Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans

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

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

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

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

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

Chemically striped surfaces: drop spreading

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

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.

Impact near the centre of the lyophobic stripe

Impact near a lyophilic stripe

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.

80 o /90 o

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

80 o /90 o

Characteristic spreading velocity A. Wagner and A. Briant

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

Hysteresis

slips at angle advancing

Hysteresis pinned until

Hysteresis pinned until

Hysteresis slips smoothly across hydrophobic stripe

Hysteresis slips smoothly across hydrophobic stripe

Hysteresis jumps back to

Hysteresis stick slip jump (slip) advancing

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

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

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

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

Hysteresis: 3 dimensions AB squares hydrophilic squares hydrophobic

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

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

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

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

Superhydrophobic surfaces

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

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

Hysteresis: suspended state 180 o

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

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

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

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

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

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

200  m Drop collapse: Mathilde Reyssat and David Quere

Drop collapse: simulations

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

Drop collapse: short posts

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

Drop collapse: shallow posts

Drop collapse: long posts

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

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

Drop collapse: two dimensions

Drop position with decreasing contact angle

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

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

With thanks to Alexandre Dupuis Halim Kusumaatmaja

Droplet velocity Drop velocity: suspended drop Drop velocity

Dynamics of collapsed droplets Drop velocity: collapsed drop Drop velocity

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

With thanks to Alexandre Dupuis Halim Kusumaatmaja

Chemically striped surfaces: drop motion

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

80 o /90 o

60 o /110 o

Base radius as a function of time

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

Mathilde Callies and David Quere 2006