A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops

Chiara Sorgentone*, Anna Karin Tornberg, Petia Vlahovska

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate interacting 3D drops (no axisymmetric simplification) in close proximity, can consider different viscosities, is adaptive in time and able to handle substantial drop deformation. For each drop global representations of the variables based on spherical harmonics expansions are used and the spectral accuracy is achieved by designing specific numerical tools: a specialized quadrature method for the singular and nearly singular integrals that appear in the formulation, a general preconditioner for the implicit treatment of the surfactant diffusion and a reparametrization procedure able to ensure a high-quality representation of the drops also under deformation. Our numerical method is validated against theoretical, numerical and experimental results available in the literature, as well as a new second-order theory developed for a surfactant-laden drop placed in a quadrupole electric field.

Original languageEnglish (US)
Pages (from-to)111-127
Number of pages17
JournalJournal of Computational Physics
Volume389
DOIs
StatePublished - Jul 15 2019

Fingerprint

boundary integral method
Electrohydrodynamics
Boundary Integral Method
electrohydrodynamics
Surfactant
Surface active agents
surfactants
Numerical methods
Electric fields
Electric Field
formulations
Nearly Singular Integrals
Numerical Methods
electric fields
spherical harmonics
Reparametrization
Quadrature Method
simplification
quadratures
Formulation

Keywords

  • Boundary integral method
  • Electric field
  • Small deformation theory
  • Spherical harmonics
  • Stokes flow
  • Surfactant

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

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title = "A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops",
abstract = "We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate interacting 3D drops (no axisymmetric simplification) in close proximity, can consider different viscosities, is adaptive in time and able to handle substantial drop deformation. For each drop global representations of the variables based on spherical harmonics expansions are used and the spectral accuracy is achieved by designing specific numerical tools: a specialized quadrature method for the singular and nearly singular integrals that appear in the formulation, a general preconditioner for the implicit treatment of the surfactant diffusion and a reparametrization procedure able to ensure a high-quality representation of the drops also under deformation. Our numerical method is validated against theoretical, numerical and experimental results available in the literature, as well as a new second-order theory developed for a surfactant-laden drop placed in a quadrupole electric field.",
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A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops. / Sorgentone, Chiara; Tornberg, Anna Karin; Vlahovska, Petia.

In: Journal of Computational Physics, Vol. 389, 15.07.2019, p. 111-127.

Research output: Contribution to journalArticle

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AU - Tornberg, Anna Karin

AU - Vlahovska, Petia

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AB - We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate interacting 3D drops (no axisymmetric simplification) in close proximity, can consider different viscosities, is adaptive in time and able to handle substantial drop deformation. For each drop global representations of the variables based on spherical harmonics expansions are used and the spectral accuracy is achieved by designing specific numerical tools: a specialized quadrature method for the singular and nearly singular integrals that appear in the formulation, a general preconditioner for the implicit treatment of the surfactant diffusion and a reparametrization procedure able to ensure a high-quality representation of the drops also under deformation. Our numerical method is validated against theoretical, numerical and experimental results available in the literature, as well as a new second-order theory developed for a surfactant-laden drop placed in a quadrupole electric field.

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