Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans

1. Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans

2. Summary The model Chemically patterned surfaces Spreading on stripes Hysteresis Superhydrophobic surfaces Introduction Hysteresis Transitions between states Dynamics

3. Equations of motion Navier-Stokes equations continuity Navier-Stokes No-slip boundary conditions on the velocity

4. Equilibrium free energy bulk term interface free energy surface term Van der Waals controls surface tension controls contact angle

5. Controlling the contact angle Surface free energy Minimising the free energy leads to: Boundary condition on the Euler-Lagrange equation A relation between the contact angle and the surface field

6. Summary The model Chemically patterned surfaces Spreading on stripes Hysteresis Superhydrophobic surfaces Introduction Hysteresis Transitions between states Dynamics

7. Chemically striped surfaces: drop spreading

8. Experiments (J.Léopoldès and D.Bucknall) 64o / 5o

9. LB simulations on substrate 4 • Two final (meta-)stable state observed depending on the point of impact. • Dynamics of the drop formation traced. • Quantitative agreement with experiment. Simulation vs experiments Evolution of the contact line

10. Impact near the centre of the lyophobic stripe

11. Impact near a lyophilic stripe

12. LB simulations on substrate 4 • Two final (meta-)stable state observed depending on the point of impact. • Dynamics of the drop formation traced. • Quantitative agreement with experiment. Simulation vs experiments Evolution of the contact line

13. 80o /90o

14. Two wide stripes: 110o /130o hydrophilic hydrophobic hydrophilic

15. 80o /90o

18. Characteristic spreading velocityA. Wagner and A. Briant

19. Summary The model Chemically patterned surfaces Spreading on stripes Hysteresis Superhydrophobic surfaces Introduction Hysteresis Transitions between states Dynamics

20. Hysteresis

21. Hysteresis

22. Hysteresis

23. Hysteresis

24. Hysteresis

25. Hysteresis

26. Hysteresis

27. Hysteresis

28. Hysteresis

30. Hysteresis slips at angle advancing

31. Hysteresis pinned until

32. Hysteresis pinned until

33. Hysteresis slips smoothly across hydrophobic stripe

34. Hysteresis slips smoothly across hydrophobic stripe

35. Hysteresis jumps back to

36. Hysteresis advancing stick slip jump (slip)

37. Hysteresis advancing stick slip jump (slip) receding stick (slip) jump slip

38. (Hysteresis) loop a a a contact angle volume advancing contact angle receding contact angle

39. (Hysteresis) loop slip jump stick contact angle volume advancing contact angle receding contact angle

40. Hysteresis: 3 dimensions A. squares 60o background 110o B. squares 110o background 60o

41. Hysteresis: 3 dimensions A B squares hydrophilic squares hydrophobic

42. Hysteresis: 3 dimensions macroscopic contact angle versus volume A B stick jump

43. Hysteresis: 3 dimensions macroscopic contact angle versus volume A B 94o 92o 110/60

45. Hysteresis on chemically patterned surfaces 1.Slip, stick, jump behaviour, but jumps at different volumes in different directions (but can be correlated) 2. Contact angle hysteresis different in different directions 3. Advancing angle (92o) bounded by qmax (110o) Receding angle (80o) bounded by qmin (60o) 4. Free energy balance between surface / drop interactions and interface distortions determines the hysteresis

46. Summary The model Chemically patterned surfaces Spreading on stripes Hysteresis Superhydrophobic surfaces Introduction Hysteresis Transitions between states Dynamics

47. Superhydrophobic surfaces

48. Superhydrophobic surfaces

49. Two drop states suspended drop collapsed drop He et al., Langmuir, 19, 4999, 2003

50. Suspended and collapsed drops Suspended, q~160o Collapsed, q~140o Homogeneous substrate, qeq=110o