been calculated. A Galerkin finite-element scheme has been used to provide numerical solutions of the nonlinear Poisson-Boltzmann equation for electrostatic interactions and of the Navier-Stokes equations for hydrodynamic interactions, with the Newton sequence technique being used to solve the Poisson-Boltzmann equation. The results show that the electrostatic interactions can play a crucial role in controlling the approach and entry of such a particle to a pore.

Original language | English |
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Title of host publication | Proceedings - Royal Society of London, A |

Pages | 2121-2140 |

Number of pages | 20 |

Volume | 452 |

Edition | 1952 |

Publication status | Published - 1 Dec 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - Royal Society of London, A*(1952 ed., Vol. 452, pp. 2121-2140)

**The hydrodynamic and electrostatic interactions on the approach and entry of a charged spherical particle to a charged cylindrical pore in a charged planar surface with implications for membrane separation processes.** / Bowen, W. R.; Sharif, A. O.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Proceedings - Royal Society of London, A.*1952 edn, vol. 452, pp. 2121-2140.

}

TY - CHAP

T1 - The hydrodynamic and electrostatic interactions on the approach and entry of a charged spherical particle to a charged cylindrical pore in a charged planar surface with implications for membrane separation processes

AU - Bowen, W. R.

AU - Sharif, A. O.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - The application of membrane separation processes, such as microfiltration and ultrafiltration, is one of the most important developments in chemical engineering in recent years. The paper presents a quantification of both electrostatic and hydrodynamic effects to identify conditions for the operation of such processes with much greater efficiency. In particular, the hydrodynamic and electrostatic forces on a charged spherical particle as a function of distance of approach and entry to a charged cylindrical pore in a charged planar surface have been calculated. A Galerkin finite-element scheme has been used to provide numerical solutions of the nonlinear Poisson-Boltzmann equation for electrostatic interactions and of the Navier-Stokes equations for hydrodynamic interactions, with the Newton sequence technique being used to solve the Poisson-Boltzmann equation. The results show that the electrostatic interactions can play a crucial role in controlling the approach and entry of such a particle to a pore.

AB - The application of membrane separation processes, such as microfiltration and ultrafiltration, is one of the most important developments in chemical engineering in recent years. The paper presents a quantification of both electrostatic and hydrodynamic effects to identify conditions for the operation of such processes with much greater efficiency. In particular, the hydrodynamic and electrostatic forces on a charged spherical particle as a function of distance of approach and entry to a charged cylindrical pore in a charged planar surface have been calculated. A Galerkin finite-element scheme has been used to provide numerical solutions of the nonlinear Poisson-Boltzmann equation for electrostatic interactions and of the Navier-Stokes equations for hydrodynamic interactions, with the Newton sequence technique being used to solve the Poisson-Boltzmann equation. The results show that the electrostatic interactions can play a crucial role in controlling the approach and entry of such a particle to a pore.

UR - http://www.scopus.com/inward/record.url?scp=0030449199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030449199&partnerID=8YFLogxK

M3 - Chapter

VL - 452

SP - 2121

EP - 2140

BT - Proceedings - Royal Society of London, A

ER -