### Abstract

A solution to the conduction equation has been developed for two equal size, nonconducting spheres with the line between centers perpendicular to the applied field. The solution, valid when the gap between the spheres is small compared to their radius, is based on a matched asymptotic expansion. For the case when the conductivity is uniform everywhere (i.e., Laplace's equation), the solution agrees well with numerical results obtained from an infinite series solution in bispherical coordinates. An example with a nonuniform conductivity in the gap is presented to demonstrate how the method can be extended to more general conduction problems.

Original language | English (US) |
---|---|

Pages (from-to) | 1209-1217 |

Number of pages | 9 |

Journal | Physics of Fluids |

Volume | 9 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*9*(5), 1209-1217. https://doi.org/10.1063/1.869260

}

*Physics of Fluids*, vol. 9, no. 5, pp. 1209-1217. https://doi.org/10.1063/1.869260

**Conduction in the small gap between two spheres.** / Solomentsev, Yuri; Velegol, Darrell; Anderson, John L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Conduction in the small gap between two spheres

AU - Solomentsev, Yuri

AU - Velegol, Darrell

AU - Anderson, John L.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - A solution to the conduction equation has been developed for two equal size, nonconducting spheres with the line between centers perpendicular to the applied field. The solution, valid when the gap between the spheres is small compared to their radius, is based on a matched asymptotic expansion. For the case when the conductivity is uniform everywhere (i.e., Laplace's equation), the solution agrees well with numerical results obtained from an infinite series solution in bispherical coordinates. An example with a nonuniform conductivity in the gap is presented to demonstrate how the method can be extended to more general conduction problems.

AB - A solution to the conduction equation has been developed for two equal size, nonconducting spheres with the line between centers perpendicular to the applied field. The solution, valid when the gap between the spheres is small compared to their radius, is based on a matched asymptotic expansion. For the case when the conductivity is uniform everywhere (i.e., Laplace's equation), the solution agrees well with numerical results obtained from an infinite series solution in bispherical coordinates. An example with a nonuniform conductivity in the gap is presented to demonstrate how the method can be extended to more general conduction problems.

UR - http://www.scopus.com/inward/record.url?scp=0031147837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031147837&partnerID=8YFLogxK

U2 - 10.1063/1.869260

DO - 10.1063/1.869260

M3 - Article

AN - SCOPUS:0031147837

VL - 9

SP - 1209

EP - 1217

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

ER -