1. Introduction of Micro- /Nano-fluidic Flow Surface Tension 6/1/2015 1 J. L. Lin Assistant Professor Department of Mechanical and Automation Engineering

2. Outline 6/1/2015 2 Surface tension concept and origin Surface tension induced pressure, Laplace law, minimal surfaces, meniscus on a fiber Influence of gravity, capillary length, capillary rise Contact angle, Young’s law Spreading parameter Zismann equation Contact angle measurements, contact angle hysteresis Surface roughness, Wenzel and Cassie-Baxter equations Superhydrophobic surfaces Electrowetting, electrically tunable surfaces

3. Surface tension

4. Liquid Jet 4

5. jet speed 10 km/s

6. Liquid Jet 6 case explosiveliner

7. Liquid Jet

8. Surface tension U U/2 a l  dx

9. Surface tension Liquid T [°C]  [mN/m] Acetone 20 23.7 Diethyl ether 20 17.0 Ethanol 20 22.27 Glycerol 20 63 n-Hexane 20 18.4 Isopropanol 20 21.7 Mercury 15 487 Methanol 20 22.6 n-Octane 20 21.8 Water 0 75.64 Water 25 71.97 Water 50 67.91 Water 100 58.85

10. Laplace Equation Δp for water drops of different radii Droplet radius 1 mm 0.1 mm 1 μm 10 nm Δp (atm) 0.0014 0.0144 1.436 143.61

11. Zero curvature surface z  x b 

12. Capillary length, capillary rise h 2R2R 

13. Contact angle solid liquid 

14. Youngs' Equation Contact angle  is determined by the interfacial tensions  : solid liquid  dxdx  SL  SV  LV  Equilibrium

15. Spreading parameter - total wetting - partial wetting

16. Zismann equation cc cos   1 - const (  -  c ) (Fox & Zismann (1950))

17. Contact angle measurements Camera 1 (control) Camera 2 (measurement) Sample Experimental setup deposition system

18. Contact angle hysteresis no stick-slip advancing receding stick-slip - hysteresis

19. Wenzel Equation Contact angle  is determined by the interfacial tensions  : dxdx  SL  SV  LV  Equilibrium solid liquid

20. Composite surfaces liquid solid A 1 A 2 00 3  m 0 = Cassie & Baxter (1944) Cassie – Baxter equation

21. Superhydrophobic surfaces Solvent evaporation induced i-PP gel Porous isotactic polypropylene (i-PP) Fractal alkylketene dimer (AKD) AKD solidified from melt  0 = 109°  0 = 174° fractal  0 = 160° porous flat H.Y. Erbil, A.L. Demirel,Y. Avcy, O. Mert (2003) S. Shibuichi, T. Onda, N. Satoh, K. Tsujii (1996) 5  m  0 = 104° flat

22. Superhydrophobic surfaces

23. Topography hierarchy in lotus leaves A. Large-scale SEM image of the lotus leaf. Every epidermal cell forms a papilla and has a dense layer of epicuticular waxes superimposed on it. B. Magnified image on a single papilla of A. Micro- and nanostructures on the lotus leaf (Nelumbo nucifera)

24. Superhydrophobic surfaces Examples

25. Superhydrophobic surfaces Self-cleaning surfaces

26. Superhydrophobic surfaces Examples Nanostructured surface of the superhydrophobic wings of cicada (Cicada orni).

27. Superhydrophobic surfaces Examples Nanostructured surface of the superhydrophobic legs of the water strider (Gerris remigis).

28. Electrowetting conducting liquid V conductive electrode dielectric film d Example: Water droplet on Cytop® surface  [º] Equilibrium

29. Electrowetting Equation Contact angle  is determined by the interfacial tensions  : dxdx  SL  SV  LV  Equilibrium solid liquid

30. Electrowetting Substrate : Si / 60 nm SiO 2 / 20 nm CF 1.55 (CVD) Liquid:1-ethyl-3-methyl-1 H-imidazolium tetrafluoroborate 0 V – 80 V – 0 V

31. Electrowetting Substrate : ITO / 250 nm SiN x / 1  m Cytop 0 V – 60 V – 0 V

32. Lubrication principle Possible sources of hysteresis and stick-slip –mechanical roughness –compositional inhomogeneity –chemical contamination  =  1  =  2  =  3 L F S  S F L

33. Tunable superhydrophobic surfaces 10  m Rolling ball Sticky droplet superhydrophobic slip boundary hydrophilic no slip liquid solid superhydrophobic hydrophilic

34. f 2 >> f 1 cos  ~ f strongly nonlinear effect contact angle control contact angle hysteresis control V = 0 V  0 liquid solid 00 liquid solid f1f1 f2f2 conductor isolator low-energy coating Tunable superhydrophobic surfaces

35. Rolling ball Sticky droplet Tunable superhydrophobic surfaces

36. Electrowetting induced transitions molten salt *,  = 62 mN/m * 1-ethyl-3-methyl-1 H-imidazolium tetrafluoroborate 3  m pitch 4  m Tunable superhydrophobic surfaces

37. 180° 90° cos  V 2 [V 2 ] pitch 1.05  m pitch 4  m Tunable superhydrophobic surfaces