### Abstract

The effect of many-body interactions on the electrostatic force between spheres in a chain of charged spheres confined in a long charged pore has been quantified by solving the non-linear Poisson-Boltzmann equation (PBE), using the adaptive finite element method (AFEM) combined with error minimisation techniques. The equation is solved for conditions of constant surface potential and constant surface charge density. The computed force indicates that the force between any two spheres in a long chain of spheres in a long charged tube does not differ significantly from the force between only two spheres in a tube. This trend is also observed for an unconfined chain of spheres, where the force between two isolated spheres is again very similar to the force between any two spheres in a long unbounded chain. The results also quantify the effect of many-body interactions on the reduction of the repulsion force between the spheres. A significant reduction in the repulsion force between the spheres is observed when the radial distance between the pore wall and the chain of spheres is reduced. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and significant reduction of the force observed as the dimensionless radius is reduced.

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

Pages (from-to) | 76-81 |

Number of pages | 6 |

Journal | Powder Technology |

Volume | 135-136 |

DOIs | |

Publication status | Published - 2 Oct 2003 |

Externally published | Yes |

### Fingerprint

### Keywords

- Adaptive finite element method
- Chain of spheres
- Many-body electrostatic interactions
- Poisson-Boltzmann equation

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Physical and Theoretical Chemistry

### Cite this

*Powder Technology*,

*135-136*, 76-81. https://doi.org/10.1016/j.powtec.2003.08.006

**The effect of many-body interactions on the electrostatic force on a finite chain of spheres confined in a long charged tube.** / Sharif, Adel O.; Afshar, M. H.; Moghadasi, J.; Williams, T. J.

Research output: Contribution to journal › Article

*Powder Technology*, vol. 135-136, pp. 76-81. https://doi.org/10.1016/j.powtec.2003.08.006

}

TY - JOUR

T1 - The effect of many-body interactions on the electrostatic force on a finite chain of spheres confined in a long charged tube

AU - Sharif, Adel O.

AU - Afshar, M. H.

AU - Moghadasi, J.

AU - Williams, T. J.

PY - 2003/10/2

Y1 - 2003/10/2

N2 - The effect of many-body interactions on the electrostatic force between spheres in a chain of charged spheres confined in a long charged pore has been quantified by solving the non-linear Poisson-Boltzmann equation (PBE), using the adaptive finite element method (AFEM) combined with error minimisation techniques. The equation is solved for conditions of constant surface potential and constant surface charge density. The computed force indicates that the force between any two spheres in a long chain of spheres in a long charged tube does not differ significantly from the force between only two spheres in a tube. This trend is also observed for an unconfined chain of spheres, where the force between two isolated spheres is again very similar to the force between any two spheres in a long unbounded chain. The results also quantify the effect of many-body interactions on the reduction of the repulsion force between the spheres. A significant reduction in the repulsion force between the spheres is observed when the radial distance between the pore wall and the chain of spheres is reduced. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and significant reduction of the force observed as the dimensionless radius is reduced.

AB - The effect of many-body interactions on the electrostatic force between spheres in a chain of charged spheres confined in a long charged pore has been quantified by solving the non-linear Poisson-Boltzmann equation (PBE), using the adaptive finite element method (AFEM) combined with error minimisation techniques. The equation is solved for conditions of constant surface potential and constant surface charge density. The computed force indicates that the force between any two spheres in a long chain of spheres in a long charged tube does not differ significantly from the force between only two spheres in a tube. This trend is also observed for an unconfined chain of spheres, where the force between two isolated spheres is again very similar to the force between any two spheres in a long unbounded chain. The results also quantify the effect of many-body interactions on the reduction of the repulsion force between the spheres. A significant reduction in the repulsion force between the spheres is observed when the radial distance between the pore wall and the chain of spheres is reduced. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and significant reduction of the force observed as the dimensionless radius is reduced.

KW - Adaptive finite element method

KW - Chain of spheres

KW - Many-body electrostatic interactions

KW - Poisson-Boltzmann equation

UR - http://www.scopus.com/inward/record.url?scp=0242383882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242383882&partnerID=8YFLogxK

U2 - 10.1016/j.powtec.2003.08.006

DO - 10.1016/j.powtec.2003.08.006

M3 - Article

AN - SCOPUS:0242383882

VL - 135-136

SP - 76

EP - 81

JO - Powder Technology

JF - Powder Technology

SN - 0032-5910

ER -