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

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) A.Tay (PhD) J. Dupas (PhD) C. Monteux T. Narita E. Verneuil PPMD/ESPCI D. Bendejacq Rhodia M. Ramaioli L. Forny Nestle ANR Depsec Many thanks to

Coffee stain Deegan 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  viscosity  : interfacial tension liq/vap V : 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 D H20 gaz = m 2 /s C H2O gaz/sat =25g/m 3  H20 liq =10 6 g/m 3 Diffusive drying L= droplet radius Convective drying L~ air boundary layer Thermal effects are negligible for water, As well as Marangoni J 0 ~ m 3/2.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 solution 90 nm diameter Stobber silica Ph = 9 Various 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- ) + J 0  1/2 inputoutputdrying Solutes balance Q.  0 = Q’. Water balance Hydrodynamics Q = 0.2 U.h U  Q Q’ 00  c > h Neglecting lateral diffusion Assuming horizontal fast diffusion = average volume fraction in the corner Concentration diverges at the contact line

- =   = particle diameter d Criteria for pinning  create a solid a the edge U 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 RH=50% J 0 = m 3/2 /s RH=10% J 0 = m 3/2 /s RH=80% J 0 = m 3/2 /s Cox -Voinov Regime ~ no influence of evaporation V adv (mm/s) 3-033-03 RH = 50% V adv (mm/s) 3-033-03 RH = 10% RH = 50% V adv (mm/s) 3-033-03 RH = 80% RH = 50% Polydimethylacrylamide IP=5, Mw= , 1% in water

Modelisation Scaling of the viscosity with polymer volume fraction ( n=2 in the present case) Volume fraction divergence ( balance estimation as previously) 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 aa  Fast advance : Voinov law 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. Lequeux EPL, 83 (2008)  Divergence of the viscosity at the contact line !!

Wetting on polymer coating ???

A First experiment e 0 = 200 nm ~1mm water Halperin et al., J. de physique 1986, 47, Hydrophilic polymer 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 to the hydration of the polymer ss hydrated Hydrophobic parts dry Polymer + water Mackel et al., Langmuir (2007)Haraguchi et al., JCIS (2008) U=10 -1 mm/s dry

Dynamic wetting: experiments Top view Pulled substrate Swollen droplet Free spreading Velocity U [mm/s] Lateral view Measurement of the contact angle and thickness Control of relative humidity Contact line Contact angle  Droplet Wrinkles Swollen layer Contact line Interferences  color Water free spreading onto maltodextrin DE29 e = 250 nm – a w = 0.58

6 decades of velocity are obtained from a perfect wetting at small U to a hydrophobic surface at large U  = 110° Wetting dynamics Data points Water onto maltodextrin DE29 e = 250 nm - a w = 0.58

10 mm/s  s ~20% 100 µm/s  s  ~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 e x Velocity U Contact Angle  Water content

y Evaporation and Condensation Thickness e x Velocity U Contact Angle  Water content e = film thickness U = velocity c sat = water in air at saturation D v = water diffusion in air  liaquid water density Péclet number = water convection in the polymer film / water diffusion in air

Scaling in e 0 U a 1 Cut-off length x=l Hydration kinetics x D vap : vapour diffusion coefficient c sat : concentration at saturation c ∞ : concentration in the room L: droplet size  liq : density of liquid water U: contact line velocity e 0 : coating initial thickness slope of activity/solvant volume _____fraction in the polymer (hygroscopy)

Scaling  (eU) at small eU   is a function of  in the thin film regime Rescaling  (eU) Thin film regime Maltodextrin DE29 - a w = 0.75 y Evaporation and Condensation Thickness e x Velocity U Contact Angle  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 Background Tay et al. approach Thickness increase U

SCALING in eU for small eU Breakdown of eU scaling for large eU Rescaling  (eU) Thin film regime y e x  Maltodextrin DE29 - a w = 0.75

Kinks observed in  (U) curves Wetting at small humidity  (U) curves y e x  a w < a g a w > a g Maltodextrin DE29 - a w = 0.75 Maltodextrin DE29 - a w = 0.43 SUBSTRATE GLASS TRANSITION EFFECT

Contact line is advancing onto a melt substrate U < U g a < aga < ag a > aga > ag  U UgUg xgxg Drop Wetting at small humidity Correspondence  (U) -  (x) At U < U g, the drop experiences a melt substrate At U>U g, the drop experiences a glassy substrate  U UgUg Glass transition at the contact line a < aga < ag Drop  U UgUg Contact line is advancing onto a glassy substrate U > U g a < aga < ag Drop

Theoretical arguments Prediction of U g y Evaporation and condensation e x U U g varies as expected with the thickness for different solvents (K depends on the sorption isotherm) The velocity at the ‘glass transition’ U g 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. 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) A.Tay (PhD) J. Dupas (PhD) C. Monteux T. Narita E. Verneuil PPMD/ESPCI D. Bendejacq Rhodia L. Forny Nestle ANR Depsec Many thanks to