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The effect of pH and ionic strength on the transport of alumina nanofluids in water-saturated porous media

Experimental and modeling study
  • Maliheh Zareei
  • Hossein YoozbashizadehEmail author
  • Hamid Reza Madaah Hosseini
Article

Abstract

Alumina nanofluids are one of the most useful nanofluids, especially for increasing the thermal conductivity. Due to importance of porous media in the improvement of heat transfer, this study investigates the transport and retention of gamma alumina/water nanofluid in the water-saturated porous media. For this purpose, alumina nanofluids were introduced to the porous media consisting of water-saturated glass beads possessing various pH values (4, 7 and 10) and different ionic strengths (0.001 M of KCl, CaCl2, AlCl3, K2SO4, CaSO4, Al2(SO4)3, K2CO3 and CaCO3). Then the break through curve of each experiment was drawn and modeled by combining classical filtration theory with advection–dispersion equation. Single collector efficiency (η0) and attachment efficiency (α) were calculated by classical filtration theory. Also curve fitting of experiments and modeling was achieved by minimizing the sum of squared residuals, to calculate retardation factor (R) and hydrodynamic dispersion coefficient (D) of each experiment. According to the results, in general, increase in pH and ionic strength will enhance the removal rate coefficient, retardation factor and retention while decreasing the steady-state break through concentration and the hydrodynamic dispersion coefficient. The opposite of this rule was observed and analyzed for aluminum salts. The lowest retention of nanoparticles at 31.04% can be related to their transport in background solution with pH = 4 [α = \(3.87 \times 10^{ - 2}\), Katt = \(3.33 \times 10^{ - 3}\) (min−1), R = 3.93, D = 0.91 (cm2 min−1)], and the highest retention in nanoparticle content of 94.29% was observed in background solution containing CaCO3 [α = \(14.33 \times 10^{ - 2}\), Katt = \(137.82 \times 10^{ - 3}\) (min−1), R = 12.02, D = 0.62 (cm2 min−1)]. Therefore, chemistry of water plays an important role in transport and retention parameters. The classical filtration theory and the advection–dispersion model are able to perfectly model and quantify the parameters of the alumina nanofluid transport in saturated porous media.

Keywords

Alumina nanofluid Porous media ADE model CFT Transport Retention 

List of symbols

mass%

Mass percentage

\(C\)

Concentration of nanoparticles (Kg m−3)

\(C_{\text{e}}\)

Steady-state concentration (Kg m−3)

\(C_{0}\)

Concentration in influent fluid (Kg m−3)

\(C_{\text{eff}}\)

Concentration in effluent fluid (Kg m−3)

\(t\)

Time (s)

\(t_{\text{f}}\)

Total time of injection (s)

\(x\)

Distance parallel to the flow (m)

\(R\)

Retardation factor

\(k_{\text{att}}\)

Deposition rate coefficient (s−1)

\(D\)

Dispersion coefficient (m2 s−1)

\(K_{\text{d}}\)

Partitioning coefficient (m3 Kg−1)

\(L\)

Length of porous media (m)

\(M_{\text{rec}}\)

Recovered mass of nanoparticles (Kg)

\(M_{\text{i}}\)

Total injected mass (Kg)

\(Q\)

Velocity (m s−1)

\(\% R_{\text{rec}}\)

Recovery percent of nanoparticles

\(\% R_{\text{ret}}\)

Retention percent of nanoparticles

\(d_{\text{c}}\)

Collector diameter (m)

Greek symbols

\(v\)

Pore velocity (m s−1)

θ

Porosity

\(\rho_{\text{b}}\)

Bulk density (Kg m−3)

\(\eta_{0}\)

Single collector efficiency

\(\eta_{\text{D}}\)

Diffusion efficiency

\(\eta_{\text{I}}\)

Interception efficiency

\(\eta_{\text{G}}\)

Gravity efficiency

\(\alpha\)

Attachment efficiency

Abbreviations

PV

Pore volume

CFT

Classical filtration theory

ADE

Advection–dispersion equation

BTC

Break through curve

SSR

Sum of squared residuals

Notes

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Maliheh Zareei
    • 1
  • Hossein Yoozbashizadeh
    • 2
    Email author
  • Hamid Reza Madaah Hosseini
    • 2
  1. 1.Department of Materials Science and Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Materials Science and EngineeringSharif University of TechnologyTehranIran

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