Transport in Porous Media

, Volume 128, Issue 1, pp 153–177 | Cite as

Cotransport of Suspended Colloids and Nanoparticles in Porous Media

  • G. V. C. Malgaresi
  • H. Zhang
  • C. V. Chrysikopoulos
  • P. BedrikovetskyEmail author


The objective of this study is to develop a model for cotransport of colloids and nanoparticles (NPs) in porous media under two particle capture mechanisms. The particle capture rate is proportional to the capture probability, which is a function of retained concentration, called the filtration function. Laboratory bench-scale experiments of individual transport of NPs and colloidal-size kaolinite clay particles through packed columns produced breakthrough curves (BTCs) that monotonically increased with time and stabilised at some value lower than the injected concentration. We discuss the filtration function that corresponds to BTCs stabilising at the concentration lower than the injected value. This so-called binary filtration function incorporates two particle capture mechanisms. The analytical transport model with a binary filtration function was capable to fit successfully BTCs obtained from individual transport experiments using kaolinite and NPs conducted by Chrysikopoulos et al. (Transp Porous Med 119(1):181–204, 2017). Assuming that the electrostatic particle–solid matrix interaction and the fraction of the solid matrix surface area occupied by a single attached particle (kaolinite or NP) are the same for individual transport of either kaolinite particles or NPs and for simultaneous cotransport of kaolinite particles and NPs, the proposed binary filtration function was extended for the cotransport case. Although the breakthrough data from cotransport experiments with kaolinite particles and NPs have six degrees of freedom, the developed cotransport model successfully matches the BTCs by tuning two constants only. This validates the developed model for cotransport of two colloidal populations with different attachments and straining rates.


Colloidal transport Nanoparticles Cotransport Analytical model Attachment and straining 

List of Symbols


Suspended concentration [ML−3]


Normalised suspended concentration [–]


Permeability [L2]


Retained concentration [ML−3]


Maximum attached concentration [ML−3]


Normalised retained concentration [–]


Time [T]


Dimensionless time [PVI]


Flow velocity [LT−1]


Axial coordinate [L]


Dimensionless axial coordinate [–]

Greek Letters


Porosity [–]


Initial attachment filtration coefficient [L−1]


Dimensionless initial filtration coefficient [–]


Size exclusion (straining) filtration coefficient [L−1]


Dimensionless size exclusion filtration coefficient [–]


Filtration coefficient [L2M−1]


Viscosity [ML−1T−1]





Maximum value





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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • G. V. C. Malgaresi
    • 1
  • H. Zhang
    • 1
  • C. V. Chrysikopoulos
    • 2
  • P. Bedrikovetsky
    • 1
    Email author
  1. 1.Australian School of PetroleumUniversity of AdelaideAdelaideAustralia
  2. 2.School of Environmental EngineeringTechnical University of CreteChaniaGreece

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