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Interface equations for capillary rise in random environment.

T Laurila1, C Tong, S Majaniemi

  • 1Laboratory of Physics, P.O. Box 1100, Helsinki University of Technology, FIN-02015 HUT, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
PubMed
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This study investigates quenched noise effects on capillary rise in 2D and 3D using a phase-field model. New noise terms were derived, differing quantitatively from previous studies, impacting interface dynamics with rough walls.

Area of Science:

  • Physics
  • Materials Science
  • Fluid Dynamics

Background:

  • Capillary rise is crucial in various natural and industrial processes.
  • Understanding interface dynamics under disorder is essential for predicting fluid behavior.
  • Existing models often simplify or omit the effects of quenched noise and geometric disorder.

Purpose of the Study:

  • To investigate the influence of quenched noise on interface dynamics during capillary rise in 2D and 3D.
  • To develop a systematic projection formalism for including disorder in interface motion equations.
  • To derive and analyze the dispersion relations and noise terms for meniscus and contact line motion.

Main Methods:

  • Phase-field approach with explicit inclusion of local mass conservation.

Related Experiment Videos

  • Modeling disorder in effective mobility (2D) and fluctuating geometry (3D).
  • Systematic projection formalism to derive linearized equations of motion.

    • Main Results:

    • Linearized equations of motion for meniscus and contact lines derived.
    • Dispersion relations obtained, featuring effective noise linearly proportional to velocity.
    • Deterministic parts align with existing studies, but noise terms show quantitative differences.

    Conclusions:

    • The developed formalism systematically incorporates quenched disorder into interface dynamics.
    • The derived noise terms offer a more nuanced understanding of capillary rise under realistic conditions.
    • This work provides a foundation for further studies on fluid transport in disordered media.