1. Hydrodynamic theory of coating
Jens Eggers
Hydrodynamic theory of coating
…with Bruno Andreotti, Marc Fermigier,
Jacco Snoeijer, Johanna Ziegler

2. Dynamical wetting transition
continuous transition
discontinuous transition
Deraguin+Levi 1964
de Gennes 1986
apparent contact angle at the transition?

3. U Small scale physics stationary Huh and Scriven’s paradox:
moving contact line
stationary U h

4. Lubrication equationsy nm
h(x) g
liquid bath
note additional parameter x
gravity
viscous
s.t.

5. Matching: Pull! matching impossible! U>Uc liquid bath g no overlap!
compare
curvature
: microscopic length l
U>Uc
liquid bath g
no overlap!
match!
U<Uc
liquid bath g
matching impossible!
outer meniscus

6. Critical speed
matching condition
“Cox-Voinov”
curvature

7. Wetting transition Delon et al., JFM 2007 Derjaguin+Levi 1964:
at transition
Derjaguin+Levi 1964:
transient experiment:

8. Beyond the transition h x after before h apparent contact line x sim
theory
contact line

9. Another transition
plate angle
Ziegler et al.,
EPJ `09

10. Wetting transition
new film solution!
Delon et al., JFM 2007

11. The Landau Levich Derjaguin filmII
LL-equation
I: bath

12. The dimple! II
III
balance
includes
gravity!
I: bath

13. A range of new solutions

14. Phase diagram new thick film solutions! Experiment: complete wetting
partial wetting

15. The film profile the dimple! new thick film theory LLD film theory
bath
Snoeijer et al., PRL `08

16. The big picture
1/2
Derjaguin
1/2
2/3
so far! 1

17. A fun movie made in Bristol
Bristol Evening Post
…work with
Philippe Brunet,
Robert Deegan