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Long-wavelength equation for vertically falling films.

Mohan K R Panga1, Ramesh R Mudunuri, Vemuri Balakotaiah

  • 1Department of Chemical Engineering, University of Houston, Texas 77204-4792, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary
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A new equation models wave evolution on falling viscous films, using Weber number (We) instead of Reynolds number (Re). This improved model better predicts wave behavior and matches experimental data.

Area of Science:

  • Fluid dynamics
  • Surface phenomena
  • Nonlinear waves

Background:

  • Vertically falling viscous films exhibit complex surface wave evolution.
  • Existing models often lack crucial terms like viscous dissipation and pressure correction.
  • Distinguishing viscous from inertia-dominated regimes requires appropriate dimensionless numbers.

Purpose of the Study:

  • Derive a more accurate evolution equation for surface waves on a falling viscous film.
  • Incorporate viscous dissipation and pressure correction terms.
  • Compare model predictions with existing theories and experimental data.

Main Methods:

  • Developed a new scaling approach, replacing traditional long-wavelength scaling.
  • Introduced the Weber number (We) for regime distinction.

Related Experiment Videos

  • Implemented selective regularization to create a two-mode model.
  • Performed numerical simulations in a traveling wave coordinate.

    • Main Results:

    • The derived equation offers improved agreement with Orr-Sommerfeld (OS) equation results.
    • The regularized model eliminates finite-time blowup and predicts solitary waves.
    • Simulations reveal transitions from regular to chaotic wave profiles.
    • Model predictions align well with experimental data for wave amplitude.

    Conclusions:

    • The new evolution equation provides a more accurate description of wave phenomena in falling viscous films.
    • Regularization successfully addresses model instabilities and reveals rich wave dynamics.
    • The model demonstrates strong predictive power, validated by experimental observations.