Wetting in the presence of drying: solutions and coated surfaces

1. 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

2. Many thanks to • E. Rio (Now in Orsay) • G. Berteloot • L. Limat • Daerr • CT Pham (Now in LIMSI) • T. Kajiya (Tolbiac, MSC) • H. Bodiguel • F. Doumenc • B. Guerrier • (FAST, Orsay) • M. Doi (Tokyo) • Tay (PhD) • J. Dupas (PhD) • C. Monteux • T. Narita • E. Verneuil • PPMD/ESPCI • D. Bendejacq • Rhodia • M. Ramaioli • L. Forny • Nestle ANR Depsec

3. Coffee stain Deegan Nature 97

4. Soluble solid (sugar/water) Solvent floating dissolution lumps Coating substrates solution Substrate with coating Evaporation/advancing coupling Dissolving solids Soluble solid

5. Partial dynamical wetting: textbooks • Without drying : Cox Voinov law Macroscopic scale Equilibrium angle Microscopic scale Viscous dissipation diverges at the contact line !! Recipe : take a =1 nm ( no clear answer !!) h : viscosity g : interfacial tension liq/vap V : line velocity q V

6. Drying at the edge of droplets Drying rate is in general controlled by diffusion of water molecules in air x Tip effect : the drying flux diverges in x-a With a=1/2 for small angles q Diffusive drying L= droplet radius Convective drying L~ air boundary layer Thermal effects are negligible for water, As well as Marangoni Flux written in liquid velocity units J0~10-9m3/2.s-1 DH20gaz=2.10-5m2/s CH2Ogaz/sat=25g/m3 rH20liq=106g/m3

7. Colloids

8. Droplet advance En atmosphère contrôlée or windscreen wiper blade Water solution 90 nm diameter Stobber silica Ph = 9 Various concentrations

9. Droplet advance Stable advance, water contact angle Angle versus time  rare defects   chaotic Stick-slip

10. Water and solute Balance in the corner f0 Q h <fc> Q’ U x <fc>= average volume fraction in the corner Water balance Q(1-f0) = Q’(1-<fc>) + J0x1/2 input output drying Concentration diverges at the contact line Solutes balance Q. f0 = Q’.<fc> Hydrodynamics Q = 0.2 U.h Neglecting lateral diffusion Assuming horizontal fast diffusion

11. Criteria for pinning  create a solid a the edge U - <Fc>=64%x= particle diameter d As checked experimentally, the larger the particles, the smaller the critical velocity for stick slip.

12. 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.

13. divergences • Dissipation at contact line • Drying rate at contact line

14. Polymer solutions

15. 10 1 RH = 50% q3-q03 10 0.1 RH = 10% RH = 80% 1 RH = 50% 0.01 0.0001 0.001 0.01 0.1 1 10 100 q3-q03 Vadv (mm/s) 0.1 10 0.01 0.0001 0.001 0.01 0.1 1 10 100 1 RH = 50% q3-q03 Vadv (mm/s) 0.1 0.01 0.0001 0.001 0.01 0.1 1 10 100 Vadv (mm/s) Apparent contact angle/velocity Cox -Voinov Regime ~ no influence of evaporation RH=10% J0 = 5.3 10-9 m3/2/s RH=50% J0 = 2.7 10-9 m3/2/s Polydimethylacrylamide IP=5, Mw=400 000, 1% in water RH=80% J0 = 1 10-9 m3/2/s

16. Scaling of the viscosity with polymer volume fraction ( n=2 in the present case) Volume fraction divergence ( balance estimation as previously) Modelisation 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

17. a a F Fast advance : Voinov law Log x F Non physical regime (<<molecular scale) Viscous Contact line Slow advance : new law Log x

18. 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

19. ??? Wetting on polymer coating

20. Wetting on polymer coating A First experiment water ~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

21. dry Hydrophobic parts hydrated fs The contact angle is very sensitive to the hydration of the polymer Polymer + water U=10-1mm/s dry Monteux et al., Soft Matter, (2009) Haraguchi et al., JCIS (2008) Mackel et al., Langmuir (2007)

22. Dynamic wetting: experiments Water free spreading onto maltodextrin DE29 e = 250 nm – aw = 0.58 Velocity U [mm/s] 103 Pulled substrate Contact line 102 Top view Swollen layer Droplet 101 100 Interferences  color Wrinkles Swollen droplet 10-1 10-2 Contact line Lateral view 10-3 Contact angle q Free spreading 10-4 Measurement of the contact angle and thickness Control of relative humidity

23. Wetting dynamicsData points Water onto maltodextrin DE29 e = 250 nm - aw = 0.58 q = 110° 6 decades of velocity are obtained from a perfect wetting at small U to a hydrophobic surface at large U

24. 100 µm/s fs~40% Top view q=48° f s~20% 10 mm/s q=79°

25. Evaporation and Condensation y Contact Angle q Velocity U Thickness e x Water content Rescaling q(eU) Thin film regime e = 250 nm e = 550 nm e = 1100 nm q increases with e and U

26. Evaporation and Condensation y Contact Angle q Velocity U 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 r = liaquid water density

27. Hydration kinetics a 1 Dvap: vapour diffusion coefficient csat: concentration at saturation c∞ : concentration in the room L: droplet size rliq: density of liquid water U: contact line velocity e0: coating initial thickness slope of activity/solvant volume _____fraction in the polymer (hygroscopy) x Cut-off length x=l Scaling in e0U

28. Evaporation and Condensation y Contact Angle q Velocity U Thickness e x Water content Rescaling q(eU) Thin film regime Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.75 Scaling q(eU) at small eU  q is a function of f in the thin film regime

29. BackgroundTay et al. approach Thin layers 2U Velocity increase Total water received U e f/2 Total water received U e f Total water received Thickness increase 2e f/2 f is a function of eU

30. Rescaling q(eU) Thin film regime y q e x Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.75 SCALING in eU for small eU Breakdown of eU scaling for large eU

31. Wetting at small humidity q(U) curves SUBSTRATE GLASS TRANSITION EFFECT y q e x Maltodextrin DE29 - aw = 0.75 Maltodextrin DE29 - aw = 0.43 aw < ag aw> ag Kinks observed in q(U) curves

32. Wetting at small humidity Correspondence q(U) - f(x) q q q U U U Ug Ug Ug a<ag a<ag a<ag a>ag Drop Drop Drop xg Glass transition at the contact line Contact line is advancing onto a glassy substrate U > Ug Contact line is advancing onto a melt substrate U <Ug At U < Ug, the drop experiences a melt substrate At U>Ug, the drop experiences a glassy substrate

33. 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 Evaporation and condensation y U e x -1 (K depends on the sorption isotherm) Ug varies as expected with the thickness for different solvents

34. And on a viscoelastic hydrophobic gel ? Kajiya et al, Soft Matter 2012

35. 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

36. Many thanks to • E. Rio (Now in Orsay) • G. Berteloot • L. Limat • Daerr • CT Pham (Now in LIMSI) • T. Kajiya • (Tolbiac, MSC) • H. Bodiguel • F. Doumenc • B. Guerrier • (FAST, Orsay) • M. Doi (Tokyo) • Tay (PhD) • J. Dupas (PhD) • C. Monteux • T. Narita • E. Verneuil • PPMD/ESPCI • D. Bendejacq • Rhodia • L. Forny • Nestle ANR Depsec