Marangoni flow traveling with reaction fronts: Eikonal approximation.

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.