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Institut Jean Le Rond D’[email protected]
Hydro-kinetic approach to
multi-fluid flows
Sergio ChibbaroInstitut Jean Le Rond D’alembert
Université Pierre et Marie Curie, Paris, France
Institut Jean Le Rond D’Alembert
With
R. Benzi, L. Biferale, M. Sbragaglia (University of Rome, Italy);
M. Bernaschi, F. Toschi and S. Succi (IAC, CNR, Rome Italy)
K. Binder, D. Dimitrov and A. Miltchev (University of Mainz)
Institut Jean Le Rond D’[email protected]
Moving Contact Lines….Why a Challenge ?
1) Multiscale problem (inner/outer) (from molecular to millimetric)
2) Singular problem (inner) (Divergence of viscous stress)
Huh & Scriven (1971), Dussan et al. (1974), Voinov (1979), Cox (1986), Quéré (1991), Podgorski (2001), Eggers (2004), Snoeijer (2007)
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MESOSCOPIC APPROACH: Lattice Boltzmann Equations
Institut Jean Le Rond D’[email protected]
Ideal discontinuous interface: drawbacksa)Interface close to the critical point (fat)
b)Coalescence of two air bubbles (singular at the merging)
c)Nucleation of a second phase
d)Moving boundary conditionsVan der Waals approach to diffuse
interface.
Korteweg stress
Institut Jean Le Rond D’[email protected]
1)Take a diffuse interface model with a given interface width
2)Develop an algorithm to simulate it
3)If macroscopic/mesoscopic physics-> check the robustness at changing
4)If nanoscopic physics-> check the consistency of taking statistical equilibrium
Recipes
Institut Jean Le Rond D’[email protected]
MACROSCOPIC
NAVIER-STOKES
KINETIC
(LATTICE BOLTZMANN)
MICROSCOPIC
MOLECULAR DYNAMICS
Chapman-Enskog
(particle-particle interactions)
(Particles p.d.f.)
(continuum description)
The 10 orders of magnitude hierarchy
Institut Jean Le Rond D’[email protected]
Streaming collide
Lattice Boltzmann for SINGLE-phase flows
Density
Momentum
Institut Jean Le Rond D’[email protected]
Streaming collide
Intermolecular forces Pseudo potential
Shan and Chen (1993,1994)
Non ideal gas effects Surface tension
Lattice Boltzmann for MULTI-phase flows
NON-IDEAL PRESSURE TENSORKorteweg stress
Institut Jean Le Rond D’[email protected]
Modelling wetting properties in lattice Boltzmann
Mechanical equilibrium
Liquid (l)
gas (g)
solid (s)
Boundary condition
Benzi R., Biferale L.,Sbragaglia M., Succi S. and Toschi F Phys. Rev. E 74, 021509 (2006)..
θ−π
M. Sbragaglia, R. Benzi, L. Biferale, S. Succi and F. ToschiPhys. Rev. Lett. 97, 204503 (2006).
Institut Jean Le Rond D’[email protected]
Periodic boundary conditions
H
Liquid
Gas
z
ρl
ρgvf
ρw
Effective channel
Capillary Filling
AsymptoticWashburn’s Law
Institut Jean Le Rond D’[email protected]
EFFECTS OF EVAPORATION/CONDENSATION
EFFECST OF FINITE INTERFACE WIDTH
velocity profiles
liquidgas
Capillary Filling
Institut Jean Le Rond D’[email protected]
EFFECTS OF EVAPORATION/CONDENSATION
EFFECTS OF FINITE DENSITY RATIO
velocity profiles
liquid gas
Capillary Filling
Institut Jean Le Rond D’[email protected]
Conclusions 1.
Need to reach high density ratioNeed to reach high separation of scalesImportant effects from the inlet.
a)Smooth walls: the role of density ratio and of interface width.
European journal of physics ST 171, 237-243 (2009) arXiv : 0801.4223Lattice Boltzmann simulations of capillary filling: finite vapour density effectsAuthors: F. Diotallevi, L.Biferale, S. Chibbaro, G. Pontrelli, F. Toschi, S. Succi
European journal of physics ST 166, 111 (2009) arXiv:0707.0945Title: Capillary filling using Lattice Boltzmann Equations: the case of multi-phase flowsAuthors: F. Diotallevi, L. Biferale, S. Chibbaro, A. Lamura, G. Pontrelli, M. Sbragaglia, S. Succi, F. Toschi
Capillary Filling
Institut Jean Le Rond D’[email protected]
b) Perfectly wetting walls: the dynamics of precursor film.
Capillary Filling
Lennard-Jones Molecular Dynamics
ULJ (r) =4ε σ / r( )12 − σ / r( )6⎡⎣
⎤⎦
ε =1.4 σ =1.0
Institut Jean Le Rond D’[email protected]
interface profiles
de Gennes RMP 1985
Capillary Filling
Contact angle
meniscus
Precursor
1.Washburn’s Law still holds at nanoscopic scales2.Wetting can be quantitatively described by hydro-kinetic methods like LB
S. Chibbaro, L. Biferale, F. Diotallevi, S. Succi, K. Binder, D. Dimitrov, A. Milchev Europhysics Letters, 84 (2008) 44003,
Institut Jean Le Rond D’[email protected]
Obstacle and roughness: Concus-Finn/Gibbs criterionCapillary Filling
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40°
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50°
LBCF does not hold
Fluctuations are important at the critical point at these
scales
MD
S. Chibbaro, L. Biferale, K. Binder, D. Dimitrov, F. Diotallevi, A. Milchev, S. Succi JSAT: Theory and expermients (2009) P06007
S. Chibbaro, E. Costa, D. I. Dimitrov, F. Diotallevi, A. Milchev, D. Palmieri, S. SucciLangmuir, 2009, 25 (21), pp 12653–12660
Institut Jean Le Rond D’[email protected]
State of the art and point of view
Microscopic simulations : molecular dynamics and spin glass models.
MD is computational demanding (available number of particles, short time-scale)
Spin glass models are “reference state” to achieve theoretical understanding
no microscopic model aimed at investigating the “hydrodynamic-like” behavior of soft glasses.
New approach kinetic/mesoscopic dynamics of soft-glassy materials
Diffuse interface/Lattice Boltzmann Equation for a two fluid system + “frustration”
Model scale
Micro-emulsions
A B
Two fluids : A and B
repulsive interactions A-B
“non ideal” (Shan-Chen) self attraction interaction (A-A, B-B)
σAB surface tension between the two fluids
• No frustration
• Phase separation between A and B (spinodal decomposition)
Standard multi-component model
Institut Jean Le Rond D’[email protected]
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Next-to-next neighbour
BA
Soft-glassy materialsIntroducing frustration : Surfactant effect
Under Shear Non ergodic behaviour and structural arrest
Emergent Herschel-Bulkley rheologyR. Benzi, S. Chibbaro & S. Succi, Phys. Rev. Lett. 102, 026002 (2009)R. Benzi, M. Sbragaglia, S. Succi, M. Bernaschi & S.Chibbaro, Jour. Chem. Phys. 131, 104903 (2009)
Institut Jean Le Rond D’[email protected]
Aging leads the system to be trapped in a deep valleyStrong enough drive can force to leave the valley
A small extra drive can keep the system above the treshold
Ludovic Berthier, Jean-Louis Barrat and Jorge Kurchan (2000)
Decreasing shear
Yield-fluid
τw = 2 ×105
Aging under shear
Micro-emulsions
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Aging properties in glassesMolecular dynamics simulations of binary mixture
N = number of different initial conditions
In our case:
U0 =0.02
τw = 3 ×105 ; U0 = 0.03
1.Validation of diffuse-interface LB method•Need to reach high density ratio
•Need to reach high separation of scales
•Important effects from the inlet.
2. Quantitative description (MD/LB) of capillary filling at nanoscopic scales
•Dynamic law of precursors
•Washburn’s law holds
3. Study of geometrical roughness•Analysis of the effect of roughness on front dynamics
•Concus-Finn criterion not valid
4. Development of a new kinetic approach to flowing soft-glasses
CONCLUSIONS