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Jacco Snoeijer
PHYSICS OF FLUIDS
dynamics
dynamics freezing
dynamics freezing
microscopics of capillarity
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1. surface tension: thermodynamics & microscopics2. wetting (statics): thermodynamics & microscopics
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1. surface tension: thermodynamics & microscopics2. wetting (statics): thermodynamics & microscopics
3. contact line dynamics4. similarity solutions for capillary flows
(with Michiel Kreutzer)
5. capillarity: force vs energy
surface tension & wetting
http://designbeep.com/
surface tension & wetting
http://designbeep.com/ some movies taken from the book by De Gennes, Brochard-Wyart and Quere
surface tension & wetting
http://designbeep.com/ some movies taken from the book by De Gennes, Brochard-Wyart and Quere
goal: relate macroscopic phenomena to molecular origin
- thermodynamic & mechanical definition
- a very simple liquid (Lennard-Jones)
- an even simpler liquid (Laplace’s theory)
surface tension
!
- thermodynamic & mechanical definition
- a very simple liquid (Lennard-Jones)
- an even simpler liquid (Laplace’s theory)
surface tension
!
course material:
- copies from lecture notes- article: Marchand et al. Am. J. Phys. 79, 999 (2011)- book: Rowlinson & Widom “Molecular Theory of Capillarity” (Ch. 1 & 2)
thermodynamics
L (liquid)
thermodynamics
L (liquid)
!
!
L
L
!
!F = " !A
thermodynamics
!
increase in free energy:
LL
L
water = not so simple liquid
Shih et al. Phys. Rev. Lett. 2012
a simpler liquid
u(r)
r/d
r
a simpler liquid
u(r)
r/d
r
attraction(van der Waals)
repulsion
a simpler liquid
u(r)
r/d
r
Lennard-Jones potential
u(r) = 4!
!"d
r
#12
!"
d
r
#6$
attraction(van der Waals)
repulsion
liquid/vapor interface
Molecular Dynamics Joost Weijs
u(r) = 4!
!"d
r
#12
!"
d
r
#6$
liquid/vapor interface
Molecular Dynamics Joost Weijs
u(r) = 4!
!"d
r
#12
!"
d
r
#6$
liquid/vapor interface
liquid/vapor interface
bulk: isotropic stress
liquid/vapor interface
bulk: isotropic stresssurface: anisotropic stress
liquid/vapor interface
bulk: isotropic stresssurface: anisotropic stress surface tension
Kirkwood & Buff 1949
!
even simpler: Laplace 1820’s
!
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase- ignore thermal motion
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase- ignore thermal motion- attraction: u(r)
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase- ignore thermal motion- attraction: u(r) - repulsion: internal pressure (incompressible)
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase- ignore thermal motion- attraction: u(r) - repulsion: internal pressure (incompressible)
u(r)
!
even simpler: Laplace 1820’s
!
- homogeneous phase- ignore thermal motion- attraction: u(r) - repulsion: internal pressure (incompressible)
u(r)
! = !"
2
! !
0dr r3u(r)
surface tension: conclusion
surface tension: conclusion
liquidvapor
surface tension: conclusion
liquidvapor
! =!
"F
"A
"
T,V,N
excess “surface energy”
surface tension: conclusion
excess force: “surface tension”liquidvapor
! =!
"F
"A
"
T,V,N
excess “surface energy”
!
! !
0dh f(h) = !2!
surface tension: conclusion
excess force: “surface tension”liquidvapor
! =!
"F
"A
"
T,V,N
excess “surface energy”
!
origin: molecular interactions
f(h)
! !
0dh f(h) = !2!
surface tension: conclusion
excess force: “surface tension”liquidvapor
! =!
"F
"A
"
T,V,N
excess “surface energy”
!
origin: molecular interactions
f(h)
cut-off by repulsive interaction
- thermodynamics: spreading parameter
- contact angle from microscopics
- disjoining pressure
wetting
S = !SV ! (!SL + !LV )= !LV (cos " ! 1)
(only solutions for S < 0)
S = !SV ! (!SL + !LV )= !LV (cos " ! 1)
(only solutions for S < 0)
uij = !cij
r6
contact angles: microscopics?
van der Waals interactions:
uij = !cij
r6
contact angles: microscopics?
van der Waals interactions:
cos ! = 2cSL
cLL! 1Laplace’s model:
0 0.2 0.4 0.6 0.8 10
50
100
150
cSL
cLL
!
uij = !cij
r6
contact angles: microscopics?
van der Waals interactions:
cos ! = 2cSL
cLL! 1Laplace’s model:
0 0.2 0.4 0.6 0.8 10
50
100
150
cSL
cLL
!
uij = !cij
r6
contact angles: microscopics?
van der Waals interactions:
cos ! = 2cSL
cLL! 1Laplace’s model:
How accurate is this?
verify in MD
Lennard-Jones: vary solid-liquid and liquid-liquid interaction
cSL
cLL
0 0.2 0.4 0.6 0.8 10
50
100
150
contact angles: microscopics?
cSL
cLL
!
Weijs, Marchand, Andreotti, Lohse & Snoeijer, Phys. Fluids 2011
instability of thin films
“spinodal dewetting” (can be described by disjoining pressure)
thickness ~ 40 nm
instability of thin films
“spinodal dewetting” (can be described by disjoining pressure)
thickness ~ 40 nm
instability of thin films
“spinodal dewetting” (can be described by disjoining pressure)
thickness ~ 40 nm
!(h)
! !
0dh !(h) = "LV + "SL ! "SV
= !S
- macroscopics: spreading parameter & Young’s law
- thin films: disjoining pressure
conclusion: wetting
!(h)
! !
0dh !(h) = "LV + "SL ! "SV
= !S
- macroscopics: spreading parameter & Young’s law
- thin films: disjoining pressure
conclusion: wetting
cut-off by repulsive interaction
!(h)
! !
0dh !(h) = !S p = !!" + #(h)
- macroscopics: spreading parameter & Young’s law
- thin films: disjoining pressure
conclusion: wetting