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Marangoni flow traveling with reaction fronts: Eikonal approximation.

Roberto Guzman1, Desiderio A Vasquez1

  • 1Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú Av. Universitaria 1801, San Miguel, Lima 32, Peru.

Chaos (Woodbury, N.Y.)
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Chemical reaction fronts create surface tension gradients, driving fluid motion (Marangoni flow) that alters front shape and speed. This study models front propagation, coupling it with fluid dynamics for a comprehensive understanding.

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Area of Science:

  • Fluid dynamics
  • Chemical kinetics
  • Surface phenomena

Background:

  • Chemical reaction fronts in liquids induce surface tension gradients.
  • These gradients drive fluid motion, known as Marangoni flow.
  • Marangoni flow significantly influences reaction front dynamics, affecting shape and propagation speed.

Purpose of the Study:

  • To model the propagation of chemical reaction fronts influenced by surface tension-driven fluid flow.
  • To couple a front evolution equation with fluid velocity derived from Stokes equations.
  • To investigate the impact of boundary conditions on front propagation dynamics.

Main Methods:

  • Utilized the Eikonal relation to model front propagation, linking curvature to normal speed.
  • Incorporated surface tension gradients (delta function) into Stokes equations for fluid velocity.
  • Derived analytical solutions for fluid vorticity under stress-free boundary conditions.
  • Employed numerical methods to solve for no-slip boundary conditions.

Main Results:

  • Developed a model coupling front evolution with Marangoni flow.
  • Obtained analytical and numerical solutions for fluid velocity fields.
  • Demonstrated good agreement with Kardar-Parisi-Zhang and reaction-diffusion models for small surface tension differences.

Conclusions:

  • Marangoni flow plays a crucial role in modulating chemical reaction front propagation.
  • Boundary conditions at the liquid layer's base influence the flow dynamics.
  • The developed model provides a robust framework for studying reactive flows with surface tension effects.