drops on patterned surfaces halim kusumaatmaja alexandre dupuis julia yeomans
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Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans. Summary. The model Chemically patterned surfaces Spreading on stripes Hysteresis Superhydrophobic surfaces Introduction Hysteresis - PowerPoint PPT PresentationTRANSCRIPT
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