### 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) |
---|---|

Pages (from-to) | 850-875 |

Number of pages | 26 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 79 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

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*SIAM Journal on Applied Mathematics*, vol. 79, no. 3, pp. 850-875. https://doi.org/10.1137/18M1195668

**Dielectric spherical particle on an interface in an applied electric field.** / Hu, Yi; Vlahovska, Petia; Miksis, Michael J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dielectric spherical particle on an interface in an applied electric field

AU - Hu, Yi

AU - Vlahovska, Petia

AU - Miksis, Michael J

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Electric fields

KW - Multipole expansions

KW - Particle interactions

KW - Transform methods

UR - http://www.scopus.com/inward/record.url?scp=85070561754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070561754&partnerID=8YFLogxK

U2 - 10.1137/18M1195668

DO - 10.1137/18M1195668

M3 - Article

AN - SCOPUS:85070561754

VL - 79

SP - 850

EP - 875

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -