Modeling the Transport of Hazardous Colloidal Suspensions of Nanoparticles Within Soil of Landfill Layers Considering Multicomponent Interactions

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The technological applications of the newly developed nanoparticles are continuously increasing. Nevertheless, their reduced size forming colloidal suspensions may facilitate the transport and bioaccumulation in the environment. The particular properties of each nanoparticle and its interaction with the dissolved organic matter (DOM) and the living organisms are important issues in this scenario. The landfill waste disposal method is still worldwide dominant. In the landfill, the nanoparticles can undergo phenomena such as leaching, agglomeration, flocculation, complexation, adsorption, dissolution, and neoformations. Among the concerns, it is recognized that the nanoparticles behave as carriers for the contaminants in the environment strongly impacting the water resources. This research is focused on the development of a mathematical model having an ability to predict the transports of TiO2, SiO2, ZnO, and CuO nanoparticles and their mutual interactions within soils commonly used as protective layers of controlled landfill for municipal waste disposal. A combined methodology based on numerical procedures using inverse method principles, and controlled experimental column experiments are carried out. First, the model parameters are determined, and second, the model is validated against numerical and experimental data. The model formulated newly address the interactions phenomena of colloidal suspensions of nanoparticles percolating through protective layers of landfill soils. It has been found that SiO2 nanoparticles presented the strongest deleterious effect on the efficiency of the soil protective layers, while ZnO plays a positive role promoting flocculation and complexation with soil particles and enhance their effectiveness.

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C d :

Drag coefficient for liquid motion in wet porous media (–)

\( f\left( {\varepsilon_{\text{s}} ,\;P_{\text{s}} ,\;d_{\text{s}} } \right) \) :

Volume compaction function due to soil packing arrangement, compaction pressure, and particle’s diameter (m3 m−3)

\( F_{j}^{\text{S}} \) and \( F_{j}^{\text{L}} \) :

Interaction forces on the liquid or solid phase acting on the j direction (j = 1, 2, 3) (N m−3)

d s :

Soil average particle diameter (m)

\( D_{i}^{\text{L}} \) and \( D_{i}^{\text{s}} \) :

Apparent diffusion coefficients of the nanoparticle species, respectively, in the liquid and solid phases (m2 s−1)

\( g_{j} \) :

Gravity acceleration component (j = 1, 2, 3) (m s−2)

\( k_{i}^{\text{Leaching}} \) :

Rate constant of the mass transfer of nanoparticles species due to leaching from soil to colloidal suspension (i = TiO2, SiO2, CuO, ZnO) (s−1)

\( k_{i}^{\text{ad}} \) :

Rate constant of the mass transfer of nanoparticles species due to adsorption/desorption from colloidal suspension on the soil particle surfaces (i = TiO2, SiO2, CuO, ZnO) (s−1)

\( k_{i}^{\text{adh}} \) :

Rate constant of the mass transfer of nanoparticles species due to adhesion from colloidal suspension on the soil particle surfaces (i = TiO2, SiO2, CuO, ZnO) (s−1)

\( k_{i}^{\text{c}} \) :

Rate constant of the mass transfer of nanoparticles species due to complexation, reactions, and neoformation from colloidal suspension on the soil particle surfaces (i = TiO2, SiO2, CuO, ZnO) (s−1)

P s :

Compaction pressure (Pa)

\( r_{\text{h}} \) :

Hydraulic radius (m)

\( \text{Re}_{\text{L}} \) :

Modified soil particle Reynolds number (–)

\( S_{i} = S_{i}^{\text{Leaching}} \; + \;S_{i}^{\text{ad}} \; + \;S_{i}^{\text{adh}} \; + \;S_{i}^{\text{c}} \) :

Overall sources or sinks of nanoparticles species (i = TiO2, SiO2, CuO, ZnO) (kg m−3 s−1)

\( {\text{Sc}}_{i} \) :

Modified nanoparticles Schmidt dimensionless number (–)

\( {\text{Sh}}_{i} \) :

Modified nanoparticles Sherwood dimensionless number (–)

t :

Time (s)

\( u_{j}^{L} \) and \( u_{j}^{\text{s}} \) :

Velocity components of the liquid and solid phases (j = 1,2,3) (s)

\( x_{k} \) :

Spatial coordinate system (k = 1, 2, 3) (m)

\( \varepsilon_{\text{L}} \), \( \varepsilon_{\text{s}} \) and \( \varepsilon_{\text{air}} \) :

Phase volume fractions of liquid, solid, and air, respectively (–)

\( \rho_{\text{L}} \) and \( \rho_{\text{s}} \) :

Phase apparent densities of liquid and solid, respectively (kg m−3)

\( \varphi_{i} \) :

Mass fraction of the nanoparticles species (i = TiO2, SiO2, CuO, ZnO) (kg kg−1)

\( \phi_{\text{s}} \) :

Soil particles shape factor (–)

\( \mu_{\text{L}} \) :

Liquid-phase apparent viscosity (Pa.s)

\( \xi_{\text{s}} \) :

Soil structure tortuosity factor (–)

\( \varTheta_{\text{ad}} \) :

Fractions of activated sites for adsorption in the soil structure (–)


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The authors acknowledge the financial support of agencies: CAPES—Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil; CNPq—National Council for Scientific and Technological Development; and Faperj-Rio de Janeiro Research Foundation.


This study was funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro.

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Correspondence to Amauri Garcia.

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de Oliveira, E.M., do Carmo Paresque, M.C., Ferreira, I.L. et al. Modeling the Transport of Hazardous Colloidal Suspensions of Nanoparticles Within Soil of Landfill Layers Considering Multicomponent Interactions. J. Sustain. Metall. 5, 581–593 (2019).

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  • Nanoparticles
  • Adsorption
  • Modeling
  • Multicomponent interactions
  • Soil landfill layers