Straight contact lines on a soft, incompressible solid.

Area of Science:

• Soft matter physics
• Surface science
• Materials science

Background:

• Understanding the deformation of soft substrates by liquid interfaces is crucial for various applications.
• Existing models often struggle with the complex interplay between surface tension and elasticity at contact lines.

Purpose of the Study:

• To analytically calculate the deformation of an incompressible soft substrate by a straight contact line.
• To apply these findings to a static rivulet system and analyze substrate distortion.
• To investigate the implications for modeling hysteresis in systems with plastic and elastic properties.

Main Methods:

• Developed a Stokes-like description for substrate elasticity.
• Calculated the ridge profile for a single contact line, incorporating substrate surface tension and shear modulus.
• Utilized the single contact line solution as a Green function to analyze the rivulet geometry.
• Combined Neumann and Young equations to determine substrate slopes.

Main Results:

• The ridge profile near a single contact line shifts by the elastocapillary length, replacing divergence with Neumann equilibrium.
• The substrate slopes in the rivulet case are inversely proportional to substrate surface tensions.
• A method combining Neumann and Young equations was proposed to resolve ambiguities in slope determination.

Conclusions:

• The deformation model provides a more accurate description of soft substrate behavior at contact lines.
• The results have significant implications for understanding and modeling hysteresis in complex materials.
• This work advances the theoretical framework for soft matter--interface interactions.