Hydrodynamics of wetting phenomena. Jacco Snoeijer PHYSICS OF FLUIDS
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1 Hydrodynamics of wetting phenomena Jacco Snoeijer PHYSICS OF FLUIDS
2 Outline 1. Creeping flow: hydrodynamics at low Reynolds numbers (2 hrs) 2. Thin films and lubrication flows (3 hrs + problem session 1.5 hrs) A. Bubble entrapment, instabilities, coalescence B. Landau-Levich films C. Problem session (from classic and recent papers) 3. Static and moving contact lines (3 hrs) hidden theme: 4. Wetting on soft substrates (depending on time) scaling & similarity solutions
3 Influence of air pressure on impact event 1 atm 0.2 atm Xu, Zhang, Nagel, PRL (2005)
4 Earlier indications on role of air: Air bubble entrapment Van Dam, Le Clerc, Phys. Fluids (2004)
5 Sketch of impacting drop falling droplet pressure buildup! Dimple-formation!
6 Thin film interference Oil films Use the information coded in the color! Soap bubbles Applications in e.g. anti-reflective coatings
7
8 Maximum air bubble Bouwhuis et al, Phys. Rev. Lett. (2012)
9 Bubbles: a major nuisance Immersion Lithography
10 Bubbles: a major nuisance before after Keij, Winkels, Casteleijns, Riepen & Snoeijer, submitted to Phys. Fluids
11 Lubrication for capillary flows nonlinear PDE for h(x,t) h t + 1 3η x [h 3 { γ 3 h x 3 Φ x }] =0 gravity: van der Waals: Φ = ρgh Φ = A 12πh 2
12 merging of steps polysterene films ( nm) McGraw, Salez, Baumchen, Raphael, Dalnoki-Veress, Phys. Rev. Lett. 2012
13 merging of steps polysterene films McGraw, Salez, Baumchen, Raphael, Dalnoki-Veress, Phys. Rev. Lett. 2012
14 capillary flows: intermediate conclusion - lubrication theory: extremely useful - similarity solutions can often be used - next: coalescence phenomena
15 capillary flows: intermediate conclusion - lubrication theory: extremely useful - similarity solutions can often be used - next: coalescence phenomena
16 coalescence R reduction capillary energy E γr 2 surface tension
17 coalescence spherical water drops (timescale ~ millisecond) r(t) Aarts et al. Phys. Rev. Lett. 2005
18 w r
19 w = r2 R w r
20 p γ w γr r 2 w = r2 R w r
21 surface tension vs inertia p γr r 2 p ρ ( dr dt ) 2 w r(t) r(t) t 1/2 Eggers, Lister & Stone, J. Fluid Mech Duchemin, Josserand & Eggers, J. Fluid Mech. 2003
22 2 regimes r ~ t 1/2 inertial r ~ t viscous Paulsen, Burton & Nagel, Phys. Rev. Lett Paulsen et al, PNAS 2012
23
24 sessile drops
25 sessile drops complications: geometry solid wall: no slip moving contact line!
26 sessile drops very viscous silicone oil r(t) experimentally: r(t) ~ t 1/2 Ristenpart, McCalla, Roy & Stone, Phys. Rev. Lett 2006 Narhe, Beysens & Pomeau, Europhys. Lett. 2008
27 coalescence of drops on substrate silicone oil (12.500x water) 100 µm 1D lubrication model
28 mechanism silicone oil (12.500x water) low capillary pressure: p ~ - γ/h flux: Q ~ - dp/dx liquid flux Q
29 mechanism silicone oil (12.500x water) low capillary pressure: p ~ - γ/h flux: Q ~ - dp/dx liquid flux Q mass conservation: h t + Q x =0
30 bridge growth silicone oil (12.500x water) h0 coalescence dynamics: h0(t)?
31 bridge growth h0 ~ t
32 bridge shape silicone oil (12.500x water) x h(x,t) shape of bridge: h(x,t)?
33 self-similarity! h/h0 x θ/h0
34 bridge shape silicone oil (12.500x water) shape of bridge: h(x,t)?
35 self-similarity! h/h0 x θ/h0 Problem session: Hernandez-Sanchez, Lubbers, Eddi & Snoeijer Phys. Rev. Lett. 2012
36 lubrication theory h t + Q x =0 h t + γ 3η x ( h 3 3 h x 3 ) =0
37 back to topview... r ~ t 1/2?
38 geometry T =0 = = T = T = w ~ h ~ t H X w ~ r 2 /R Ristenpart, McCalla, Roy & Stone, Phys. Rev. Lett 2006 Narhe, Beysens & Pomeau, Europhys. Lett r ~ t 1/2!
39 water drops on substrate (inertial) - exponent 1/2? - self-similarity? Anonin Eddi, Koen Winkels & JHS, submitted
40 water drops Photron SA1.1 Synchronization and computer 10X Lens Photron APX-RS
41 water drops - side view frames/second
42 self-similar! 9 Rescaled profiles for frames 7,15,25,40,70 h/h Y/h b X/h b x/h0
43 self-similar! h/h0 2D Potential flow: Billigham & King, JFM 2005 x/h0
44 exponent: 2/3 2/3
45 exponent: 2/3 Keller and Miksis (1983) P iner ρv 2 v h 0 t P cap γ w w = h 0 tan θ h 0 ( γ tan θ ρ ) 1/3t 2/3
46 exponent: 2/3 h 0 = D 0 ( γ tan θ ρ ) 1/3t 2/3 2/3 D 0 =0.89
47 capillary flows - lubrication theory: extremely useful - similarity solutions can often be used - coalescence phenomena (show movie Marangoni)
48 Outline 1. Creeping flow: hydrodynamics at low Reynolds numbers (2 hrs) 2. Thin films and lubrication flows (3 hrs + problem session 1.5 hrs) A. Bubble entrapment, instabilities, coalescence B. Landau-Levich films C. Problem session (from classic and recent papers) 3. Static and moving contact lines (3 hrs) 4. Wetting on soft substrates (depending on time)
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Hydrodynamics of wetting phenomena. Jacco Snoeijer PHYSICS OF FLUIDS
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