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Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans

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

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

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

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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

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

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Chemically striped surfaces: drop spreading

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

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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.

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Impact near the centre of the lyophobic stripe

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Impact near a lyophilic stripe

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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.

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80 o /90 o

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

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80 o /90 o

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Characteristic spreading velocity A. Wagner and A. Briant

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

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Hysteresis

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slips at angle advancing

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Hysteresis pinned until

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Hysteresis pinned until

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Hysteresis slips smoothly across hydrophobic stripe

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Hysteresis slips smoothly across hydrophobic stripe

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Hysteresis jumps back to

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Hysteresis stick slip jump (slip) advancing

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

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

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

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

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Hysteresis: 3 dimensions AB squares hydrophilic squares hydrophobic

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

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

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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

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

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Superhydrophobic surfaces

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

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

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Hysteresis: suspended state 180 o

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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

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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

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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

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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

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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

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

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200 m Drop collapse: Mathilde Reyssat and David Quere

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Drop collapse: simulations

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

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Drop collapse: short posts

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

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Drop collapse: shallow posts

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Drop collapse: long posts

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

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Variation of free energy with post height e e

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Drop collapse: two dimensions

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Drop position with decreasing contact angle

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

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

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With thanks to Alexandre Dupuis Halim Kusumaatmaja

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Droplet velocity Drop velocity: suspended drop Drop velocity

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Dynamics of collapsed droplets Drop velocity: collapsed drop Drop velocity

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

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With thanks to Alexandre Dupuis Halim Kusumaatmaja

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Chemically striped surfaces: drop motion

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

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80 o /90 o

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60 o /110 o

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Base radius as a function of time

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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

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Mathilde Callies and David Quere 2006

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