Interaction of elastic bodies via surface forces. 2. Exponential decay

Area of Science:

• Continuum mechanics
• Surface physics
• Materials science

Background:

• Interactions between elastic solids are crucial in various physical phenomena.
• Surface forces, particularly those involving thin liquid films, are complex and influenced by material properties.
• Understanding deformation effects is key to accurately modeling these interactions.

Purpose of the Study:

• To theoretically investigate the influence of surface deformation on exponentially decaying interactions between elastic solids.
• To quantify the contribution of elasticity to the total force in such systems.
• To analyze the length scales and dependencies of deformation and elastic forces.

Main Methods:

• Application of continuum elastic theory.
• Development and use of a novel asymptotic technique.
• Calculation of surface deformation and elastic force contributions.

Main Results:

• Surface deformation is significant at the interaction length scale and decays exponentially.
• The elastic contribution to the force also decays exponentially, with half the decay length of the surface interaction.
• Elastic force strength depends on elastic constants, solid size, and the original surface force's magnitude and gradient.
• Elasticity can manifest as attractive or repulsive forces depending on detection methods.

Conclusions:

• Deformation and elasticity play a critical role in the interaction forces between elastic solids separated by liquid films.
• The findings provide a new method for recalculating measured forces to interaction free energy.
• This work enhances the theoretical understanding of surface forces and their elastic contributions.