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