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Transport and retention of microparticles in packed sand columns at low and intermediate ionic strengths: experiments and mathematical modeling


Functional relationships correlating particle filtration coefficients and porewater ionic strength are herein proposed and validated, based on deposition experiments of micrometer-sized particles onto siliceous sand. Experiments were conducted using one-dimensional laboratory columns and stable monodisperse aqueous suspensions of negatively charged latex particles with a mean size of 1.90 μm. The role of ionic strength was systematically investigated and six different monovalent salt concentrations (1, 3, 10, 30, 100, 300 mM) were employed by addition of sodium chloride to the aqueous solution. A mathematical advection–dispersion-deposition transport model was adopted assuming that attachment and detachment of particles in the porous medium are concurrent mechanisms of particle filtration, and including a Langmuir-type blocking function to account for availability in deposition sites. The system of equations modeling colloid transport was solved numerically. Attachment rate and detachment rate coefficients were thereby determined for each employed ionic strength, as well as a blocking coefficient in the form of a maximum particle concentration in the solid phase. Therefore, functional relationships expressing the dependence of these coefficients on ionic strength were proposed, based on literature findings and present experimental observations. The existence of a critical salt deposition concentration (and release concentration) separating a favorable attachment (and detachment) regime from an unfavorable condition is assumed. In respect to the blocking coefficient, a power–law dependence on ionic strength is hypothesized. The proposed functional relationships proved adequate to reproduce the coefficient trends extrapolated from data fitting by the transport model. They may represent a powerful tool to describe and predict microparticle mobility in saturated porous media if embedded a priori in the related mathematical transport models.

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Colloid filtration theory




Electrostatic double-layer


Van der Waals


Critical deposition concentration


Critical release concentration

α :

Attachment efficiency [–]

βa, βd, βS :

Fitting exponents for k a, k d, s max models [–]

γ s :

Fitting coefficient for s max [–]

ε 0 :

Permittivity of free space [M−1 L−3 T4E2]

ε r :

Relative permittivity [–]

η0 :

Single-collector contact efficiency for favorable deposition [–]

Θ :

Mean fractional collector surface coverage [–]

θ :

Fractional collector surface coverage [–]

κ :

Debye–Huckel reciprocal length [L−1]

λ :

Characteristic Van der Waals interaction wavelength [L]

ρ b :

Bulk density of the solid matrix [M L−3]

ρ p :

Density of the latex colloids [M L−3]

ϕ 1 :

Particle surface potential [M L2 T−3 E−1]

ϕ 2 :

Collector surface potential [M L2 T−3 E−1]

ψ :

Blocking function [–]

A :

Hamaker constant [M L2 T−2]

A 123 :

Hamaker constant for latex–silica interaction [M L2 T−2]

A 11 :

Hamaker constant for silica [M L2 T−2]

A 22 :

Hamaker constant for water [M L2 T−2]

A 33 :

Hamaker constant for latex [M L2 T−2]


Critical deposition concentration [M L−3]


Critical release concentration [M L−3]

c :

Particle concentration in the liquid phase [L−3]

c 0 :

Influent particle concentration [L−3]

D :

Hydrodynamic dispersion coefficient [L2 T−1]

d 50 :

Average diameter of the collector grains [L]

d p :

Average diameter of the colloidal particles [L]

h :

Surface-to-surface separation distance [L]

I :

Ionic strength [M L−3]

k a :

Attachment coefficient [T−1]

k a,∞ :

Asymptotic attachment coefficient in k a model [T−1]

k d :

Detachment coefficient [T−1]

k d,0 :

Asymptotic detachment coefficient in k d model [T−1]

n :

Packed bed porosity [–]

L :

Length of the column [L]

Pe :

Peclet number [–]

PV :

Pore volume [L3]

PVt :

Breakthrough time of 1 pore volume [T]

q :

Darcian velocity [L T−1]

s :

Number of particles retained per dry unit mass of sand [M−1]

s fin :

Final number of particles retained per dry unit mass of sand in the column [M−1]

s max :

Maximum concentration on the solid phase [M−1]


Electrical double-layer interaction [M L2 T−2]


Total interaction energy [M L2 T−2]

V VdW :

Van der Waals interaction [M L2 T−2]

v :

Effective flow velocity [L T−1]


  • Adamczyk Z, Siwek B, Zembala M, Belouschek P (1994) Kinetics of localized adsorption of colloid particles. Adv Colloid Interface Sci 48:151–280

    Article  Google Scholar 

  • Bales RC, Hinkle SR, Kroeger TW, Stocking K, Gerba CP (1991) Bacteriophage adsorption during transport through porous-media–chemical perturbations and reversibility. Environ Sci Technol 25(12):2088–2095

    Article  Google Scholar 

  • Bauer RD, Rolle M, Kurzinger P, Grathwohl P, Meckenstock RU, Griebler C (2009) Two-dimensional flow-through microcosms–versatile test systems to study biodegradation processes in porous aquifers. J Hydrol 369(3–4):284–295. doi:10.1016/j.jhydrol.2009.02.037

    Article  Google Scholar 

  • Bradford SA, Yates SR, Bettahar M, Simunek J (2002) Physical factors affecting the transport and fate of colloids in saturated porous media. Water Resour Res 38(12):1327. doi:10.1029/2002wr001340

    Google Scholar 

  • Bradford SA, Simunek J, Bettahar M, Van Genuchten MT, Yates SR (2003) Modeling colloid attachment, straining, and exclusion in saturated porous media. Environ Sci Technol 37(10):2242–2250. doi:10.1021/Es025899u

    Article  Google Scholar 

  • Bradford SA, Simunek J, Bettahar M, van Genuchten MT, Yates SR (2006) Significance of straining in colloid deposition: Evidence and implications. Water Resour Res 42(12):W12s15. doi:10.1029/2005wr004791

  • Bunn RA, Magelky RD, Ryan JN, Elimelech M (2002) Mobilization of natural colloids from an iron oxide-coated sand aquifer: effect of ph and ionic strength. Environ Sci Technol 36(3):314–322

    Article  Google Scholar 

  • Camesano TA, Logan BE (1998) Influence of fluid velocity and cell concentration on the transport of motile and nonmotile bacteria in porous media. Environ Sci Technol 32(11):1699–1708

    Article  Google Scholar 

  • Coleman TF, Li YY (1996) An interior trust region approach for nonlinear minimization subject to bounds. SIAM J Optim 6(2):418–445

    Article  Google Scholar 

  • Comba S, Sethi R (2009) Stabilization of highly concentrated suspensions of iron nanoparticles using shear-thinning gels of xanthan gum. Water Res 43(15):3717–3726. doi:10.1016/j.watres.2009.05.046

    Article  Google Scholar 

  • Dalla Vecchia E, Coisson M, Appino C, Vinai F, Sethi R (2009a) Magnetic characterization and interaction modeling of zerovalent iron nanoparticles for the remediation of contaminated aquifers. J Nanosci Nanotechnol 9(5):3210–3218. doi:10.1166/Jnn.2009.047

    Article  Google Scholar 

  • Dalla Vecchia E, Luna M, Sethi R (2009b) Transport in porous media of highly concentrated iron micro- and nanoparticles in the presence of xanthan gum. Environ Sci Technol 43(23):8942–8947. doi:10.1021/Es901897d

    Article  Google Scholar 

  • Elimelech M (1991) Kinetics of capture of colloidal particles in packed beds under attractive double layer interactions. J Colloid Interface Sci 146(2):337–352

    Google Scholar 

  • Elimelech M, O’Melia CR (1990) Kinetics of deposition of colloidal particles in porous-media. Environ Sci Technol 24(10):1528–1536

    Article  Google Scholar 

  • Elimelech M, Gregory J, Jia X, Williams RA (1995) Particle deposition and aggregation. Butterworth, Heinemann

    Google Scholar 

  • Gregory J (1981) Approximate expressions for retarded vanderwaals interaction. J Colloid Interface Sci 83(1):138–145

    Article  Google Scholar 

  • Grolimund D, Borkovec M, Barmettler K, Sticher H (1996) Colloid-facilitated transport of strongly sorbing contaminants in natural porous media: a laboratory column study. Environ Sci Technol 30(10):3118–3123

    Article  Google Scholar 

  • Grolimund D, Elimelech M, Borkovec M (2001) Aggregation and deposition kinetics of mobile colloidal particles in natural porous media. Colloids Surf A Physicochem Eng Aspects 191(1–2):179–188

    Article  Google Scholar 

  • Hogg R, Healy TW, Fuersten, Dw (1966) Mutual coagulation of colloidal dispersions. Trans Faraday Soc 62(522P):1638–1651

    Google Scholar 

  • Hunter RJ (2001) Foundations of colloid science. Oxford University Press, New York

    Google Scholar 

  • Johnson PR, Elimelech M (1995) Dynamics of colloid deposition in porous-media–blocking based on random sequential adsorption. Langmuir 11(3):801–812

    Article  Google Scholar 

  • Johnson WP, Li XQ, Yal G (2007) Colloid retention in porous media: mechanistic confirmation of wedging and retention in zones of flow stagnation. Environ Sci Technol 41(4):1279–1287. doi:10.1021/Es061301x

    Article  Google Scholar 

  • Khilar KC, Fogler HS (1984) The existence of a critical salt concentration for particle release. J Colloid Interf Sci 101(1):214–224

    Article  Google Scholar 

  • Ko CH, Elimelech M (2000) The “Shadow effect” in colloid transport and deposition dynamics in granular porous media: measurements and mechanisms. Environ Sci Technol 34(17):3681–3689. doi:10.1021/Es0009323

    Article  Google Scholar 

  • Kosmulski M, Maczka E, Janusz W, Rosenholm JB (2002) Multiinstrument study of the electrophoretic mobility of quartz. J Colloid Interf Sci 250(1):99–103. doi:10.1006/jcis.2002.8330

    Article  Google Scholar 

  • Kretzschmar R, Borkovec M, Grolimund D, Elimelech M (1999) Mobile subsurface colloids and their role in contaminant transport. Adv Agron 66:121–193

    Google Scholar 

  • Kuznar ZA, Elimelech M (2007) Direct microscopic observation of particle deposition in porous media: role of the secondary energy minimum. Colloids Surf Physicochem Eng Aspects 294(1–3):156–162. doi:10.1016/j.colsurfa.2006.08.007

    Article  Google Scholar 

  • Lenhart JJ, Saiers JE (2003) Colloid mobilization in water-saturated porous media under transient chemical conditions. Environ Sci Technol 37(12):2780–2787. doi:10.1021/Es025788v

    Article  Google Scholar 

  • McCarthy JF, McKay LD (2004) Colloid transport in the subsurface: past, present, and future challenges. Vadose Zone J 3(2):326–337

    Google Scholar 

  • Milano G, Guerra G (2009) Understanding at molecular level of nanoporous and co-crystalline materials based on syndiotactic polystyrene. Prog Mater Sci 54(1):68–88. doi:10.1016/j.pmatsci.2008.07.001

    Article  Google Scholar 

  • Nowack B, Bucheli TD (2007) Occurrence, behavior and effects of nanoparticles in the environment. Environ Pollut 150(1):5–22. doi:10.1016/j.envpol.2007.06.006

    Article  Google Scholar 

  • Ouyang Y, Shinde D, Mansell RS, Harris W (1996) Colloid-enhanced transport of chemicals in subsurface environments: a review. Crit Rev Environ Sci Technol 26(2):189–204

    Article  Google Scholar 

  • Pelley AJ, Tufenkji N (2008) Effect of particle size and natural organic matter on the migration of nano- and microscale latex particles in saturated porous media. J Colloid Interface Sci 321(1):74–83. doi:10.1016/j.jcis.2008.01.046

    Article  Google Scholar 

  • Privman V, Frisch HL, Ryde N, Matijevic E (1991) Particle adhesion in model systems. 13. Theory of multilayer deposition. J Chem Soc Faraday Trans 87(9):1371–1375

    Article  Google Scholar 

  • Redman JA, Walker SL, Elimelech M (2004) Bacterial adhesion and transport in porous media: role of the secondary energy minimum. Environ Sci Technol 38(6):1777–1785. doi:10.1021/Es0348871

    Article  Google Scholar 

  • Rolle M, Eberhardt C, Chiogna G, Cirpka OA, Grathwohl P (2009) Enhancement of dilution and transverse reactive mixing in porous media: experiments and model-based interpretation. J Contam Hydrol 110(3–4):130–142. doi:10.1016/j.jconhyd.2009.10.003

    Article  Google Scholar 

  • Ryan J, Elimelech M (1996) Colloid mobilization and transport in groundwater. Colloids Surf Physicochem Eng Aspects 107:1–56

    Article  Google Scholar 

  • Ryan JN, Elimelech M, Baeseman JL, Magelky RD (2000) Silica-coated titania and zirconia colloids for subsurface transport field experiments. Environ Sci Technol 34(10):2000–2005

    Article  Google Scholar 

  • Saiers JE, Ryan JN (2006) Introduction to special section on colloid transport in subsurface environments. Water Resour Res 42(12):W12s01. doi:10.1029/2006wr005620

  • Schijven JF, Hassanizadeh SM (2000) Removal of viruses by soil passage: overview of modeling, processes, and parameters. Crit Rev Environ Sci Technol 30(1):49–127

    Article  Google Scholar 

  • Simunek J, van Genuchten MT, Sejna M (2005) The hydrus-1d software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media. United States Department of Environmental Sciences, University of California Riverside, Riverside, California

  • Song L, Elimelech M (1993) Dynamics of colloid deposition in porous-media–modeling the role of retained particles. Colloids Surf A Physicochem Eng Aspects 73:49–63

    Article  Google Scholar 

  • Tiraferri A, Sethi R (2008) Enhanced transport of zerovalent iron nanoparticles in saturated porous media by guar gum. J Nanopart Res. doi:10.1007/s11051-008-9405-0

  • Torkzaban S, Tazehkand SS, Walker SL, Bradford SA (2008) Transport and fate of bacteria in porous media: coupled effects of chemical conditions and pore space geometry. Water Resour Res 44(4):W04403. doi:10.1029/2007wr006541

  • Tosco T, Sethi R (2009) Mnm1d: a numerical code for colloid transport in porous media: Implementation and validation. Am J Environ Sci 5(4):517–525

    Article  Google Scholar 

  • Tosco T, Sethi R (2010) Transport of non-newtonian suspensions of highly concentrated micro- and nanoscale iron particles in porous media: a modeling approach. Environ Sci Technol (submitted)

  • Tosco T, Tiraferri A, Sethi R (2009) Ionic strength dependent transport of microparticles in saturated porous media: modeling mobilization and immobilization phenomena under transient chemical conditions. Environ Sci Technol 43(12):4425–4431. doi:10.1021/Es900245d

    Article  Google Scholar 

  • Tufenkji N (2006) Application of a dual deposition mode model to evaluate transport of escherichia coli d21 in porous media. Water Resour Res 42(12):W12s11. doi:10.1029/2005wr004851

  • Tufenkji N (2007) Modeling microbial transport in porous media: traditional approaches and recent developments. Adv Water Resour 30(6–7):1455–1469. doi:10.1016/j.advwatres.2006.05.014

    Article  Google Scholar 

  • Tufenkji N, Elimelech M (2004a) Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ Sci Technol 38(2):529–536

    Article  Google Scholar 

  • Tufenkji N, Elimelech M (2004b) Deviation from the classical colloid filtration theory in the presence of repulsive dlvo interactions. Langmuir 20(25):10818–10828. doi:10.1021/La0486638

    Article  Google Scholar 

  • Tufenkji N, Elimelech M (2005a) Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities. Langmuir 21(3):841–852. doi:10.1021/La048102g

    Article  Google Scholar 

  • Tufenkji N, Elimelech M (2005b) Spatial distributions of cryptosporidium oocysts in porous media: evidence for dual mode deposition. Environ Sci Technol 39(10):3620–3629. doi:10.1021/Es048289y

    Article  Google Scholar 

  • Tufenkji N, Redman J, Elimelech M (2003) Interpreting deposition patterns of microbial particles in laboratory-scale column experiments. Environ Sci Technol 37(3):616–623

    Article  Google Scholar 

  • Tufenkji N, Dixon DR, Considine R, Drummond J (2006) Multi-scale cryptosporidium/sand interactions in water treatment. Water Res 40(18)

  • Turner NB, Ryan JN, Saiers JE (2006) Effect of desorption kinetics on colloid-facilitated transport of contaminants: Cesium, strontium, and illite colloids. Water Resour Res 42(12):W12s09. doi:10.1029/2006wr004972

  • van Genuchten MT (1981) Non-equilibrium transport parameters from miscible displacement experiments. vol Research Report n° 119. United States Department of Agriculture Science and Education Administration, US Salinity Laboratory, Riverside, California

  • Xu SP, Gao B, Saiers JE (2006) Straining of colloidal particles in saturated porous media. Water Resour Res 42(12):W12s216. doi:10.1029/2006wr004948

  • Yao K-M, Habibian MT, O’Melia CR (1971) Water and waste water filtration: concepts and applications. Environ Sci Technol 5:1105–1112

    Article  Google Scholar 

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This work was partially supported by the Project CIPE-C30 funded by Regione Piemonte, Italy. The authors wish to thank Dr. Daniele Marchisio at DISMIC Department, Politecnico di Torino (Torino), for the kind permission to use the DLS instruments, and Alberto Marnetto for the assistance in the development of numerical code.

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Correspondence to Rajandrea Sethi.

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Tiraferri, A., Tosco, T. & Sethi, R. Transport and retention of microparticles in packed sand columns at low and intermediate ionic strengths: experiments and mathematical modeling. Environ Earth Sci 63, 847–859 (2011).

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  • Modeling particle transport
  • Ionic strength
  • Saturated sand columns
  • Filtration theory
  • Porous media
  • Particle deposition