Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary

Hsien-Hung Wei, David Halpern, James B. Grotberg

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.

Original languageEnglish
Pages (from-to)769-780
Number of pages12
JournalJournal of Colloid And Interface Science
Volume285
Issue number2
DOIs
Publication statusPublished - 2005 May 15

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Surface-Active Agents
Surface active agents
Fluids
Asymptotic analysis
Steady flow
Pressure gradient
Surface tension
Thin films

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Surfaces, Coatings and Films
  • Colloid and Surface Chemistry

Cite this

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Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary. / Wei, Hsien-Hung; Halpern, David; Grotberg, James B.

In: Journal of Colloid And Interface Science, Vol. 285, No. 2, 15.05.2005, p. 769-780.

Research output: Contribution to journalArticle

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