Transcript Wetting in the presence of drying: solutions and coated

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
A. Tay (PhD)
J. Dupas (PhD)
C. Monteux
T. Narita
E. Verneuil
PPMD/ESPCI
D. Bendejacq
Rhodia
M. Ramaioli
L. Forny
Nestle
E. Rio (Now in Orsay)
G. Berteloot
L. Limat
A. Daerr
CT Pham (Now in LIMSI)
T. Kajiya (Tolbiac, MSC)
H. Bodiguel
F. Doumenc
B. Guerrier
(FAST, Orsay)
M. Doi (Tokyo)
ANR Depsec
Coffee stain
Deegan Nature 97
Coating substrates
solution
Substrate with coating
Evaporation/advancing coupling
Dissolving solids
Soluble solid
Soluble solid
(sugar/water)
Solvent
floating
dissolution
lumps
Partial dynamical wetting:
textbooks
•
Without drying : Cox Voinov law
Macroscopic scale
V
L
  9
Log  

a
Equilibrium angle
3
3
eq
 : viscosity
 : interfacial tension liq/vap
V : line velocity

V
Microscopic scale
Viscous dissipation diverges at
the contact line !!
Recipe : take a =1 nm ( no
clear answer !!)
Drying at the edge of droplets
x
Drying rate is in general
controlled by diffusion of
water molecules in air
Tip effect : the drying flux diverges in x-a
With a=1/2 for small angles 
Flux written in liquid velocity units


DHgaz20 CHgaz2O/ sat  CHgaz20/  1/ 2
J ( x) 
x
 J 0 .x 1/ 2
liq
 H 2O
2L
DH20gaz=2.10-5m2/s
CH2Ogaz/sat=25g/m3
Diffusive drying L= droplet radius
Convective drying L~ air boundary layer
Thermal effects are negligible for water,
As well as Marangoni
J0~10-9m3/2.s-1
H20liq=106g/m3
Colloids
Droplet advance
En atmosphère contrôlée
or windscreen wiper blade
Water solution
90 nm diameter Stobber silica
Ph = 9
Various concentrations
Droplet advance
Angle versus time

 chaotic
 rare defects

Stick-slip
Stable advance,
water contact
angle
Water and solute Balance in the corner
f0
h
<fc>
Q
Q’
U
x
<fc>= average volume fraction in the corner
Water balance
Q(1-f0) = Q’(1-<fc>) + J0x1/2
input
output
Solutes balance
drying
Concentration diverges at the contact line
Q. f0 = Q’.<fc>
Hydrodynamics
Q = 0.2 U.h
Neglecting lateral diffusion
Assuming horizontal fast diffusion

J 10 
<  c    0 1  01/ 2 
 Ux  
Criteria for pinning
 create a solid a the
edge
U
- <c>=64% x= particle diameter d
 0 .J 0
10
U stick slip 
 max   0  d 1/ 2
As checked experimentally, the larger the particles,
the smaller the critical velocity for stick slip.
Criteria for stick slip
 stable
 rare defects
 chaotic
 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
Cox -Voinov Regime
~ no influence of evaporation
10
RH = 10%
3-03
1
RH = 50%
0.1
RH = 80%
0.01
0.0001
0.001
0.01
0.1
1
10
100
Vadv (mm/s)
RH=10% J0 = 5.3 10-9 m3/2/s
RH=50% J0 = 2.7 10-9 m3/2/s
RH=80% J0 = 1 10-9 m3/2/s
Polydimethylacrylamide IP=5, Mw=400 000, 1% in water
Modelisation
J0 

   0 1  1 / 2

 x U 
  0
  xxx h  
n
 ( x)V
h2
Volume fraction divergence ( balance
estimation as previously)
Scaling of the viscosity with polymer volume
fraction ( n=2 in the present case)
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

Fast advance : Voinov law
   eq
3
3
 
 ( 0 )V
3
log L
a

Log x
0 J 0
V
a

Non physical regime (<<molecular scale)
Viscous Contact line
Slow advance : new law
Log x
a
0 J 0
V
  0 J 0   ( 0 )

 .
n 1
a

V


n
 n 3   eq n 3
Scaling are OK
At the crossover, the polymer
volume fraction is double at only
5 nm from the 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.
 Divergence of the viscosity at the contact line !!
C. Monteux, Y. Elmaallem, T. Narita and F. Lequeux
EPL, 83 (2008) 34005
Wetting on polymer coating
???
Wetting on polymer coating
A First experiment
~1mm
Halperin et al., J. de physique 1986, 47, 1243-1247
Vue de dessus – temps réel ~5 minutes
e0 = 200 nm
Hydrophilic
polymer
e
In practice the wetting is not very good
dry
U=10-1mm/s
Hydrophobic
parts
hydrated
dry
The contact angle is very sensitive to
the hydration of the polymer
Monteux et al., Soft Matter, (2009)
Haraguchi et al., JCIS (2008)
fs
Polymer + water
Mackel et al., Langmuir (2007)
Dynamic wetting: experiments
Water free spreading onto maltodextrin DE29
e = 250 nm – aw = 0.58
Velocity U
[mm/s]
103
Pulled substrate
102
101
Contact line
Top
view
Swollen
layer
Droplet
100
Swollen droplet
Wrinkles
10-1
Interferences
 color
10-2
10-3
Free spreading
Lateral
view
Contact line
Contact angle 
10-4
Measurement of the contact angle and thickness
Control of relative humidity
Wetting dynamics
Data points
Water onto maltodextrin DE29
e = 250 nm - aw = 0.58
120
Contact Angle  [°]
 = 110°
100
80
60
40
20
0 -4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
Contact line speed U [mm/s]
6 decades of velocity are obtained from a perfect wetting
at small U to a hydrophobic surface at large U
fs ~40%
100 µm/s
Top view
=48°
f s~20%
10 mm/s
=79°
Rescaling (eU)
Evaporation and
Condensation
Thin film regime
y
Contact
Angle 
Velocity U
f x, y 
Thickness e
Water content
x
e = 250 nm
e = 550 nm
e = 1100 nm
 increases with e and U
Evaporation and
Condensation
y
Contact
Angle 
Velocity U
f x, y 
Thickness e
x
Water content
Péclet number = water convection in the polymer film / water diffusion in air
e = film thickness
U = velocity
csat = water in air at saturation
Dv = water diffusion in air
  liaquid water density
Hydration kinetics
a
a
x
Cut-off length x=l
1
Dvap: vapour diffusion coefficient
csat: concentration at saturation
c∞ : concentration in the room
L: droplet size
liq: density of liquid water
U: contact line velocity
e0: coating initial thickness
slope of activity/solvant volume
a
_____fraction in the polymer (hygroscopy)
fs
Scaling in e0U
Rescaling (eU)
Evaporation and
Condensation
Thin film regime
y
Contact
Angle 
Velocity U
f x, y 
Thickness e
x
Water content
Maltodextrin DE29 - aw = 0.75
Maltodextrin DE29 - aw = 0.75
40
30
e=
e=
e=
e=
e=
e=
8 µm
2.7 µm
1.1 µm
550 nm
250 nm
100 nm
Contact Angle  [°]
Contact Angle [°]
40
20
10
0 -3
10
-2
10
-1
10
Contact line speed [mm/s]
0
10
30
e=
e=
e=
e=
e=
e=
8 µm
2.7 µm
1.1 µm
550 nm
250 nm
100 nm
20
10
0
0
10
2
10
Thickness x Velocity [µm²/s]
Scaling (eU) at small eU
  is a function of f in the thin film regime
4
10
Background
Tay et al. approach
Thin layers
2U
U
Velocity
increase
Total water received
e
f/2
Total water received
f
U
e
Total water received
Thickness
increase
f is a function of eU
f/2
2e
Rescaling (eU)
Thin film regime
y

e
Maltodextrin DE29 - aw = 0.75
Maltodextrin DE29 - aw = 0.75
40
e=
e=
e=
e=
e=
e=
8 µm
2.7 µm
1.1 µm
550 nm
250 nm
100 nm
Contact Angle  [°]
Contact Angle [°]
40
30
20
10
0 -3
10
x
-2
10
-1
10
Contact line speed [mm/s]
0
10
30
e=
e=
e=
e=
e=
e=
8 µm
2.7 µm
1.1 µm
550 nm
250 nm
100 nm
20
10
0
0
10
2
10
Thickness x Velocity [µm²/s]
SCALING in eU for small eU
Breakdown of eU scaling for large eU
4
10
Wetting at small humidity
(U) curves
SUBSTRATE GLASS TRANSITION EFFECT
y

e
Maltodextrin DE29 - aw = 0.75
30
e=
e=
e=
e=
e=
e=
8 µm
2.7 µm
1.1 µm
550 nm
250 nm
100 nm
Maltodextrin DE29 - aw = 0.43
40
aw > ag
Contact Angle  [°]
Contact Angle [°]
40
20
10
0 -3
10
-2
10
-1
10
x
0
10
30
e = 3.6 mm
e = 8 µm
e = 2.7 µm
e = 1.1 µm
e = 550 nm
e = 100 nm
aw < ag
20
10
0 -4
10
-3
10
-2
10
-1
10
Contact line speed U [mm/s]
Contact line speed [mm/s]
Kinks observed in (U) curves
0
10
Wetting at small humidity
Correspondence (U) - f(x)



U
Ug
Ug
a < ag
a < ag
U
Ug
a < ag
a > ag
Drop
xg
Contact line is advancing
onto a melt substrate
U < Ug
Drop
Glass transition at the
contact line
Drop
Contact line is advancing
onto a glassy substrate
U > Ug
At U < Ug, the drop experiences a melt substrate
At U>Ug, the drop experiences a glassy substrate
U
Theoretical arguments
Prediction of Ug
The
velocity at the ‘glass transition’ Ug is controled by
the amount of solvant at a cut-off distance from the
contact line
1
y
Evaporation and
condensation
U
f x 
Dv csat
Ug  K
2 e(f g  f0 )
(K depends on the sorption isotherm)
e
x
Experimental Ug [mm/s]
10
Water
DMSO
Ethylene Glycol
1,3 Propanediol
2,3 Butanediol
0
10
-1
10
-2
10
-3
10
-1
-4
10
2
10
3
10
Thickness [nm]
Ug varies as expected with the thickness for different solvents
4
10
And on a viscoelastic hydrophobic gel ?
Kajiya et al, Soft Matter 2012
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
Many thanks to
A. Tay (PhD)
J. Dupas (PhD)
C. Monteux
T. Narita
E. Verneuil
PPMD/ESPCI
D. Bendejacq
Rhodia
L. Forny
Nestle
E. Rio (Now in Orsay)
G. Berteloot
L. Limat
A. Daerr
CT Pham (Now in LIMSI)
T. Kajiya
(Tolbiac, MSC)
H. Bodiguel
F. Doumenc
B. Guerrier
(FAST, Orsay)
M. Doi (Tokyo)
ANR Depsec