Introduction to the real-coded lattice gas model of colloidal systems
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Transcript of Introduction to the real-coded lattice gas model of colloidal systems
Introduction to the real-coded lattice gas model of colloidal systems
Yasuhiro Inoue
Hirotada Ohashi, Yu Chen, Yasuhiro Hashimoto, Shinnosuke Masuda, Shingo Sato, Tasuku Otani
University of Tokyo, JAPAN
Background - Colloid -Colloid -> particles + a solvent fluid
Particle
solvent
1 nm 10 m
foodsMilk, mayonnaise, iced cream
manufacturePaintings, cosmetics, concrete
Nature
Fog, smoke, polluted water, blood
Innovate new materials,
Analysis on flows in micro devices
Interactions
Particle - Particle Particle - Molecule
External field
Electrochemical, DLVO
induce fluid flows andaffected by others
Brownian motion
fluctuate
Dispersion stabilityInternal structure
Multi-physics and Multi-scale
How to approach ?
Navier-Stokes eq. +Visco-elastic model
Macro scaleContinuum dynamics
dynamics
Micro scaleMolecular dynamics
Meso scalesolute + solvent
Numerical Models
Meso scalesolute + solvent Navier-Stokes eq.
Boltzmann eq.
Newtonian eq.
FDM, FVM
LBM, FDLBM
SPH, MPS Top down
Bottom upLGA, RLG
A particle-model is free from the difficulty of mesh generations
Complex phenomena might be reproduced or mimicked from bottom-up
Algorithm of real-coded lattice gas
Streaming (inertia)
Multi-particle collision
beforeafter
Colloid Particles
Rigid Particle
Deformable Particle
A rigid particle model
For example . . .
• Rigid objects are composed of solid cells.
• The solvent fluid is represented by RLG particles.
Object Solvent
RLG particlesolid cell
Algorithm
The RLG streaming process
The RLG collision process
The RLG - Object interaction
The rigid objects’ motionsTranslations and rotations
Collisions
Δt += τ; if ( Δt < 1 time step )τ time step interval
else1 time step interval
A rigid particle model
Object rule 1• Solid Cell and RLG particles are exclusive to each other.
Solid Cell RLG particle
before after
• Forces exerted on the rigid object surface by bombardments of RLG particles.
The momentum of rigid object is changed with -ΔP.
Calculate the RLG particles’ collision with the object,Calculate the change of their momentum ΔP.
The reflection of RLG particles
Object rule 1
2
2
1exp)( nnnn mccmcP
2
2
1exp
2)( ttt mc
mcP
Vrigid_suface
The reflection of RLG particles
where
after
A new velocity vector is generated randomlyfrom the above probability density distributions.
n
vrlg
n
An assumption: A rigid object is regarded as a heat bath.
: The normal direction of the solid surface
: The tangential direction
Vrigid_suface
before
acerigid_surfrlg Vvc
Object rule 2
Translational velocity vector
Angular velocity vector
Object Motion
before after
before afterCalculate the impulse (white arrows)
Objects Collision
Application
A simpler model on spherical particles
r
The colliding point and its normal vector
An electrochemical potential energy is defined between “center to center”
RLG
normal
Colloid particle
Colloid particle
DLVO particles
2 2 2 2
2 2 2 2
2 2 4ln
4vdwU r R R r R
kT r R r r
*ln 1 exp 2EU r r
kT R
van der Waals attractions
Electrostatic repulsions
H 6A kT
202 R kT
* R
DLVO potential curve varied with
: Amplitude of van der Waals
: Amplitude of a repulsive barrier
: Screen length ratioDLVO is the superposition of van der Waals and repulsions
Internal structures of a colloid
The amplitude of the repulsive barrier could affect the internal structure
=0 , 10 : Attractive=20 , 30 : Repulsive
t = 5000
=0 =10
=20 =30
0 10
Aggregate forms varied with
20 30
Aggregate forms varied with
Summary: a rigid particle model
Any shape of rigid objects could be modeled by solid cells
Hydrodynamic and electrochemical interparticle interactions could be implemented
Various aggregate forms depending on are demonstrated
A deformable particle model
Red blood cells Vesicles
Background on vesicles
Drug delivery systems
Contrast agents
vesicle
• vesicles could deliver medicines to the target of tissues
• improve the contrast of Doppler images
The size of vesicle should be of the order of micro meter or smaller
5nm
Vesicles are closed thin membrane separating the internal fluid from the external solvent
Fundamental structure of a bio-cell
Flow of vesicles
m
m
1 cm
100
10
1
m
ArteryRe > 100
Arteriole Re < 1
CapillaryRe << 1
Vesicles are regarded as a passive scalar
The correlation between vesicles and blood could not be neglected
A direct modeling of dynamics in this field is required
A vesicle model
Assuming that vesicles would be regarded as immiscible droplets,
vesicle
5nm
m
Neglect membrane
Immiscible droplet
Immiscible multi-component fluids
Vesicle dispersion Immiscible multi-component fluid
Immiscible dropletsExistence of membrane prohibits vesicles from coalescing
A vesicle dispersion could be modeled as an immiscible multi-component fluid
repulsiveattractive
Algorithm of immiscible multi-component rlg fluid
• Color is for difference species• Define interparticle interactions based on color
A rlg particle is colored by either red, blue, green or so oncolor
Different color Same color
Interfaces of multi-component could be reproduced by the above rules
Algorithm: color collision
)(};{
Vvq redi
ired
The Color flux
The Color field
)(};{
Vvq bluei
iblue
is the color gradient
is relative velocities to CM.
Color potential energy
cc
ccccU,
Fq
cF
The color collision is done by a rotation matrix, where U takes the minimum
Phase segregation: 3 species
An example of an immiscible multi-component fluid
6 vesicles + 1 suspending fluid = 7 fluids
1 2 3
4 5 6
12
3
4 5 6
7 7
Time evolution
Brownian motion
Stable dispersion
Aggregate form
time
Micro bifurcation
time
Re ~ 2, Ca ~ 0.001
Zipper-like flow
Flows in a complex network
Summary: a deformable model
Vesicles are regarded as immiscible droplets.
The dispersion stability is able to be controlled by model parameters.
A preliminary example for the application of flows of a vesicle-dispersion in a micro-bifurcation was demonstrated