## Abstract

Here we study the force due to an applied electric field on a spherical particle trapped at a planar interface. Electric fields applied in either a normal or tangential direction to the interface are investigated. The electric potential is found by using the Mehler-Fock integral transform, which reduces the problem to a system of Fredholm integral equations. These equations are solved numerically and asymptotically. The force on an isolated particle is identified numerically, while the far-field interaction force between two particles is identified asymptotically. Solutions are presented as a function of the ratio of the dielectric constants, the conductivities, and the contact angle of the particle with the interface. We show that, at leading order, the interaction between perfect dielectric particles is dominated by the induced dipoles and hence is repulsive. For leaky dielectric particles the induced quadrupole can become significant, and the interaction force can be either attractive or repulsive depending on material parameters.

Original language | English (US) |
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Pages (from-to) | 850-875 |

Number of pages | 26 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 79 |

Issue number | 3 |

DOIs | |

State | Published - 2019 |

### Funding

\ast Received by the editors June 20, 2018; accepted for publication (in revised form) March 11, 2019; published electronically May 30, 2019. http://www.siam.org/journals/siap/79-3/M119566.html \bfF \bfu \bfn \bfd \bfi \bfn \bfg : This work was partially supported by NSF grants DMS-1312935, DMS-1716114, CBET-1437545, and CBET-1704996. \dagger Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 ([email protected], [email protected]).

## Keywords

- Electric fields
- Multipole expansions
- Particle interactions
- Transform methods

## ASJC Scopus subject areas

- Applied Mathematics