Logical and information aspects in surface science: friction, capillarity, and superhydrophobicity

Abstract

Logical and information aspects of friction and wetting (including the adhesion, capillarity, and superhydrophobicity) are discussed. Friction involves paradoxes, such as the Painlevé paradoxes of non-existence or non-uniqueness of solutions in mechanical systems of rigid bodies with dry friction. These paradoxes can be treated by introducing ternary logic with the three basic states: rest-motion-undefined. When elastic deformation is introduced, the paradoxical solutions correspond to frictional instabilities leading to rest-motion-unstable as three states of a system. The dynamic evolution of a frictional interface towards a limit cycle can be viewed as a process of erasing the information about the interface due to the instabilities. Furthermore, while friction force is universal, it is not treated as a fundamental force and can be considered as an epiphenomenon of various synergetic mechanisms. This further relates friction to other surface effects, including the capillarity, with its binary logic of wetting states and a possibility of droplet computation for lab-on-a-chip microfluidic reactors. We discuss the logical foundation of biomimetic superhydrophobic surface design and how it is different from the conventional design. Both friction and wetting can be used for novel unconventional logical and computational devices.

A setup for frictional Painlevé paradox. Three cases are possible: Rest-Motion-No Unique Solution.

Keywords:

• Friction
• superhydrophobicity
• biomimetic surfaces
• Painlevé paradox
• wetting transitions
• microfluidics
• droplet computers