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Nonlinear model for Marangoni convection.

K S Das1, J K Bhattacharjee

  • 1Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta, 700032, India. tpksd@mahendra.iacs.res.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 17, 2001
PubMed
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We developed a model for Marangoni convection, revealing stability exchange at convection onset. Surface fluctuations cause oscillations that become chaotic with increased Marangoni number.

Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Heat and Mass Transfer

Background:

  • Marangoni convection is a key phenomenon in fluid dynamics driven by surface tension gradients.
  • Understanding the transition from steady convection to complex dynamics is crucial for various applications.
  • Previous models often simplified the conditions, neglecting factors like finite wave numbers and surface fluctuations.

Purpose of the Study:

  • To construct a Lorenz-like model for Marangoni convection incorporating a finite wave number.
  • To investigate the onset of convection and subsequent dynamic behaviors under large aspect ratio conditions.
  • To analyze the role of surface fluctuations in generating oscillatory and chaotic regimes.

Main Methods:

  • Development of a simplified mathematical model analogous to the Lorenz system.

Related Experiment Videos

  • Analysis of stability exchange at the onset of Marangoni convection.
  • Numerical investigation of system behavior as the Marangoni number is systematically increased.

    • Main Results:

    • The model predicts an exchange of stabilities at the onset of convection.
    • Surface fluctuations lead to the emergence of oscillatory behavior beyond the onset.
    • Increasing the Marangoni number drives these oscillations into a chaotic state.

    Conclusions:

    • The constructed model successfully captures key transitions in Marangoni convection.
    • Finite wave numbers and surface fluctuations are critical for understanding complex dynamics.
    • The study highlights the potential for chaotic behavior in seemingly simple fluid systems.