Introduction to the real coded lattice gas model of colloidal systems
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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. 1 nm. 10 m m. Background - Colloid -. Colloid -> particles + a solvent fluid.

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

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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

1 nm

10 mm

Background - Colloid -

Colloid -> particles + a solvent fluid

Particle

foods

Milk, mayonnaise, iced cream

manufacture

Paintings, cosmetics, concrete

Nature

Fog, smoke, polluted water, blood

solvent

Innovate new materials,

Analysis on flows in micro devices


Interactions

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


How to approach

How to approach ?

Macro scale

Continuum dynamics

Navier-Stokes eq.

+

Visco-elastic model

Meso scale

solute + solvent

dynamics

Micro scale

Molecular dynamics


Numerical models

Numerical Models

Meso scale

solute + solvent

Navier-Stokes eq.

FDM, FVM

Boltzmann eq.

LBM, FDLBM

Newtonian eq.

Top down

SPH, MPS

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


Algorithm of real coded lattice gas

Algorithm of real-coded lattice gas

Streaming (inertia)

after

before

Multi-particle collision


Colloid particles

Colloid Particles

  • Rigid Particle

  • Deformable Particle


A rigid particle model

solid cell

RLG particle

A rigid particle model

  • The solvent fluid is represented by RLG particles.

  • Rigid objects are composed of solid cells.

For example . . .

Object

Solvent


Algorithm

A rigid particle model

τ time step interval

Algorithm

The RLG streaming process

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


Object rule 1

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.


Object rule 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

after

before


Object rule 2

Object Motion

before

after

Objects Collision

before

Calculate the impulse

(white arrows)

after

Object rule 2

Translational velocity vector

Angular velocity vector


Application

Application


A simpler model on spherical particles

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


Dlvo particles

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


Internal structures of a colloid

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


Aggregate forms varied with h

Aggregate forms varied with h


Aggregate forms varied with h1

Aggregate forms varied with h


Summary a rigid particle model

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


A deformable particle model

A deformable particle model

  • Red blood cells

  • Vesicles


Background on vesicles

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


Flow of vesicles

Flow of vesicles

1 cm

Vesicles are regarded as a passive scalar

Artery

Re > 100

100

Arteriole

Re < 1

The correlation between vesicles and blood

could not be neglected

10

Capillary

Re << 1

1

A direct modeling of dynamics in this field is required


A vesicle model

A vesicle model

5nm

Neglect membrane

Immiscible droplet

vesicle

Assuming that vesicles would be regarded as immiscible droplets,


Immiscible multi component fluids

Immiscible multi-component fluids

Existence of membrane prohibits vesicles from coalescing

Immiscible droplets

Immiscible multi-component fluid

Vesicle dispersion

A vesicle dispersion could be modeled as an immiscible multi-component fluid


Algorithm of immiscible multi component rlg fluid

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

Same color

Different color

Interfaces of multi-component could be reproduced by the above rules


Algorithm color collision

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


Phase segregation 3 species

Phase segregation: 3 species


An example of an immiscible multi component fluid

An example of an immiscible multi-component fluid

6 vesicles + 1 suspending fluid = 7 fluids

1

3

1

2

3

2

7

7

5

6

4

5

6

4

Time evolution


Brownian motion

Brownian motion

Stable dispersion

time

Aggregate form


Micro bifurcation

Micro bifurcation

Re ~ 2, Ca ~ 0.001

time

Zipper-like flow


Flows in a complex network

Flows in a complex network


Summary a deformable model

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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