1. 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

2. Colloid -> particles + a solvent fluid
Background - Colloid -
Colloid -> particles + a solvent fluid　　
Particle
foods
Milk, mayonnaise, iced cream
manufacture
Paintings, cosmetics, concrete
Nature
Fog, smoke, polluted water, blood
solvent
1 nm
10 mm
Innovate new materials,
Analysis on flows in micro devices

3. Interactions Particle - Particle Particle - Molecule fluctuate
Electrochemical, DLVO
Brownian motion
Dispersion stability
Internal structure
External field
induce fluid flows
and
affected by others
Multi-physics and Multi-scale

4. How to approach ? Macro scale Continuum dynamics Navier-Stokes eq.+
Visco-elastic model
Meso scale
solute + solvent
dynamics
Micro scale
Molecular dynamics

5. Numerical Models Meso scale solute + solvent Navier-Stokes eq.
FDM, FVM
Boltzmann eq.
LBM, FDLBM
Newtonian eq.
SPH, MPS
Top down
LGA, RLG
Bottom up
A particle-model is free from the difficulty of mesh generations
Complex phenomena might be reproduced or mimicked from bottom-up

6. Algorithm of real-coded lattice gas
Streaming (inertia)
after
before
Multi-particle collision

7. Colloid Particles
Rigid Particle
Deformable Particle

8. A rigid particle model
The solvent fluid is represented by RLG particles.
Rigid objects are composed of solid cells.
For example . . .
RLG particle
solid cell
Object
Solvent

9. Algorithm The RLG streaming process The RLG - Object interaction
A rigid particle model
Algorithm
The RLG streaming process
τ time step interval
The RLG - Object interaction
Translations and rotations
The rigid objects’ motions
Collisions
Δt += τ; if ( Δt < 1 time step )
else
1 time step interval
The RLG collision process

10. Object rule 1 The reflection of RLG particles
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.
Calculate the RLG particles’ collision with the object,
Calculate the change of their momentum ΔP.
The momentum of rigid object is changed with -ΔP.

11. Object rule 1 The reflection of RLG particles An assumption:
A rigid object is regarded as a heat bath.
: The normal direction of the solid surface
: The tangential direction
where
A new velocity vector is generated randomly
from the above probability density distributions. n n
Vrigid_suface
Vrigid_suface
vrlg
before
after

12. Object rule 2 Object Motion before after Translational velocity vector
Angular velocity vector
before
after
Calculate the impulse
(white arrows)
Objects Collision

13. Application

14. A simpler model on spherical particles
Colloid particle r
Colloid particle
An electrochemical potential energy
is defined between “center to center”
normal
RLG
The colliding point and its normal vector

15. DLVO potential curve varied with h
DLVO particles
van der Waals attractions
Electrostatic repulsions
DLVO potential curve varied with h
a: Amplitude of van der Waals
h: Amplitude of a repulsive barrier
k: Screen length ratio
DLVO is the superposition of van der Waals and repulsions

16. Internal structures of a colloid
h=0
h=10
h=0，10 ： Attractive
h=20，30 ： Repulsive
h=20
h=30
The amplitude of the repulsive barrier could affect the internal structure
t = 5000

17. Aggregate forms varied with h

18. Aggregate forms varied with h

19. 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 h are demonstrated

20. A deformable particle model
Red blood cells
Vesicles

21. Background on vesicles
Vesicles are closed thin membrane separating the internal fluid from the external solvent
5nm
Fundamental structure of a bio-cell
Drug delivery systems
vesicles could deliver medicines to the target of tissues
Contrast agents
improve the contrast of Doppler images
vesicle
The size of vesicle should be of the order of micro meter or smaller

22. Flow of vesicles 1 cm Artery Vesicles are regarded as a passive scalar
100
Arteriole
Re < 1 10
The correlation between vesicles and blood
could not be neglected
Capillary
Re << 1 1
A direct modeling of dynamics in this field is required

23. A vesicle model Neglect membrane vesicle Immiscible droplet
5nm
Neglect membrane
vesicle
Immiscible droplet
Assuming that vesicles would be regarded as immiscible droplets,

24. Immiscible multi-component fluids
Existence of membrane prohibits vesicles from coalescing
Immiscible droplets
Vesicle dispersion
Immiscible multi-component fluid
A vesicle dispersion could be modeled as an immiscible multi-component fluid

25. Algorithm of immiscible multi-component rlg fluid
A rlg particle is colored by either red, blue, green or so on
color
Color is for difference species
Define interparticle interactions based on color
repulsive
attractive
Different color
Same color
Interfaces of multi-component could be reproduced by the above rules

26. Algorithm: color collision
The Color field
is the color gradient
The Color flux
is relative velocities to CM.
Color potential energy
The color collision is done by a rotation matrix, where U takes the minimum

27. Phase segregation: 3 species

28. An example of an immiscible multi-component fluid
6 vesicles + 1 suspending fluid = 7 fluids 1 1 2 3 3 2 7 7 5 4 5 6 4 6
Time evolution

29. Brownian motion
Stable dispersion
time
Aggregate form

30. Micro bifurcation
Re ～ 2, Ca ～ 0.001
time
Zipper-like flow

31. Flows in a complex network

32. 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