Unveiling unique scaling behavior in miscible, volatile Marangoni spreading

Area of Science:

• Fluid dynamics
• Interfacial phenomena
• Materials science

Background:

• Understanding liquid film spreading is crucial for various applications.
• Existing models for volatile, miscible liquid spreading do not fully capture observed dynamics.
• Ethanol-water mixtures present complex interfacial behavior due to volatility and miscibility.

Purpose of the Study:

• To investigate the expansion dynamics of a fast-spreading ethanol-water film on a water substrate.
• To develop novel scaling laws for the film's outer tip radius and velocity.
• To elucidate the underlying physical mechanisms governing the film's complex spreading behavior.

Main Methods:

• Experimental observation of ethanol-water film spreading.
• Measurement of the outer tip radius (r_o) and velocity (U_o) over time.
• Theoretical modeling to derive new scaling laws based on film structure.

Main Results:

• Observed outer tip radius (r_o) and velocity (U_o) showed complex scaling, deviating from t^(3/4) and t^(1/4).
• Proposed novel scaling laws by considering stable (r_f ~ t^(1/4)) and unstable (l_p ~ t^(3/4)) film regions.
• Derived a two-term scaling law for r_o, approximating r_o ~ t^(1/2), and validated with experimental data.

Conclusions:

• The novel scaling laws accurately describe the expansion of ethanol-water films.
• The findings provide a more comprehensive understanding of miscible, volatile liquid spreading.
• The proposed model successfully explains the interplay between Marangoni stresses, viscous forces, and plume dynamics.