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Nonexistence of two-dimensional sessile drops in the diffuse-interface model.

E S Benilov1

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This summary is machine-generated.

The diffuse-interface model (DIM) surprisingly does not allow static liquid ridges. However, these can appear as slow-moving states when the vapor-to-liquid density ratio is low, like for water.

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Area of Science:

  • Fluid dynamics
  • Interface phenomena
  • Computational modeling

Background:

  • The diffuse-interface model (DIM) is a standard numerical method for simulating fluid systems with interfaces.
  • Applications include sessile drops and liquid ridges, crucial in various scientific and industrial processes.
  • Understanding the model's limitations is vital for accurate simulations.

Purpose of the Study:

  • To investigate the existence of static solutions for liquid ridges within the diffuse-interface model.
  • To determine the conditions under which liquid ridges can be accurately represented by the DIM.
  • To explore the limitations of the DIM in describing specific fluid configurations.

Main Methods:

  • Mathematical analysis of the diffuse-interface model equations.
  • Theoretical proof of non-existence for static liquid ridge solutions.
  • Investigation of quasi-static states under specific physical conditions (low vapor-to-liquid density ratio).

Main Results:

  • The diffuse-interface model (DIM) fundamentally does not admit solutions for static liquid ridges.
  • Liquid ridges can be observed as quasi-static states when the vapor-to-liquid density ratio is sufficiently small.
  • This non-existence theorem does not apply to axisymmetric sessile drops or ridges near a vertical wall.

Conclusions:

  • The DIM has inherent limitations in modeling static liquid ridges.
  • Quasi-static approximations are necessary for simulating such phenomena under specific density conditions.
  • The model's applicability varies depending on the geometry and physical parameters of the fluid system.