Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans

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

t

t

n nu 0

nu nu u

1P u u u

3

continuity

Navier-Stokes

No-slip boundary conditions on the velocity

Equations of motion

S cV b dSndVnn )()

2)(( 2

bulk term interface free energy surface term

Van der Waals

controls surface tension1 surfacen

controls contact angle

Equilibrium free energy

1s surfacef n

1zn

Minimising the free energy leads to:

Surface free energy

Boundary condition on the Euler-Lagrange equation

1/ 21 2 1 2cos (sin ) cos (sin )

2 2 cos 1 cos3 3

eq eq1 w cp

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)

64o / 5o

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.

80o /90o

Two wide stripes:

hydrophilic hydrophobic hydrophilic

110o /130o

80o /90o

Characteristic spreading velocityA. Wagner and A. Briant

c

2n

nU

R

Summary

The model

Chemically patterned surfaces

Spreading on stripes Hysteresis

Superhydrophobic surfaces

Introduction Hysteresis Transitions between states Dynamics

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

Hysteresis

slips at angle 1

advancing

2

Hysteresis

pinned until 2

Hysteresis

pinned until 2

Hysteresis

slips smoothlyacross hydrophobic stripe

Hysteresis

slips smoothlyacross hydrophobic stripe

Hysteresis

jumps back to 1

Hysteresis

stick slip jump (slip)

advancing

Hysteresis

stick slip jump (slip)

advancing

receding

stick (slip) jump slip

(Hysteresis) loop

advancing contact anglereceding contact angle

12

contact angle

volume

a

a

a

(Hysteresis) loop

advancing contact anglereceding contact angle

12

contact angle

volume

stick

slip

jump

Hysteresis: 3 dimensions

A. squares 60o

background 110o

B. squares 110o

background 60o

CB

1 1 2 2

cos

f cos f cos

Hysteresis: 3 dimensions

A B

squares hydrophilic squares hydrophobic

Hysteresis: 3 dimensions

macroscopic contact angle versus volume

A B

stickjump

Hysteresis: 3 dimensions

macroscopic contact angle versus volume

A B

94o 92o

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 (92o) bounded by max (110o) Receding angle (80o) bounded by min (60o)

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

Superhydrophobic surfaces

collapsed drop

suspended drop

He et al., Langmuir, 19, 4999, 2003

Two drop states

Homogeneous substrate, eq=110o

Suspended, ~160o Collapsed, ~140o

Suspended and collapsed drops

Hysteresis: suspended state

eq

eq 180 o

Hysteresis: suspended state

Suspended dropAdvancing contact angle 180o: pinned on outside of postsReceding contact angle : pinned on outside of postseq

advancing receding

Hysteresis: collapsed state

Collapsed dropAdvancing contact angle 180o: pinned on outside of postsReceding contact angle -90o: pinned on outside AND inside of postseq

receding

Hysteresis: three dimensions

2D 3D

Suspended drop: advancing angle 180o

receding angle e

Collapsed drop: advancing angle 180o

receding angle e-90o

Hysteresis: three dimensions

2D 3D

Suspended drop: advancing angle 180o 180o

receding angle e > e

Free energy barrier very small

Collapsed drop: advancing angle 180o ~180o

receding angle e-90o > e-90o

Hysteresis on superhydrophobic surfaces

1. Advancing contact angles are close to 180o

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: short posts

Drop collapse: simulationsDrop collapse: simulations

Drop collapse: short posts

0

50

100

150

0 50 100 150

l 2 /h (µm)

R c (µm) 2R d / h:

Mathilde Reyssat and David Quere

Drop collapse: shallow posts

Drop collapse: long posts

Drop collapse: long posts

Deep posts: contact angle reaches e on side of posts

e

Variation of free energy with post height

ee

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 velocityDrop velocity: suspended drop

eq

Drop velocity

Dynamics of collapsed dropletsDrop velocity: collapsed drop

eq

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

110o /130o

80o /90o

60o /110o

Base radius as a function of time

tR

t0

*

1s surfacef n

1zn

Minimising the free energy leads to:

Surface free energy

Boundary condition on the Euler-Lagrange equation

1/ 21 2 1 2cos (sin ) cos (sin )

2 2 cos 1 cos3 3

eq eq1 w cp

A relation between the contact angle and the surface field

Controlling the contact angle

Mathilde Callies and David Quere 2006