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Adsorption

, Volume 22, Issue 4–6, pp 503–515 | Cite as

A refined algorithm to simulate latex colloid agglomeration at high ionic strength

  • Christophe HenryEmail author
  • K. Karin Norrfors
  • Michał Olejnik
  • Muriel Bouby
  • Johannes Luetzenkirchen
  • Susanna Wold
  • Jean-Pierre Minier
Article

Abstract

This study is focussed on the simulation of particle agglomeration at relatively high ionic strength using a refined stochastic algorithm developed in the context of parcel-tracking approaches. For that purpose, experimental data of both diffusion-limited and reaction-limited aggregation of latex particles were obtained using dynamic light scattering techniques for different initial particle sizes (diameters ranging from 24 to 495 nm) and at various chemical conditions (ionic strength between 0.5 and 2 M with NaCl or CaCl\(_2\) solutions). The experimental data collected have been compared to numerical results obtained with the refined parcel-tracking algorithm for particle agglomeration which has been developed. Results show that the evolution of the aggregate diameters over time can be properly captured by the present model with the value of the aggregate fractal dimension that is extracted from experimental data.

Keywords

Agglomeration Colloid Parcel tracking Fractal dimension 

List of symbols

\(A_{Ham}\)

Hamaker constant (J)

\(\alpha \)

Collision efficiency

\(\beta \)

Collision kernel

\(d_f\)

Aggregate fractal dimension

\(D_0\)

Initial particle diameter (m)

\(D_p\)

Particle diameter (m)

\(D_{DLS}\)

Hydrodynamic diameter (measured by DLS) (m)

\(E_{barr}\)

Energy barrier (J)

e

Electron charge (C)

\(\epsilon _0\)

Dielectric permittivity of vacuum (F m\(^{-1}\))

\(\epsilon _r\)

Dielectric constant of a medium

h

Distance between particles (m)

\(k_f\)

Fractal prefactor

\(\kappa \)

Inverse Debye length (\({\mathrm{m}^{-1}}\))

\(k_B\)

Boltzmann constant (J K\(^{-1}\))

\(\mu _f\)

Fluid dynamic viscosity (m\(^2\) s\(^{-1}\))

\(\nu _f\)

Fluid kinematic viscosity (kg m\(^{-1}\,\mathrm{s}^{-1}\))

\(n_0\)

Initial particle concentration (part \(\mathrm{m}^{-3}\))

\(N_0\)

Initial number of particles

\(N_{parc}\)

Number of parcels

\(N_{agg}\)

Number of particles in the cluster

\(R_0\)

Initial particle radius (m)

\(R_g\)

Particle gyration radius (m)

\(R_p\)

Particle radius (m)

\(R_{DLS}\)

Hydrodynamic radius (measured by DLS) (m)

t

Time (s)

\(\Delta t\)

Time step (s)

\(T_f\)

Fluid temperature (K)

\(\tau _{agg}\)

Characteristic agglomeration time (s)

\(V_C\)

Control volume (s)

W

Stability ratio

z

Ion valency

\(\zeta \)

Particle zeta potential (V)

Abbreviations

AFM

Atomic force microscopy

DLCA

Diffusion-limited colloid agglomeration

DLS

Dynamic light scattering

DLVO

Derjaguin–Landau–Verwey–Overbeek

KAP

Kinetic agglomeration parameter

PBE

Population balance equation

PCS

Photon correlation spectroscopy

PCCS

Photon cross-correlated spectroscopy

RLCA

Reaction-limited colloid agglomeration

SEM

Scanning electron microscopy

SLS

Static light scattering

Notes

Acknowledgments

The Swedish Nuclear Fuel and Waste Management Co. (SKB) is gratefully acknowledged for financial support. The experimental measurements are part of the project CP-BELBaR Fission 2010-1.1.1 and have also been supported by the European FP7 TALISMAN project, JRP no. TALI-C02-10. The authors would like to express special thanks to Dr. Jacek Pozorski (Institute of Fluid Flow Machinery, Gdańsk) for useful advice regarding the development of the agglomeration algorithm. The authors also acknowledge the EU COST Action MP1305 on Flowing Matter.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Christophe Henry
    • 1
    Email author
  • K. Karin Norrfors
    • 2
    • 3
  • Michał Olejnik
    • 1
    • 4
  • Muriel Bouby
    • 3
  • Johannes Luetzenkirchen
    • 3
  • Susanna Wold
    • 2
  • Jean-Pierre Minier
    • 5
  1. 1.Institute of Fluid-Flow MachineryPolish Academy of SciencesGdańskPoland
  2. 2.Applied Physical Chemistry, School of Chemical Science and EngineeringKTH Royal Institute of TechnologyStockholmSweden
  3. 3.Institute for Nuclear Waste Disposal (INE)Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  4. 4.Gdańsk University of Technology, Conjoint Doctoral School of IFFM PAS and GUTGdańskPoland
  5. 5.EDF R&D, Mécanique des FluidesEnergie et EnvironnementChatouFrance

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