Analytical solutions for partially wetting two-dimensional droplets

Area of Science:

• Physics
• Surface Science
• Fluid Dynamics

Background:

• Understanding droplet behavior on solid substrates is crucial in fields like microfluidics and materials science.
• Existing models often simplify complex interactions at the contact line, limiting predictive accuracy.

Purpose of the Study:

• To develop a novel analytical solution for the static shape of a 2D droplet in equilibrium with a thin film on a substrate.
• To incorporate capillarity and disjoining-conjoining pressure, accounting for solid-liquid intermolecular forces.
• To analyze the impact of droplet size on apparent contact angle and compare derived profiles with existing approximations.

Main Methods:

• Derivation of analytical solutions for droplet shape, cross-sectional area, half-width, maximum curvature, and inflection points.
• Inclusion of disjoining-conjoining pressure to model intermolecular forces.
• Analysis of droplet size effects on apparent contact angle and comparison with literature approximations.

Main Results:

• New analytical solutions for static droplet shape and related geometric parameters.
• Quantification of the influence of intermolecular forces and thin film pressure on droplet morphology.
• Identification of discrepancies between new solutions and previous approximations in the contact line region.

Conclusions:

• The developed analytical model provides a more accurate description of droplet static shapes under realistic physical conditions.
• The study highlights the importance of considering intermolecular forces and thin film effects for precise droplet profile prediction.
• The findings offer valuable insights for designing and controlling processes involving liquid droplets on solid surfaces.