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

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

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

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

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

Colloid Particles Rigid Particle Deformable Particle

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

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

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 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

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

Application

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 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

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

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 Red blood cells 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 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

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

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

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

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

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

Brownian motion Stable dispersion time Aggregate form

Micro bifurcation Re ～ 2, Ca ～ 0.001 time 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