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<b>Abstract</b>— <p>The results of mathematical modeling of the non-stationary problem of a gas bubble rising in a viscous liquid with a surfactant dissolved in it are presented. The problem statement is written taking into account the effects of adsorption and desorption of the surfactant at the interface and the dependence of the surface tension coefficient on concentration according to Langmuir’s law. The numerical solution algorithm is based on an original Lagrangian–Eulerian method, which allows for explicitly identifying a free surface at a discrete level and implementing natural boundary conditions on it. The process of establishing a steady-state bubble ascent velocity is studied and parametric studies of the influence of the volume concentration of the surfactant and the bubble size on the steady-state velocity and the flow structure in its vicinity are carried out. The distributions of the velocity vector components and surface concentration along the interface are presented, demonstrating the influence of the Marangoni effect on the ascent process.</p>

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Structure of Flow during Rising of a Single Bubble in Liquid with a Dissolved Surfactant

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • E. I. Borzenko,
  • A. S. Usanina

摘要

Abstract—

The results of mathematical modeling of the non-stationary problem of a gas bubble rising in a viscous liquid with a surfactant dissolved in it are presented. The problem statement is written taking into account the effects of adsorption and desorption of the surfactant at the interface and the dependence of the surface tension coefficient on concentration according to Langmuir’s law. The numerical solution algorithm is based on an original Lagrangian–Eulerian method, which allows for explicitly identifying a free surface at a discrete level and implementing natural boundary conditions on it. The process of establishing a steady-state bubble ascent velocity is studied and parametric studies of the influence of the volume concentration of the surfactant and the bubble size on the steady-state velocity and the flow structure in its vicinity are carried out. The distributions of the velocity vector components and surface concentration along the interface are presented, demonstrating the influence of the Marangoni effect on the ascent process.