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

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Abstract

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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Abbreviations

CFT:

Colloid filtration theory

DLVO:

Derjaguin–Landau–Verwey–Overbeek

EDL:

Electrostatic double-layer

VdW:

Van der Waals

CDC:

Critical deposition concentration

CRC:

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]

CDC:

Critical deposition concentration [M L−3]

CRC:

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]

V EDL :

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

V TOT :

Total interaction energy [M L2 T−2]

V VdW :

Van der Waals interaction [M L2 T−2]

v :

Effective flow velocity [L T−1]

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Acknowledgments

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.

Conflict of interest

No competing financial interests exist

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  1. A. Tiraferri

    Present address: Department of Chemical and Environmental Engineering, Yale University, New Haven, CT, 06520-8286, USA

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  1. Dipartimento di Ingegneria del Territorio, dell’Ambiente e delle Geotecnologie (DITAG), Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129, Turin, Italy

    A. Tiraferri, T. Tosco & 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). https://doi.org/10.1007/s12665-010-0755-4

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