A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant

Kuan Yu Chen, Ming-Chih Lai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

Many physical problems arising in biological or material sciences involve solving partial differential equations in deformable interfaces or complex domains. For instance, the surfactant (an amphiphilic molecular) which usually favors the presence in the fluid interface may couple with the surfactant soluble in one of bulk domains through adsorption and desorption processes. Thus, it is important to accurately solve coupled surface-bulk convection-diffusion equations especially when the interface is moving. In this paper, we first rewrite the original bulk concentration equation in an irregular domain (soluble region) into a regular computational domain via the usage of the indicator function so that the concentration flux across the interface due to adsorption and desorption processes can be termed as a singular source in the modified equation. Based on the immersed boundary formulation, we then develop a new conservative scheme for solving this coupled surface-bulk concentration equations which the total surfactant mass is conserved in discrete sense. A series of numerical tests has been conducted to validate the present scheme. As an application, we extend our previous work [M.-C. Lai, Y.-H. Tseng, H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, J. Comput. Phys. 227 (2008) 7279-7293] to the soluble case. The effects of solubility of surfactant on drop deformations in a quiescent and shear flow are investigated in detail.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Computational Physics
Volume257
Issue numberPA
DOIs
StatePublished - 15 Jan 2014

Keywords

  • A conservative scheme
  • Adsorption-desorption process
  • Immersed boundary method
  • Interfacial flow
  • Soluble surfactant

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