# Capillarity and wetting

From Soft-Matter

## 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

- Surface tensions
- Surface curvature
- Capillarity
- Drops, menisci, and lenses
- Floating and pendant drops
- Effects of contact angles
- Flow of thin films
- Dynamics of forced wetting
- Dynamics of total wetting
- Bibliography

## Extended Reading

- 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 <math> \kappa^{-1} </math>, beyond which gravity becomes important." "The distance<math> \kappa^{-1} </math> is generally of the order a few mm." <math> \kappa^{-1} </math> is the capillary length. p. 33
- We can also think of <math> \kappa^{-1} </math> as the screening length, meaning that the perturbation due to an object in contact with a horizontal surface will only extend a distance <math> \kappa^{-1} </math>. The decay will be exponential with characteristic length <math> \kappa^{-1} </math>,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

- Chapter 1. Capillarity; Deformable interfaces
- 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<math>^+</math> and OH<math>^-</math> play the most important role in kinetics of wetting and spreading of aqueous solutions." p. 17