FLUID PARTICLES IN MESOSCOPIC MODELLING OF COLLOIDS AND SUSPENSIONS

Witold Dzwinel1, David A.Yuen2, Krzysztof Boryczko1,2,1Institute of Computer Science, AGH University of Technology, Mickiewicza 30, 30-059 Kraków, Poland, 2Minnesota Supercomputing Institute, University of Minnesota, MN 55455, Minneapolis, USA

dzwinel@uci.agh.edu.pl, boryczko@uci.agh.edu.pl, davey@msi.umn.edu

DISPERSION IN COLLOIDAL SUSPENSIONS AbstractWhen mesoscopic features embedded within macroscopic phenomena in polymers

are coupled together with micro-structural dynamics and boundary singularities, the complex multi-resolution behavior observed in polymer dynamics are difficult to capture with the continuum models [1]. Therefore, the approaches based on the Navier-Stokes and the Cahn-Hillard equations, which use partial differential equations, become useless when employed in microscopic and mesoscopicscales. They must be augmented with discretized atomistic microscopic models, such as molecular dynamics (MD) to provide an effective solver across the diverse scales with different physics. The two-level fluid particle model [2] is a discrete-particle method, which is a mesoscopic version of molecular dynamics (MD) technique combined with fluid particle method (FPM). Unlike in MD, where the particles represent atoms and molecules, in our model they represent both colloidal beds and fluid particles. The fluid particles mimic the “lumps of fluid”, which interact with each other, not only via central conservative forces as it is in MD, but with non-central, dissipative and stochastic forces as well.

We show that by using discrete-particles we can model realistic behavior of such the mesoscopic phenomena such as the thin-film evoluation in mesoscale[3], mixing instabilities in suspensions [4,5], phase separation [6], creation of colloidal arrays [7] and colloidal aggregates [8]. The modeled multi-resolution patterns and qualitative behavior of mesoscopic features are amazingly similar to the results found in laboratory experiments and predicted by the theory. The combination of two different types of interactions: postulated by the DLVO theory -representing realistic interactions between colloidal beds - and arbitrary defined dissipative and random interactions acting between fluid particles result in spontaneous creation of many multi-resolutional structures. They represent a single micelle, colloidal crystals, large-scale colloidal aggregates up to scales of hydrodynamic instabilities [9,10] and the macroscopic phenomenon involving the clustering of red blood cells in capillaries. We can summarize the computationally homogeneous discrete particle model in the following hierarchical scheme [1,2]: non-equilibrium molecular dynamics (NEMD), dissipative particle dynamics (DPD), fluid particle model (FPM), smoothed particle hydrodynamics (SPH) and thermodynamically consistent DPD. The large scale-simulations involving up to 10 million fluid particles in 3-D were carried out on a broad range of parallel systems from IBM SP multi-computer, SGI/Origin ccNUMA multiprocessor to the shared memory clusters such as IBM/Regatta and SGI/Altix machines resulting in an efficient and universal discrete-particle algorithms and codes [11-13]. A powerful toolkit over the GRID can be formed from these discrete particle schemes to model successfully multiple-scale phenomena such as biological vascular and mesoscopic porous-media systems.

References

1. Dzwinel W, Alda W, Yuen, DA, Mol. Simul., 22, 397-418, 1999.2. Dzwinel W, Yuen DA, Boryczko K, J Mol. Modeling, 8, 33-45, 2002.3. Dzwinel W, Yuen DA, Mol. Simul., 22, 369-395, 1999.4. Dzwinel W, Alda W, Pogoda M, Yuen DA, Physica D, 137, 157-171, 2000.5. Dzwinel W, Yuen DA, Int. J. Mod Phys.C, 12/1, 91-118, 2001.6. Dzwinel W, Yuen DA, Int. J. Mod Phys.C, 11/1, 1-25, 2000.7. Dzwinel W, Yuen DA, J Colloid Int. Sci. 225, 179-19, 2000. 8. Dzwinel W, Yuen DA, Int. J. Mod Phys.C, 11/5, 1037-1067, 2000.9. Dzwinel W, Yuen DA, J Colloid Int Sci, 247, 463-480, 2002.10.Dzwinel W, Yuen DA, Boryczko K, Bridging diverse physical scales with the

discrete-particle paradigm in modeling colloidal dynamics with mesoscopicfeatures, Chemical Engineering Sci., in press 2004

11.Boryczko K, Dzwinel W, Yuen DA, Concurr&Comput: Practice and Experience, 14, 1-25, 2002.

12.Boryczko K, Dzwinel W, Yuen DA, Concurr&Comput: Practice and Experience, 15, 101-116, 2003

13.Boryczko K, Dzwinel W, Yuen DA, Concurr&Comput: Practice and Experience, submitted Feb. 2004

MULTIRESOLUTINAL STRUCTURES –COLLOIDAL AGGREGATES AND AGGLOMERATES

Multi-resolution

Particle level

Cluster level

Large feature level

NUMBER OF MD, DPD AND FPM PARTICLES 102 104 106

MD particles – colloid CP DPD particles – solvent SP

FPM particles – in bulk solvent

Micelles Colloidal clusters

Colloidal agglomerate

MD-DPD-FPM DISCRETE PARTICLE MODEL

Fractal dimension, power laws

SP and CP are of similar size

Micro-scale Macro-scale

ab initioMD

quantummechanics

MDLong-range and multipleinteractions

MDShort-range pair

interactions

PM1

andPPPM1

LatticeBoltzmann

gas

Lattice Gas

set oflinear eqs.

ABYSSBETWEEN

MACROAND

MICRO

? ?

quasi-particlemodels:

• SPH

• Part ic le -in-Ce llPIC

Model of particles

Meso-scale

Space scale (in number of atoms →)103 109 1026

Continuum modelDownscaling ←→Upscaling

Statisticalmechanics

Newtonianmechanics

Particle-meshhybrid model

Lattice gas• space and time

discretization• mesh• collision rules

Static Monte Carlo, cellular automata and fractal based methods(Metropolis Monte Carlo, Diffusion Limited Aggregation, Percolation etc.)

Conservation rulesmass, momentum,

energy conservationPartial diffe re n t ial

equations• s p a ce a n d t i m e

d i scre t i z a t i o n• m e s h

FEMFDM

Ordinary diffe rent ialequations

• t i m e d i s c r e t i z a t i o n• m o b i l e p a r t i c l e s

Time scale (sec.) →10-11 10-9 1

heterogeneous parallel models1 PM - Particle-Mesh and PPPM - Particle-Particle-Particle-Mesh, MD algorithms

FUTURE DIRECTIONS

The discrete particle methods can be used as the components of the problem solving environment (PSE) based on the conception of multi-resolution wavelets. As shown below the whole series of simulations can be performed over three different spatio-temporal levels similarly as it is for wavelets but here the various shapes of "wavelets" will depend on the model of particle (atom, DPD droplet, FPM drop, SPH chunk of fluid) and consequently the interactions between particles. In fact, the shapes of short ranged interaction can be treated as some sort of wavelets. The interactions are short ranged with compact support and well localized in space. The final total forces acting on each particle are linear combinations of “wavelets” of various locations.

However, unlike wavelets we cannot get "details" for the whole macroscopic spatial domain but rather representative part of it. It does not matter for homogeneous system but gets clumsily for more interesting - anisotropic system. Thus the global simulation should start from the coarsest SPH level (“approximation”) and focalize on interesting areas in subsequent “details” (DPD and MD, respectively). This focalization procedure resembles thresholding of wavelets coefficients, setting them to 0 for all uninteresting parts of spatial domain. From the coarse system we remove the areas, which have to be simulated by using more detailed model. We can find these regions self-adaptatively by using regular wavelets, exploiting clustering schemes or they can be extracted interactively by the user from visualized on-line snapshots from the simulations.In result we will obtain, such as it is in wavelets, multi-resolution approximation of the system. The user will define only the physical properties of the medium and will get "details" (MD, DPD) and "approximations" for each level.

SPH force

DPD force

MD force

SPH level

DPD level

MD level

DESKTOP PSE

SPH level macroscale

MD level microscale

DPD level mesoscale

VISU

AL

IZA

TIO

N A

ND

OF

F-SC

RE

EN

RE

ND

ER

ING

Spatial decomposition

experience wavelet anlaysis

clustering analysis ...

Distribute problems onto solvers

approximation

detail 1

detail 2

CGI

MMMAAASSSSSS SSSTTTOOORRRAAAGGGEEE LLLAAAPPPTTTOOOPPPSSS

LLLAAANNN CCCLLLIIIEEENNNTTTSSS

CCCLLLIIIEEENNNTTT

Spatial decomposition

CCCrrraaayyy XXX111

AAAMMMIIIRRRAAA SSSEEERRRVVVEEERRR

HHHIIIEEERRRAAARRRCCCHHHIIICCCAAALLL DDDIIISSSCCCRRREEETTTEEE PPPAAARRRTTTIIICCCLLLEEE

SSSOOOLLLVVVEEERRR

SPH

DPD+FPM

MD

DDDAAATTTAAA MMMIIINNNIIINNNGGG TTTOOOOOOLLLSSS

feature selector

clustering

wavelet transform