, 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


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.


Agglomeration Colloid Parcel tracking Fractal dimension 

List of symbols


Hamaker constant (J)

\(\alpha \)

Collision efficiency

\(\beta \)

Collision kernel


Aggregate fractal dimension


Initial particle diameter (m)


Particle diameter (m)


Hydrodynamic diameter (measured by DLS) (m)


Energy barrier (J)


Electron charge (C)

\(\epsilon _0\)

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

\(\epsilon _r\)

Dielectric constant of a medium


Distance between particles (m)


Fractal prefactor

\(\kappa \)

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


Boltzmann constant (J K\(^{-1}\))

\(\mu _f\)

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

\(\nu _f\)

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


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


Initial number of particles


Number of parcels


Number of particles in the cluster


Initial particle radius (m)


Particle gyration radius (m)


Particle radius (m)


Hydrodynamic radius (measured by DLS) (m)


Time (s)

\(\Delta t\)

Time step (s)


Fluid temperature (K)

\(\tau _{agg}\)

Characteristic agglomeration time (s)


Control volume (s)


Stability ratio


Ion valency

\(\zeta \)

Particle zeta potential (V)



Atomic force microscopy


Diffusion-limited colloid agglomeration


Dynamic light scattering




Kinetic agglomeration parameter


Population balance equation


Photon correlation spectroscopy


Photon cross-correlated spectroscopy


Reaction-limited colloid agglomeration


Scanning electron microscopy


Static light scattering



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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