Recent advances in glassy physics September 27-30, 2005, Paris Direct Numerical Simulations of Non-Equilibrium Dynamics of Colloids Ryoichi Yamamoto Department of Chemical Engineering, Kyoto University Project members: Dr. Kang Kim Dr. Yasuya Nakayama Financial support: Japan Science and Technology Agency (JST) Outline: 1.
Introduction: colloid vs. molecular liquid Hydrodynamic Interaction (HI) Screened Columbic Interaction (SCI) 2. Numerical method: SPM to compute full many-body HI and SCI 3. Application 1: Neutral colloid dispersion External electric field: E 4.
Application 2: Charged colloid dispersion Double layer thickness: Mobility: Radius of colloid: 5. Summary and Future:
a Charge of colloid: - Ze Hydrodynamic Interactions (HI) in colloid dispersions -> long-ranged, many-body Models for simulation Brownian Dynamics only with Drag Friction 1/Hmm
Brownian Dynamics with Oseen Tensor Hnm long-range HI Stokesian Dynamics (Brady), Lattice-Boltzman (Ladd)
Hnm Oseen tensor (good for low colloid density) no HI long-range HI + two-body short-range HI Direct Numerical Simulation of Navier-Stokes Eq. full many body HI
Importance of HI: Sedimentation 1) No HI 2) Full HI Gravity Color map Blue: u = 0 Red: u = large Gravity Gravity
due to external field E linearized, neglect many-body effects no external field Direct Numerical Simulation of Ionic density by solving Poisson Eq. External force full many body SCI
(with external field) DNS of colloid dispersions: Density field of Ions Coulomb (Poisson) Colloid particles 2. DNS of charged colloid dispersions
(HI + SCI) Convection + Diffusion Hydro (NS) Velocity field of solvents 1. DNS of neutral colloid dispersions (HI)
Finite Element Method (NS+MD): Joseph et al. FEM V1 R1 R2 V2 Boundary condition (BC) (to be satisfied in NS Eq. !!) Irregular mesh
(to be re-constructed every time step!!) Smoothed Profile Method for HI: SPM Profile function Phys. Rev. E. 71, 036707 (2005) No boundary condition, but body force appears Regular Cartesian mesh
Definition of the body force: SPM (RY-Nakayama 2005) FPD (Tanaka-Araki 2000): Colloid: solid body Colloid: fluid with a large viscosity particle velocity intermediate fluid velocity (uniform f )
>> Numerical test of SPM: 1. Drag force This choice can reproduce the collect Stokes drag force within 5% error. Numerical test of SPM: 2. Lubrication force h F Two particles are approaching
with velocity V under a constant force F. V tends to decrease with decreasing the separation h due to the lubrication force. Demonstration of SPM: 3. Repulsive particles + Shear flow Demonstration of SPM: 3. Repulsive particles + Shear flow Dougherty-Kriger Eqs. Einstein Eq.
Demonstration of SPM: 4. LJ attractive particles + Shear flow attraction clustering shear fragmentation ? DNS of colloid dispersions: Charged systems
Density field of Ions Coulomb (Poisson) Colloid particles 2. DNS of charged colloid dispersions (HI + SCI) Convection + Diffusion
Hydro (NS) Velocity field of solvents 1. DNS of colloid dispersions (HI) SPM for Charged colloids + Fluid + Ions: need (x) in F
SPM for Electrophoresis (Single Particle) E = 0.01 E = 0.1 E: small double layer is almost isotropic. E: large double layer becomes anisotropic. Theory for single spherical particle: Smoluchowski(1918), Hcke(1924), OBrien-White (1978) Dielectric constant: Fluid viscosity: External electric field: E
Drift velocity: V Colloid Radius: a Double layer thickness: Zeta potential: Electric potential at colloid surface SPM for Electrophoresis (Single spherical particle) Simulation vs OBrien-White
Z= -100 Z= -500 SPM for Electrophoresis (Dense dispersion) E = 0.1 E = 0.1 Theory for dense dispersions Ohshima (1997) Cell model (mean field)
E b a SPM for Electrophoresis (Dense dispersion) SPM for Electrophoresis (Dense dispersion) Nonlinear regime No theory for E = 0.1 E = 0.5
E: small regular motion. E: large irregular motion (pairing etc). Summary We have developed an efficient simulation method applicable for colloidal dispersions in complex fluids (Ionic solution, liquid crystal, etc). So far:
Applied to neutral colloid dispersions (HI): sedimentation, coagulation, rheology, etc Applied to charged colloid dispersions (HI+SCI): electrophoresis, crystallization, etc All the single simulations were done within a few days on PC Future: Free ware program (2005/12) Big simulations on Earth Simulator (2005-) Smoothed Profile method (SPM) : Basic strategy
Particle Field smoothening superposition Newtons Eq. Navier-Stokes Eq. + body force Numerical implementation of the additional force in SPM:
=" Although the equations are not shown Usual boundary method ( ) here, rotational motions of colloids also taken into account correctly. Implicit method Explicitare method Our strategy: Solid interface -> Smoothed Profile Smoothening
Full domain Fluid (NS) Particle (MD) Demonstration of SPM: 1. Aggregation of LJ particles (2D) 1) Stokes friction Color mapp Blue: small p 2) Full Hydro Red: large p
Pressure heterogeneity -> Network Smoothed Profile Method for SCI: charged colloid dispersions Charge density of colloid along the line 0-L FEM 0 SPM L Present SPM
Numerical method to obtain (x) Iteration with BC vs. FFT without BC (much faster!) Numerical test: 2. Interaction between a pair of charged rods (cf. LPB)
D Deviations from LPB become large for r - 2a < D . For 0.01 < / 2a < 0.1, deviations are within 5% even at contact position. r r-2a=D contact Part 1. Charged colloids + ions: Working
equations for charged colloid dispersions Free energy functional: Grand potential: for charge neutrality Hellmann-Feynman force: Numerical test: 1. Electrostatic Potential around a Charged Rod (cf. PB) 1% Smoothed Profile Method becomes almost exact for r -a >
Acknowledgements 1) Project members: Dr. Kang Kim Dr. Yasuya Nakayama (charged colloids) (hydrodynamic effect) 2) Financial support from JST
Helicobacter pylori Vaccine Development Catherine O. Johnson March 9, 2006 Pathogen Background Gram negative bacteria Colonizes the human gastrointestinal tract and stomach Oral-Oral or Oral-Fecal routes of person-to-person transmission Requisite Nasty Pictures Nasty Pictures (2) Mechanism of Infection H. pylori...
Understanding and Interpreting Body Language. Introduction. Humans pride themselves on their seemingly unique ability to verbalize feelings and ideas. While the mouth tells one story, gestures and posture may tell a different story.
Graphics should make a key concept clearer. Place your graphics in a similar location within each screen. Numbers and Statistics Big numbers are confusing. If you have more than 5 numbers on a slide, it's too many. Numbers and Stats...
For example, white led (blue + phosphor) Color code : 001 Guard codes : 011, 100 The criteria used for defining a guard color channel could be based on out-of-band leakage, exceeding a certain value (for example, 10 -20 dB)...
Always click this 'Home' icon to save your progress and log off. This is very important! EXAMPLE COURSE INFECTION CONTROL TRAINING SEPT - MANDATORY TRAINING INFECTION CONTROL TRAINING SEPT - MANDATORY TRAINING To complete the Infection Control training please click...
The play charts the downfall of the family due to the appalling way they treat Eva Smith. Ironically,Eric seems most shaken by the Inspector's visit. He is seen as a lazy thieving drunk, a womaniser and as a fairly pathetic...
Agriscience Research Examples. Service learning combines community service with a structured school-based opportunity for reflection about that service, emphasizing the connections between service experiences and what is taught in the agriculture class. ... Types of SAE Last modified by ...
Ready to download the document? Go ahead and hit continue!