Superhydrophobic surfaces. José Bico PMMH-ESPCI, Paris

Transcription

1 Superhydrophobic surfaces José Bico PMMH-ESPCI, Paris

2 Superhydrophobic surfaces José Bico PMMH-ESPCI, Paris?

3 Rain droplet on a window film pinning tear 180? mercury calefaction Leidenfrost point, T = 150 C Anne-Laure Biance Christophe Clanet, David Quéré

4 "Lotus" effect Setcreasea Ginkgo Biloba Natural water-repellent surfaces: some plant leaves insect wings water spiders silk nests

5 Impacts

6 Ingredients for super-hydrophobicity Chemical hydrophobicity 20 µm Lotus leaf Barthlott & Neinhuis (1997) + Taylored surface 200 µm hydrophobic wax Onda et al. (1996) 10 µm 1 µm textured surfaces with C.Marzolin & D.Quéré recent insights: Mathilde Reyssat

7 hysteresis heterogeneities? θ a θ r flat rough wax surface initially rough, then progressively heated up to smooth it down by partial melting Dettre & Johnson (1964)

8 Mechanism: fakir carpet air air trapped under the liquid

9 Macroscopic contact angle θ * γ LV φ S = top of asperities apparent area γ * SL γ * SV "effective solid" = φ S solid + (1-φ S ) air γ SV * = φ S γ SV + (1-φ S ) γ VV γ SL * = φ S γ SL + (1-φ S ) γ LV cosθ * * * γ LV = γ SV - γ SL cosθ * = -1 + φ S (1 + cosθ ) cosθ = γ SV - γ SL γ LV Cassie & Baxter (1944) angle on a flat surface of the same material

10 Slippery surfaces u classical experimental facts: u s = 0 λ u s Navier's concept of possible slip (1823): u u s = λ z surf λ : slip length recent experiments and molecular dynamics simulations - on smooth hydrophobic surfaces: λ ~ nm - on textured super-hydrophobic surfaces: λ ~ texture size (µm) review J.Rothstein (2009)

11 Drag reduction? ex: Poiseuille flow between 2 plates λ P u h λ P = 12η u h2 h h + 6λ h 2 P 12η u λ / h

12 Slip length on textured surfaces <u> u s = <u> L u s = 0 b dilute pillars: <σ > ~ φ S η <u> ~ η <u> b λ eff low Reynolds numbers Stokes flow (laplacian) scale ~ b λ eff ~ b φ S ~ L φ S Ybert & al. (2007) see also Lauga & al.

13 Slip length on textured surfaces cone-plate rheometer λeff λeff 1 - φs L Lee & al. (2008) also PIV measurements e.g. P.Tsai & al. (2009)

14 "Fat fakir"? ΔP b dh dv = A (1-φ S ) dh φ ds = 2 A S dh (pillars surface) b ΔP dv = (γ SL -γ SV ) ds = γ cosθ ds ΔP crit = 2γ b φ S 1-φ S

15 From big to skinny fakirs 100 µm Mathilde Reyssat et al. (2008)

16 R crit Critical radius

17 2 scenarios Critical pressure R crit b 2γ = ΔPcrit? R crit 1-φ R crit = b S φs usually too small Touch down R crit R interface = R macroscopic R crit L h R crit ~ L 2 h Reyssat et al. (2008)

18 A metastable state?? roughness factor: r = actual area apparent area ΔE S = (r - φ s ) (γ SL - γ SV ) - (1- φ s ) γ LV ΔE S < 0 if θ < θ c, cosθ c = φ s r - φ s with U.Thiele & D.Quéré

19 Wenzel regime θ * liquid inside the roughness actual surface amplified "effective solid" = r solid γ SV * = r γ SV γ SL * = r γ SL cosθ * = r cosθ Wenzel (1949)

20 Super-hydrophilic surfaces? Nanotubes forests with K.Teo, K.Lau, M.Chhowalla, G.A.G. Amaretunga, W.I. Milne, G.McKinley & K.Gleason imbibition dynamics Mathilde & Étienne Reyssat

21 Condition for imbibition dz top dry dz φ S = r = top of asperities apparent area real area apparent area L de S /L = (r - φ S ) (γ SL - γ SV ) dz + (1 - φ S ) γ LV dz top dry γ SL cosθ imbibition if de S < 0 θ < θ c cosθ c = 1 - φ S r - φ S r porous media: rise if θ < 90º r 1 flat surface: rise if θ = 0

22 Contact angle on an imbibed surface θ * "effective solid" = φ S solid + (1-φ S ) liquid γ SV * = φ S γ SV + (1-φ S ) γ LV γ SL * = φ S γ SL + (1-φ S ) γ LL cosθ * = 1 - φ S (1 - cosθ )

23 From anti-rain to anti-fog materials 1 - φ S cosθ * r anti-fogging θ * φ S r - φ S 1 - φ S r - φ S 1 cosθ anti-rain θ * π stable métastable -1 + φ S

24 Coated droplets hydrophobic particles, θ > 90º (if θ < 90º, particles immersed in the liquid) Adhesion of the particles? ΔE S /S = γ SV + γ LV - γ SL = γ LV ( 1 + cosθ ) > 0 always some adhesion

25 Liquid marbles shape: centrifuge forces / surface tension Ω << 1 sphere Ω ~ 1 peanut, doughnut Ω >> 1 breakup Pascale Aussillous

26

27 A well defined contact angle? θ? Young's relation: D.Quéré, C. Clanet, M. Fermigier

28 Contact angle hysteresis θ a θ r D.Quéré, C. Clanet, M. Fermigier hysteresis "clean" surface: θ a - θ r ~ 5º

29 Droplet sticking on a window θ r θ a stuck

30 Index in a straw balance for: θ r L θ a moves if: R

31 heterogeneities on surfaces: chemistry 1 2 Origin of hysteresis θ a = θ 1 θ θ 2 2 θ r = θ 1 geometry θ α α θ α θ θ a = θ + α θ a = θ - α