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Wetting in the presence of drying: solutions and coated surfaces. Basics : Wetting, drying and singularities Wetting with colloidal and polymer suspensions Wetting coated surfaces. Coffee stain Deegan Nature 97. Many thanks to. E. Rio (Now in Orsay) G. Berteloot L. Limat Daerr - PowerPoint PPT Presentation
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Wetting in the presence of drying:solutions and coated surfaces
• Basics : Wetting, drying and singularities
• Wetting with colloidal and polymer suspensions
• Wetting coated surfaces
Coffee stainDeegan Nature 97
E. Rio (Now in Orsay)G. BertelootL. LimatA. DaerrCT Pham (Now in LIMSI)T. Kajiya (Tolbiac, MSC)H. BodiguelF. DoumencB. Guerrier (FAST, Orsay)
M. Doi (Tokyo)
A. Tay (PhD)J. Dupas (PhD)C. MonteuxT. NaritaE. VerneuilPPMD/ESPCI
D. BendejacqRhodia
M. RamaioliL. FornyNestle
ANR Depsec
Many thanks to
Coffee stainDeegan Nature 97
floating
Solvent
dissolution
Soluble solid (sugar/water)
lumps
Substrate with coating
solution
Soluble solid
Evaporation/advancing coupling
Coating substrates
Dissolving solids
Partial dynamical wetting: textbooks
• Without drying : Cox Voinov law
a
LLog
Veq
933
viscosity: interfacial tension liq/vapV : line velocity
Microscopic scale Viscous dissipation diverges at the contact line !!
Recipe : take a =1 nm ( no clear answer !!)
Macroscopic scale
Equilibrium angle
V
Drying at the edge of droplets
Tip effect : the drying flux diverges in x-
With =1/2 for small angles
x
2/10
2/1
2
/20
/220 .
2)(
xJxCC
L
DxJ
liqOH
gazH
satgazOH
gazH
DH20gaz=2.10-5m2/s
CH2Ogaz/sat=25g/m3 H20
liq=106g/m3
Diffusive drying L= droplet radiusConvective drying L~ air boundary layer
Thermal effects are negligible for water,As well as Marangoni
J0~10-9m3/2.s-1
Flux written in liquid velocity units
Drying rate is in general controlled by diffusion of water molecules in air
Colloids
Droplet advance
En atmosphère contrôlée
Water solution90 nm diameter Stobber silica Ph = 9Various concentrations
or windscreen wiper blade
Droplet advance
rare defects
chaotic
Angle versus time
Stick-slip
Stable advance, water contact angle
Water and solute Balance in the corner
Q(1-0) = Q’(1-<c>) + J01/2
input output drying
Solutes balance
Q. 0 = Q’.<c>
Water balance
HydrodynamicsQ = 0.2 U.h
U
Q
Q’
0
c>
h
Neglecting lateral diffusionAssuming horizontal fast diffusion
10
12/1
00 U
Jc
<c>= average volume fraction in the corner
Concentration diverges at the contact line
- <c>= = particle diameter d
Criteria for pinning create a solid a the
edge
U
2/10max
00 10.
d
JU slipstick
As checked experimentally, the larger the particles, the smaller the critical velocity for stick slip.
Criteria for stick slip
stablerare defectschaotic
stick-slip
Model ( no adjustable parameter)
Divergence of the concentration induced by drying !!Rio E., Daerr A., Lequeux F. and Limat L., Langmuir,
22 (2006) 3186.
divergences
• Dissipation at contact line
• Drying rate at contact line
Polymer solutions
Apparent contact angle/velocity
RH=50% J0 = 2.7 10-9 m3/2/s
RH=10% J0 = 5.3 10-9 m3/2/s
RH=80% J0 = 1 10-9 m3/2/s
Cox -Voinov Regime~ no influence of evaporation
0.01
0.1
1
10
0.0001 0.001 0.01 0.1 1 10 100
Vadv (mm/s)
3-
03
RH = 50%
0.01
0.1
1
10
0.0001 0.001 0.01 0.1 1 10 100
Vadv (mm/s)
3-
03
RH = 10%
RH = 50%
0.01
0.1
1
10
0.0001 0.001 0.01 0.1 1 10 100
Vadv (mm/s)
3-
03
RH = 80%
RH = 50%
Polydimethylacrylamide IP=5, Mw=400 000, 1% in water
Modelisation
n 0Scaling of the viscosity with polymer volume
fraction ( n=2 in the present case)
U
J
x 0
2/10 1Volume fraction divergence ( balance estimation as previously)
2
)(
h
Vxhxxx
Hydrodynamical equation
Solved analyticaly using some approximations
Ansatz for the solution in G. Berteloot, C.-T. Pham, A. Daerr, F. Lequeux and L. Limat
EPL, 83 (2008) 14003
Log x
a
a
Log x
V
J00
V
J00
Fast advance : Voinov law
100033 )(
.
n
nn
eqn
Va
J
aLV
eq log)(
3 033
Non physical regime (<<molecular scale)
Slow advance : new law
Viscous Contact line
Accumulating polymer over a few nanometer is enough to slow down the contact line advance !Remember that the dissipation diverges at the contact line.
Scaling are OK
At the crossover, the polymer volume fraction is double at only
5 nm from the contact line.
C. Monteux, Y. Elmaallem, T. Narita and F. LequeuxEPL, 83 (2008) 34005
Divergence of the viscosity at the contact line !!
Wetting on polymer coating
???
A First experiment
e0 = 200 nm
~1mm
water
Halperin et al., J. de physique 1986, 47, 1243-1247
Hydrophilicpolymer
In practice the wetting is not very good
e
Vue de dessus – temps réel ~5 minutes
Wetting on polymer coating
Monteux et al., Soft Matter, (2009)
The contact angle is very sensitive tothe hydration of the polymer
s
hydrated
Hydrophobicparts
dry
Polymer + water
Mackel et al., Langmuir (2007)Haraguchi et al., JCIS (2008)
U=10-1mm/s
dry
Dynamic wetting: experiments
Top view
Pulled substrate
Swollen droplet
Free spreading
Velocity U [mm/s]
103
102
101
100
10-1
10-2
10-3
10-4
Lateral view
Measurement of the contact angle and thicknessControl of relative humidity
Contact line
Contact angle
Droplet
Wrinkles
Swollen layer
Contact line
Interferences color
Water free spreading onto maltodextrin DE29 e = 250 nm – aw = 0.58
Contact line speed U [mm/s]
Con
tact
Ang
le
[°]
10-4
10-3
10-2
10-1
100
101
102
103
1040
20
40
60
80
100
120
6 decades of velocity are obtained from a perfect wetting at small U to a hydrophobic surface at large U
= 110°
Wetting dynamicsData points
Water onto maltodextrin DE29 e = 250 nm - aw = 0.58
10 mm/ss~20%
100 µm/ss~40%
=48°
=79°
Top view
increases with e and U
Rescaling (eU)Thin film regime
e = 250 nm
e = 550 nm
e = 1100 nm
y
Evaporation and Condensation
Thickness ex
Velocity UContact Angle
yx,Water content
y
Evaporation and Condensation
Thickness ex
Velocity UContact Angle
yx,Water content
e = film thicknessU = velocitycsat = water in air at saturationDv = water diffusion in airliaquid water density
Péclet number = water convection in the polymer film / water diffusion in air
Scaling in e0U
a1
a
s
a
Cut-off length x=l
Hydration kinetics
x
Dvap: vapour diffusion coefficientcsat: concentration at saturationc∞ : concentration in the roomL: droplet sizeliq: density of liquid waterU: contact line velocitye0: coating initial thickness slope of activity/solvant volume _____fraction in the polymer (hygroscopy)
Thickness x Velocity [µm²/s]C
onta
ct A
ngle
[
°]
100
102
1040
10
20
30
40e = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 250 nme = 100 nm
Scaling (eU) at small eU is a function of in the thin film regime
Rescaling (eU)Thin film regime
Contact line speed [mm/s]
Con
tact
Ang
le [
°]
10-3
10-2
10-1
1000
10
20
30
40e = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 250 nme = 100 nm
Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.75
y
Evaporation and Condensation
Thickness ex
Velocity UContact Angle
yx,Water content
Thin layers
e
Total water received
2U
e/2
Total water received
U
2e/2
Total water received
Velocity increase
is a function of eU
BackgroundTay et al. approach
Thickness increase
U
Thickness x Velocity [µm²/s]C
onta
ct A
ngle
[
°]
100
102
1040
10
20
30
40e = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 250 nme = 100 nm
SCALING in eU for small eUBreakdown of eU scaling for large eU
Rescaling (eU)Thin film regime
y
ex
Contact line speed [mm/s]
Con
tact
Ang
le [
°]
10-3
10-2
10-1
1000
10
20
30
40e = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 250 nme = 100 nm
Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.75
Contact line speed U [mm/s]C
onta
ct A
ngle
[
°]
10-4
10-3
10-2
10-1
1000
10
20
30
40e = 3.6 mme = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 100 nm
Kinks observed in (U) curves
Wetting at small humidity(U) curves
y
ex
Contact line speed [mm/s]
Con
tact
Ang
le [
°]
10-3
10-2
10-1
1000
10
20
30
40e = 8 µme = 2.7 µme = 1.1 µme = 550 nme = 250 nme = 100 nm
aw < agaw > ag
Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.43
SUBSTRATE GLASS TRANSITION EFFECT
Contact line is advancing onto a melt substrate
U < Ug
a < ag
a > ag
UUg
xgDrop
Wetting at small humidityCorrespondence (U) - (x)
At U < Ug, the drop experiences a melt substrateAt U>Ug, the drop experiences a glassy substrate
UUg
Glass transition at the contact line
a < ag
Drop
UUg
Contact line is advancing onto a glassy substrate
U > Ug
a < ag
Drop
Theoretical argumentsPrediction of Ug
)(2 0
gsatv
g e
cDKU
y
x
Evaporation and condensation
ex
U
Ug varies as expected with the thickness for different solvents
Thickness [nm]
Exp
erim
enta
l Ug [m
m/s
]
102
103
10410
-4
10-3
10-2
10-1
100
101
WaterDMSOEthylene Glycol1,3 Propanediol2,3 Butanediol
-1
(K depends on the sorption isotherm)
The velocity at the ‘glass transition’ Ug is controled by the amount of solvant at a cut-off distance from the contact line
Kajiya et al, Soft Matter 2012
And on a viscoelastic hydrophobic gel ?
Complex wetting :
One observes only the macroscopic behavior :( it is very difficult to measure something at 1 mm/s at the scale of 10 nm !!)
Many singularities at the contact line viscous dissipation, viscosity, water exchange
This makes the problem simple : physics is driven by the dominant term at small distance (cut-offs).
Very similar to fracture
E. Rio (Now in Orsay)G. BertelootL. LimatA. DaerrCT Pham (Now in LIMSI)T. Kajiya(Tolbiac, MSC)H. BodiguelF. DoumencB. Guerrier (FAST, Orsay)
M. Doi (Tokyo)
A. Tay (PhD)J. Dupas (PhD)C. MonteuxT. NaritaE. VerneuilPPMD/ESPCI
D. BendejacqRhodiaL. FornyNestle
ANR Depsec
Many thanks to