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Introduction to the real-coded lattice gas model of colloidal systems

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Presentation on theme: "Introduction to the real-coded lattice gas model of colloidal systems"— Presentation transcript:

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


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