Jacco Snoeijer PHYSICS OF FLUIDS
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1 Jacco Snoeijer PHYSICS OF FLUIDS
2 dynamics
3 dynamics freezing
4 dynamics freezing microscopics of capillarity
5 Menu 1. surface tension: thermodynamics & microscopics 2. wetting (statics): thermodynamics & microscopics
6 Menu 1. surface tension: thermodynamics & microscopics 2. wetting (statics): thermodynamics & microscopics 3. contact line dynamics 4. similarity solutions for capillary flows (with Michiel Kreutzer) 5. capillarity: force vs energy
7 surface tension & wetting
8 surface tension & wetting some movies taken from the book by De Gennes, Brochard-Wyart and Quere
9 surface tension & wetting goal: relate macroscopic phenomena to molecular origin some movies taken from the book by De Gennes, Brochard-Wyart and Quere
10 surface tension - thermodynamic & mechanical definition γ - a very simple liquid (Lennard-Jones) - an even simpler liquid (Laplace s theory)
11 surface tension - thermodynamic & mechanical definition γ - a very simple liquid (Lennard-Jones) - an even simpler liquid (Laplace s theory) 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)
12 L (liquid) thermodynamics
13 thermodynamics L (liquid) L γ γ L
14 thermodynamics L L γ γ L increase in free energy: δf = γδa
15 water = not so simple liquid Shih et al. Phys. Rev. Lett. 2012
16 a simpler liquid u(r) r r/d
17 a simpler liquid u(r) repulsion r attraction (van der Waals) r/d
18 a simpler liquid Lennard-Jones potential u(r) repulsion [ (d ) 12 u(r) = 4ɛ r ( ) ] 6 d r r attraction (van der Waals) r/d
19 liquid/vapor interface Molecular Dynamics Joost Weijs [ (d ) 12 u(r) = 4ɛ r ( ) ] 6 d r
20 liquid/vapor interface Molecular Dynamics Joost Weijs [ (d ) 12 u(r) = 4ɛ r ( ) ] 6 d r
21 liquid/vapor interface
22 liquid/vapor interface bulk: isotropic stress
23 liquid/vapor interface bulk: isotropic stress surface: anisotropic stress
24 liquid/vapor interface bulk: isotropic stress surface: anisotropic stress surface tension Kirkwood & Buff 1949
25 even simpler: Laplace 1820 s u(r) γ γ
26 even simpler: Laplace 1820 s u(r) γ γ - homogeneous phase
27 even simpler: Laplace 1820 s u(r) γ γ - homogeneous phase - ignore thermal motion
28 even simpler: Laplace 1820 s u(r) γ γ - homogeneous phase - ignore thermal motion - attraction: u(r)
29 even simpler: Laplace 1820 s u(r) γ γ - homogeneous phase - ignore thermal motion - attraction: u(r) - repulsion: internal pressure (incompressible)
30 even simpler: Laplace 1820 s u(r) γ γ - homogeneous phase - ignore thermal motion - attraction: u(r) - repulsion: internal pressure (incompressible)
31 even simpler: Laplace 1820 s u(r) γ γ γ = π dr r 3 u(r) - homogeneous phase ignore thermal motion - attraction: u(r) - repulsion: internal pressure (incompressible)
32 surface tension: conclusion
33 surface tension: conclusion vapor liquid
34 surface tension: conclusion vapor liquid γ = ( ) F excess surface energy A T,V,N
35 surface tension: conclusion vapor liquid γ = ( ) F excess surface energy A T,V,N excess force: surface tension γ
36 surface tension: conclusion vapor liquid γ = ( ) F excess surface energy A T,V,N excess force: surface tension γ origin: molecular interactions 0 dh f(h) = 2γ f(h)
37 surface tension: conclusion vapor liquid γ = ( ) F excess surface energy A T,V,N excess force: surface tension γ origin: molecular interactions 0 dh f(h) = 2γ f(h) cut-off by repulsive interaction
38 wetting - thermodynamics: spreading parameter - contact angle from microscopics - disjoining pressure
39 S = γ SV (γ SL + γ LV ) = γ LV (cos θ 1) (only solutions for S < 0)
40 S = γ SV (γ SL + γ LV ) = γ LV (cos θ 1) (only solutions for S < 0)
41 contact angles: microscopics? van der Waals interactions: u ij = c ij r 6
42 contact angles: microscopics? van der Waals interactions: Laplace s model: u ij = c ij r 6 cos θ =2 c SL c LL 1
43 contact angles: microscopics? van der Waals interactions: u ij = c ij r 6 Laplace s model: 150 cos θ =2 c SL c LL 1 θ c SL c LL
44 contact angles: microscopics? van der Waals interactions: u ij = c ij r 6 Laplace s model: 150 cos θ =2 c SL c LL 1 θ 100 How accurate is this? c SL c LL
45 verify in MD Lennard-Jones: vary solid-liquid and liquid-liquid interaction c SL c LL
46 contact angles: microscopics? θ Weijs, Marchand, Andreotti, Lohse & Snoeijer, Phys. Fluids 2011 c SL c LL
47 instability of thin films thickness ~ 40 nm spinodal dewetting (can be described by disjoining pressure)
48 instability of thin films thickness ~ 40 nm spinodal dewetting (can be described by disjoining pressure)
49 instability of thin films thickness ~ 40 nm spinodal dewetting (can be described by disjoining pressure)
50 conclusion: wetting - macroscopics: spreading parameter & Young s law - thin films: disjoining pressure π(h) 0 dh π(h) = γ LV + γ SL γ SV = S
51 conclusion: wetting - macroscopics: spreading parameter & Young s law - thin films: disjoining pressure π(h) 0 dh π(h) = γ LV + γ SL γ SV cut-off by repulsive interaction = S
52 conclusion: wetting - macroscopics: spreading parameter & Young s law - thin films: disjoining pressure π(h) 0 dh π(h) = S p = γκ + π(h)
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