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Exact solutions for viscous Marangoni spreading.

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This study provides exact solutions for Marangoni spreading of surfactants on liquid interfaces. Different initial surfactant distributions lead to unique spreading behaviors, offering valuable reference solutions for experiments.

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Area of Science:

  • Fluid dynamics
  • Surface science
  • Nonlinear transport phenomena

Background:

  • Marangoni flows govern surfactant spreading at liquid interfaces.
  • Exact solutions for Marangoni spreading are scarce.
  • Previous work mapped 2D Stokes flow surfactant spreading to a complex Burgers equation.

Purpose of the Study:

  • To derive and present simple solutions for Marangoni spreading of insoluble surfactants.
  • To investigate the influence of initial surfactant distribution on spreading dynamics.
  • To analyze the role of surface diffusion and explore effective diffusion approximations.

Main Methods:

  • Derivation of the complex Burgers equation for 2D Stokes flow.
  • Obtaining explicit solutions for various initial surfactant distributions (pulse, hole, periodic).
  • Analysis of the fundamental solution to assess surface diffusion effects.

Main Results:

  • Explicit solutions reveal distinct spreading behaviors based on initial surfactant distribution.
  • Identified conditions where spreading approximates an effective diffusion process.
  • Demonstrated that the effective diffusion approximation is not universally valid.
  • Briefly considered the 3D axially symmetric flow case.

Conclusions:

  • The study provides reference solutions for Marangoni spreading, applicable to 2D and 3D flows.
  • Experimental validation using fluorescent or photoswitchable surfactants is suggested.
  • Understanding spreading dynamics is crucial for applications involving surface-active molecules.