Dynamical theory of the inverted cheerios effect

Area of Science:

• Soft matter physics
• Fluid dynamics
• Surface science

Background:

• Liquid drops on deformable substrates exhibit complex interactions.
• This phenomenon is analogous to the Cheerios effect but with reversed roles of liquid and solid.
• Understanding these interactions is crucial for various applications involving soft materials.

Purpose of the Study:

• To develop a dynamical theory for the inverted Cheerios effect.
• To investigate the influence of substrate properties (elasticity, capillarity, viscoelasticity) on droplet interactions.
• To compare the developed theory with experimental observations and simplified models.

Main Methods:

• Formulation of a dynamical theory incorporating elasticity, capillarity, and viscoelastic rheology of the substrate.
• Computation of droplet interaction velocities as a function of separation.
• Comparison of the theoretical model with a simplified model treating viscoelastic dissipation as a localized force.

Main Results:

• The developed theory accurately describes the mutual interactions of liquid drops on deformable substrates.
• Droplet attraction or repulsion velocities were computed based on their separation.
• The full theory and the simplified model showed agreement, differing only at small droplet separations.

Conclusions:

• The study presents a robust dynamical theory for the inverted Cheerios effect.
• The theory successfully explains experimental observations of liquid drop interactions on soft substrates.
• The findings provide insights into capillary-mediated interactions in soft matter systems.