# Capillarity and wetting

## Introduction

"As I glance out my window in the early morning, I can see beads of droplets gracing a spider web...I take my morning shower. The moment I step out, I dry off by way of evaporation and dewetting... As I rush into my car under a pelting rain, my attention is caught by small drops stuck on my windshield... The traffic light suddently turns red. I slam on the breaks and the car skis before finally coming to a halt..Foams are desirable in a shamppoo but can be a nuisance in a dishwasher...A child tosses a stone into a lake. (She) delights in watching capillary waves..." P.-G. de Gennes; F. Brochard-Wyart; D. Quéré in Capillarity and wetting phenomena; Springer: New York; 2004. (Who else could they possibly be?)

## Topics

• de Gennes (2004)
• Chapter 1. Capillarity; Deformable interfaces
• "A liquid surface can be thought of as a stretched membrane characterized by a surface tension that opposes it's distortion." p. 1
• Surface tension can be thought of as the energy necessary to increase the area of a liquid, or the force that a surface can exert. p. 4,5
• "Surface tension is at the origin of the overpressure existing in the interior of drops and bubbles." p. 6
• If there is no pressure difference between either side of a curved surface, then the surface will have zero curvature. p.13
• "High-energy surfaces are those for which the chemical binding energy is of order 1 eV, on which nearly any liquid spreads. High energy surfaces are made of materials that are ionic, covalent, or metallic." p. 18
• "Low-energy surfaces, for which the chemical binding energy is of the order of kT, are generally hardly wettable. They include molecular crystals and plastics." p. 18
• "A liquid spreads completely if it is less polarizable than the solid." p. 20
• "Practically no liquid spreads on a fluorinated surface." p. 23
• Chapter 2. Capillarity and gravity.
• "There exists a particular length, denoted $\kappa^{-1}$, beyond which gravity becomes important." "The distance$\kappa^{-1}$ is generally of the order a few mm." $\kappa^{-1}$ is the capillary length. p. 33
• We can also think of $\kappa^{-1}$ as the screening length, meaning that the perturbation due to an object in contact with a horizontal surface will only extend a distance $\kappa^{-1}$. The decay will be exponential with characteristic length $\kappa^{-1}$,except very close to the object. p. 34,35
• "Capillarity will never be able to generate a jet. In order for a liquid to come gushing out of a tube, it would have to be in a state of overpressure, which would produce an inverted meniscus. But such a scenario would be incompatible with a rising liquid (which, as we know, implies an underpressure to balance the hydrostatic pressure)." p. 53
• Chapter 6. Dynamics of the triple line.
• Concerning the dynamics of total wetting, "It turns out there ahead of the drop is a precursor film a few nanometers thick, which extends much farther out than the drop itself." p. 149
• Krotov; Chapter 7. Some simplest problems of hydrodynamics of capillary systems.
• Starov ; Chapter 1. Surface forces and the equilibrium of liquids on solids.
• "Note that the two ions H$^+$ and OH$^-$ play the most important role in kinetics of wetting and spreading of aqueous solutions." p. 17