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

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

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

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) 64 o / 5 o

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

10. Impact near the centre of the lyophobic stripe

11. Impact near a lyophilic stripe

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

13. 80 o /90 o

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

15. 80 o /90 o

18. Characteristic spreading velocity A. 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

30. 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 stick slip jump (slip) advancing

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

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

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

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

41. Hysteresis: 3 dimensions AB 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 94 o 92 o 110/60

45. 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 (92 o ) bounded by  max (110 o ) Receding angle (80 o ) bounded by  min (60 o ) 4. Free energy balance between surface / drop interactions and interface distortions determines the hysteresis Hysteresis on chemically patterned surfaces

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

47. Superhydrophobic surfaces

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

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

51. Hysteresis: suspended state 180 o

52. Hysteresis: suspended state Suspended drop Advancing contact angle 180 o : pinned on outside of posts Receding contact angle : pinned on outside of posts advancing receding

53. Hysteresis: collapsed state Collapsed drop Advancing contact angle 180 o : pinned on outside of posts Receding contact angle -90 o : pinned on outside AND inside of posts receding

54. Hysteresis: three dimensions 2D 3D Suspended drop: advancing angle 180 o receding angle  e Collapsed drop: advancing angle 180 o receding angle  e -90 o

55. Hysteresis: three dimensions 2D 3D Suspended drop: advancing angle 180 o 180 o receding angle  e >  e Free energy barrier very small Collapsed drop: advancing angle 180 o ~ 180 o receding angle  e -90 o >  e -90 o

56. Hysteresis on superhydrophobic surfaces 1.Advancing contact angles are close to 180 o 2.Hysteresis smaller for suspended than collapsed drop High receding contact angle -- weak adhesion Small contact angle hysteresis – slides easily?? 3. Free energy balance between drop -- surface interactions and interface distortion determines the hysteresis ?? Forced hysteresis ?? Changing relative length scales ?? Relation between hysteresis and easy run off

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

58. 200  m Drop collapse: Mathilde Reyssat and David Quere

59. Drop collapse: simulations

60. 1.Curvature driven collapse : short posts 2.Free energy driven collapse : long posts

61. Drop collapse: short posts

63. Drop collapse: simulations Drop collapse: short posts Mathilde Reyssat and David Quere

64. Drop collapse: shallow posts

65. Drop collapse: long posts

66. Deep posts: contact angle reaches  e on side of posts ee

67. Variation of free energy with post height  e  e

68. Drop collapse: two dimensions

69. Drop position with decreasing contact angle

70. Collapse on superhydrophobic surfaces Shallow posts: curvature driven collapse Deep posts: 2 dimensions – free energy driven collapse Deep posts: 3 dimensions – is collapse possible ??

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

72. With thanks to Alexandre Dupuis Halim Kusumaatmaja

74. Droplet velocity Drop velocity: suspended drop Drop velocity

75. Dynamics of collapsed droplets Drop velocity: collapsed drop Drop velocity

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

77. With thanks to Alexandre Dupuis Halim Kusumaatmaja

81. Chemically striped surfaces: drop motion

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

83. 80 o /90 o

88. 60 o /110 o

89. Base radius as a function of time

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

93. Mathilde Callies and David Quere 2006