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