Numerical Approximation of a Phase-Field Surfactant Model with Fluid Flow

Guangpu Zhu, Jisheng Kou, Shuyu Sun*, Jun Yao, Aifen Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Modeling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of two Cahn–Hilliard-type equations and incompressible Navier–Stokes equation. With the introduction of two auxiliary variables, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. By certain subtle explicit-implicit treatments to stress and convective terms, we construct first and second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving only a sequence of linear elliptic equations, and computations of phase-field variables, velocity and pressure are fully decoupled. We further establish a rigorous proof of unconditional energy stability for the first-order scheme. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow, where the increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

Original languageEnglish (US)
Pages (from-to)223-247
Number of pages25
JournalJournal of Scientific Computing
Volume80
Issue number1
DOIs
StatePublished - Jul 15 2019

Keywords

  • Energy stability
  • Navier–Stokes
  • Phase-field modeling
  • Surfactant
  • Two-phase flows

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • Numerical Analysis
  • Computational Theory and Mathematics

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