1. Dynamic drying transition via free-surface cusps
Jens Eggers
Dynamic drying transition via
free-surface cusps
Catherine Kamal
James Sprittles
Jacco Snoeijer

2. Two small Ca-Re problems
silicone drop,
advancing contact angle:
stable
Chen, `88
liquid bath U
receding contact angle:
transition
liquid bath

3. Two fundamental points
There cannot be a “universal”
contact line law that works for
any material
The moving contact line represents
a global, coupled problem: there is
no strictly local description
…but global effects are small for advancing
contact lines at low speeds

4. Wetting transition Delon et al., JFM 2007 above transition
at transition

5. Plunging plate experiment

6. Experiment and simulation
broad agreement
between experiment
and finite element
simulation using simple
slip model
Vandre, Kumar 2014

7. Failure of low-Ca expansion
Ca small
saddle-node bifurcation
GL:
no bifurcation for small M!
Cox:

8. Mechanism for bifurcation (M<<1)
air pressure builds
up here
first solve M=0 problem!

9. Benney+Timson solution
Jacqmin, JFM 2002

10. A solution for arbitrary Ca
free
uniform flow
Stokes:
boundary conditions: !

11. An inner solution (M=0) In analogy with Jeong and Moffatt, JFM 1992 U
Stokeslet R

12. Mechanism for bifurcation (M<<1)
extra contribution to the velocity:
steady shape:
viewed from a distance…
Stokes flow around a loaded crack!

13. Similarity theory
FEM simulation
theory
with gas-liquid slip

14. Conclusions Solution differs qualitatively from prediction of
low-Ca theory
(formally) production of sub-sliplength length scales
wetting behavior obliterated
Eddi, Winkels, Snoeijer, PF “Short time dynamics of viscous drop spreading”
Latka, Boelens, Nagel, de Pablo, PF 2018 “Drop splashing is independent of substrate wetting”