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
Equations of motion
Navier-Stokes equations
continuity
 t n     nu    0
Navier-Stokes
 t  nu       nu  u  
1


   P       u     u     u   
3


No-slip boundary conditions on the velocity
Equilibrium free energy

2
   ( b (n)   n  ) dV    c (n) dS
V
S
2
bulk term
interface free energy
surface term
Van der Waals
controls surface tension
1nsurface
controls contact angle
Controlling the contact angle
f s  1nsurface
Surface free energy
Minimising the free energy leads to:
1
zn  

Boundary condition on
the Euler-Lagrange equation
A relation between the contact angle and the surface field
1  2  w
1/ 2

 cos (sin  eq )  
 cos (sin  eq )   
2 pc cos 
 1  cos 
  

3
3


 

  
1
2
1
2
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
• 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
Impact near the centre of the lyophobic
stripe
Impact near a lyophilic stripe
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
80o /90o
Two wide stripes:
hydrophilic
110o /130o
hydrophobic
hydrophilic
80o /90o
Characteristic spreading velocity
A. Wagner and A. Briant
U
  nc
 n 
2
 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
advancing
1
2
Hysteresis
pinned until
2
Hysteresis
pinned until
2
Hysteresis
slips smoothly
across hydrophobic stripe
Hysteresis
slips smoothly
across hydrophobic stripe
Hysteresis
jumps back to
1
Hysteresis
advancing
stick slip
jump (slip)
Hysteresis
advancing
stick slip
jump (slip)
receding
stick (slip) jump
slip
(Hysteresis) loop
a
contact
angle
a
a
volume
advancing contact angle
receding contact angle
2
1
(Hysteresis) loop
slip
contact
angle
stick
jump
volume
advancing contact angle
receding contact angle
2
1
Hysteresis: 3 dimensions
A. squares 60o
background 110o
B. squares 110o
background 60o
cos CB 
f1 cos 1  f 2 cos 2
Hysteresis: 3 dimensions
A
squares hydrophilic
B
squares hydrophobic
Hysteresis: 3 dimensions
macroscopic contact angle versus volume
A
stick
B
jump
Hysteresis: 3 dimensions
macroscopic contact angle versus volume
A
B
94o
92o
110/60
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 max (110o)
Receding angle (80o) bounded by min (60o)
4. Free energy balance between surface / drop
interactions and interface distortions determines the
hysteresis
Summary
The model
Chemically patterned surfaces
Spreading on stripes
Hysteresis
Superhydrophobic surfaces
Introduction
Hysteresis
Transitions between states
Dynamics
Superhydrophobic surfaces
Superhydrophobic surfaces
Two drop states
suspended drop
collapsed drop
He et al., Langmuir, 19, 4999, 2003
Suspended and collapsed drops
Suspended, ~160o
Homogeneous
substrate, eq=110o
Collapsed, ~140o
Hysteresis: suspended state
eq
eq
180 o
Hysteresis: suspended state
advancing
receding
Suspended drop
Advancing contact angle 180o: pinned on outside of posts
Receding contact angle  eq: pinned on outside of posts
Hysteresis: collapsed state
receding
Collapsed drop
Advancing contact angle 180o: pinned on outside of posts
Receding contact angle  eq -90o: pinned on outside AND inside of posts
Hysteresis: three dimensions
2D
Suspended drop: advancing angle 180o
receding angle
e
Collapsed drop: advancing angle 180o
receding angle
e-90o
3D
Hysteresis: three dimensions
2D
Suspended drop: advancing angle 180o
receding angle
e
3D
180o
> e
Free energy barrier very small
Collapsed drop: advancing angle 180o
receding angle
e-90o
~180o
> 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
Drop collapse:
Mathilde Reyssat and David Quere
200 m
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: short posts
150
2
R : d /h
R c (µm)
100
Dropcollapse:
collapse: simulations
Drop
simulations
50
0
0
50
100
150
l 2 /h (µm)
Mathilde Reyssat and David Quere
Drop collapse: shallow posts
Drop collapse: long posts
Drop collapse: long posts
e
Deep posts: contact angle reaches e on side
of posts
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
Drop velocity:
Dropletsuspended
velocity drop
Drop
velocity
eq
Drop velocity:
collapseddroplets
drop
Dynamics
of collapsed
Drop
velocity
eq
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
110o /130o
hydrophobic
hydrophilic
80o /90o
60o /110o
Base radius as a function of time

t 
t
 R0
*
Controlling the contact angle
f s  1nsurface
Surface free energy
Minimising the free energy leads to:
1
zn  

Boundary condition on
the Euler-Lagrange equation
A relation between the contact angle and the surface field
1  2  w
1/ 2

 cos (sin  eq )  
 cos (sin  eq )   
2 pc cos 
 1  cos 
  

3
3


 

  
1
2
1
2
Mathilde Callies and David Quere 2006