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Falling films and the Marangoni effect.

V Ya Shkadov1, M G Velarde, V P Shkadova

  • 1Instituto Pluridisciplinar, Universidad Complutense de Madrid, Paseo Juan XXIII, n. 1, 28040 Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Investigating falling liquid film instability, this study reveals new Marangoni-driven diffusion modes. These modes, influenced by surfactant dynamics, lead to complex film surface patterns and resonances.

Area of Science:

  • Fluid Dynamics
  • Surface Science
  • Chemical Engineering

Background:

  • Falling liquid films are crucial in industrial processes.
  • Surface tension gradients, driven by the Marangoni effect, significantly influence film stability.
  • Understanding surfactant adsorption-desorption dynamics is key to controlling film behavior.

Purpose of the Study:

  • To investigate the instability of falling liquid films with surfactant adsorption-desorption.
  • To analyze the emergence and characteristics of Marangoni-driven modes.
  • To explore the conditions leading to patterned film surfaces and mode resonances.

Main Methods:

  • Reduction of Navier-Stokes and Fick equations to nonlinear evolution equations.
  • Linear stability analysis to derive and solve a dispersion equation.

Related Experiment Videos

  • Numerical computation of eigenvalues for various dimensionless parameters.

    • Main Results:

    • Identification of up to four new Marangoni-driven diffusion modes alongside the known hydrodynamic mode.
    • Characterization of diffusion modes: two traveling with liquid velocity, two independent.
    • Discovery of a monotonic instability mode leading to patterned film surfaces.
    • Prediction of mode resonance for specific parameter combinations.

    Conclusions:

    • Surfactant adsorption-desorption significantly enriches the instability mechanisms of falling liquid films.
    • The Marangoni effect, coupled with diffusion, introduces complex dynamic behaviors.
    • Film surface patterns and resonances are controllable through surface stress, adsorption kinetics, and surface tension properties.