Jacco Snoeijer Physics of Fluids - University of Twente · 2019. 9. 17. · Jacco Snoeijer Physics...
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Jacco Snoeijer Physics of Fluids - University of Twente contact angle hysteresis small droplets can ‘stick’ to window
Transcript of Jacco Snoeijer Physics of Fluids - University of Twente · 2019. 9. 17. · Jacco Snoeijer Physics...
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Jacco Snoeijer
Physics of Fluids - University of Twente
contact angle hysteresis
small droplets can ‘stick’ to window
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force on contact line
balance:γ cos θe
γslγsv
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force on contact line
balance:
fcl = γ (cos θ - cos θe)
γ cos θe
γslγsv
force on contact line:
γ cos θ
γslγsv
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advancing - receding angles
hysteresis: no unique value for contact angle
pinning force: H = γ (cos θr - cos θa)
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’sticky’ drops
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microscopic origin
geometric heterogeneity
θe θe
small scale ‘roughness’
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microscopic origin
geometric heterogeneity chemical heterogeneity:θe(x,y)
θe θe
large θe smaller θesmall scale ‘roughness’
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contact line shape?
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contact line shape?
heterogeneity at larger scale: macroscopic ‘wetting defects’
single defect (500µm) many defects (10µm)
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contact line shape?
heterogeneity at larger scale: macroscopic ‘wetting defects’
single defect (500µm) many defects (10µm)
‘simple’ dynamics collective dynamicscontact line is very ‘rough’
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what will we do:
• contact line deformation of single defect• Joanny - De Gennes model for hysteresis• implications for dynamics...
literature:
Joanny & De Gennes, J. Chem. Phys. 81, 552 (1984)
Bonn, Eggers, Indekeu, Meunier, Rolley, to appear Rev. Mod. Phys. (2009)
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contact line shape
θ0
z
y
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contact line shape
θ0
z
y
yx
z
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contact line shape
ycontact line position
z
x
y
η(x)
z
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interface
contact line position
z
y
η(x)
interface h(x,y) ?
!
h(x,y) = "0y + ....
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interface
contact line position
z
y
η(x)
Δh ~ e-qy
interface h(x,y) ?
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h(x,y) = "0y + Ae
iqxe#qy
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interface
contact line position
z
y
η(x)
change in local contact angle: Δθ(x)
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interface
contact line position
z
y
η(x)
increase of area
ΔE ~ γ q A2
Δθ(x)
contact line ‘elasticity’
Joanny & De Gennes 1984
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sinusoidal perturbations
contact line position
z
y
increase of area:
ΔE ~ γ q A2 Δθ(x)
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sinusoidal perturbations
z
y
increase of area:
ΔE ~ γ q A2 Δθ(x)
relaxation rate σ
qDelon et al. JFM 2008
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single defect
wetting defect is ‘pulling’, but....
large deformations cost energy
θ = 0
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single defect
contact line shape ?η(x)
θ = 0
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single defect
contact line shape ?η(x)
θ = 0
!
h(x,y) = "0y + ...
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single defect
contact line shape ?η(x)
θ = 0
!
h(x,y) = "0y #
"0
2$dq ˜ % & (q) eiqxe#qy
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single defect
contact line shape ?η(x)
θ = 0
!
h(x,y) = "0y #
"0
2$dq ˜ % & (q) eiqxe#qy
imposing θ(x) at the contact line η(x)
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single defect
contact line shape ?η(x)
θ = 0
!
h(x,y) = "0y #
"0
2$dq ˜ % & (q) eiqxe#qy
!
" #$h
$y= "
0+"
0
2%dq ˜ & ' (q) q eiqxe(qy
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single defect
contact line shape ?η(x)
θ = 0
!
h(x,y) = "0y #
"0
2$dq ˜ % & (q) eiqxe#qy
!
"(x) #"0
+"
0
2$dq ˜ % (q) q{ }& eiqx
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single defect
η(x)θ = 0
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"(x) ~Fdefect
#ln L / x( )
Nadkarni & Garoff 1992
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Fdefect ~ d" 1# cos$e( )
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model for hysteresis
advancing
‘jump’
receding
asymmetry between advancing and receding
(for defects that are strong enough)
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model for hysteresis
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" cos#r$ cos#
a( ) ~ % Fd&max
advancing
‘jump’
receding
non-interacting defects, density ρ
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contact line dynamics, revisited
many defects (10µm)
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contact line dynamics, revisited
if we go very slowly...
... thermally activated ‘hopping’ of molecules
many defects (10µm)
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contact line dynamics, revisited
Rolley & Guthmann PRL 2007
Fcl
spee
d
!
U ~ exp "E " fcl lmicro
2
kBT
#
$ %
&
' (
thermally activated ‘hopping’ of molecules
Fcl ~ γ(cosθ - cosθe)
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contact line dynamics, revisitedthermally activated ‘depinning’ of contact line
Rolley & Guthmann PRL 2007
Fcl
spee
d
!
U ~ exp "E " fcl lmicro
2
kBT
#
$ %
&
' (
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coupling to hydrodynamics?for significant Ca: lubrication + slip
microscopics shows up as ‘boundary conditions’
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conclusion
- microscopic description of hysteresis
- ’interacting defects’ are difficult... depinning, contact line roughness
- coupling to hydrodynamics??
