jens eggers
DESCRIPTION
Jens Eggers. Hydrodynamic theory of coating . …with Bruno Andreotti, Marc Fermigier, Jacco Snoeijer, Johanna Ziegler. Dynamical wetting transition. continuous transition. discontinuous transition. Deraguin+Levi 1964. de Gennes 1986. apparent contact angle at the transition?. - PowerPoint PPT PresentationTRANSCRIPT
Jens Eggers
Hydrodynamic theory of coating
…with Bruno Andreotti, Marc Fermigier, Jacco Snoeijer, Johanna Ziegler
Dynamical wetting transition
crU
2 cL
Deraguin+Levi 1964
crU
2 cL
continuous transition discontinuous transition
de Gennes 1986
apparent contact angle at the transition?
Small scale physics
moving contact lineHuh and Scriven’s paradox: no motion for 0!micro
stationary
Uh
23 ln( / )micro
L
diss microdzU Lh
Lubrication equations
liquid bath
gh(x)
x
y
plate
/slip e /plate e viscous s.t. gravity
(0) 0, (0) 1, ( )h h h
cin units of /( ) :g 33 /( )eCa U
( ,0) slipuu x Uy
eqnm
(0) eqh
2 3Ca h h
h h
note additional parameter
outer meniscus
( ) ( ) xout apph x e
Matching: Pull!
U<Uc
liquid bath
gmatch!
U>Uc
liquid bath
g
no overlap!
inh outh
compare
0
curvature
matching impossible!
: microscopic length
2
33in
in in
Cahh h
1(3 )( ) 3in advh x H x
ap
Critical speed
0
curvatureouth
app
1/ 3
2/3 1/(3 )1
1/3 21 1
2 ( )( ) 3 2 ( )
CaAi s eCa Ai s Ai s
1solve for !s
2/3 1/31
1
2 ( )( )ap
Ca Ai sAi s
Ca
crCa
inh
1/3 1/(3 )
1/3 212 ( )
CaCa eAi s
1/3 1/(3 )
1/3 2max2 ( )
Ca
crCa eAi s
1/3 1/(3 )
1/32 0.287
Ca
crCa e
1
1/3 2max
1 ln3 54 ( )
crcr
CaCa
Ai s
“Cox-Voinov”
3 2( 1)1 3 ln3ap Ca
matching condition
Wetting transition
Delon et al., JFM 2007
transient experiment:
pl crU U
0app at transition
•Derjaguin+Levi 1964:
2cl
c
x
Ca
0.3plate eq
410
simtheory
Beyond the transition
h
x
before
contact line
apparentcontact line
h
x
after
Another transition
Ca
plate angle
Ziegler et al.,EPJ `09
Wetting transition
Delon et al., JFM 2007
*Ca Ca0q
new film solution!
The Landau Levich Derjaguin film
fhCa
2
31 1 qh
Cah
I: bath
2
2
3 1 QHH H
LL-equation
II
2/31/3Ca
Caxh H
2/3q QCa
2/30.95f Cah
2H ( ) 0H
The dimple!
fhCa
I: bath
2 II
2/31/3Ca
Caxh H
2/3q QCa
2H ( ) 0H III
1/ 21/ 6
xh Ca HCa
balance
includes
gravity!
2
31 1 qh
Cah
A range of new solutions
2/31/3Ca
Caxh H
2/3q QCa
2H
( ) 0H
0Q
2
3 1 QHH H
max 1.376Q Q
Phase diagram
Ca
fh0Q
max 1.376Q Q
2
31 1 qh
Cah
1/ 2 2 /332fQCh a Ca
new thick filmsolutions!
2/30.95f Cah partial wettingcomplete wetting
Experiment:
The film profile
fh
Snoeijer et al., PRL `08bath
39.3 10Ca 38.1 10Ca
new thickfilm
theory
LLDfilm
theory
the dimple!
The big picture
log( )Ca1
log( )fh
2/3
1/2
so far!
1/2
sinfp
Cah
Derjaguin
A fun movie made in Bristol
…work withPhilippe Brunet,Robert Deegan
Bristol Evening Post