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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

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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.

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Abbreviations

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)

\(v\) :

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

PV:

Pore volume

CFT:

Classical filtration theory

ADE:

Advection–dispersion equation

BTC:

Break through curve

SSR:

Sum of squared residuals

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Maliheh Zareei

  2. Department of Materials Science and Engineering, Sharif University of Technology, Tehran, Iran

    Hossein Yoozbashizadeh & Hamid Reza Madaah Hosseini

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  1. Maliheh Zareei
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  2. Hossein Yoozbashizadeh
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Correspondence to Hossein Yoozbashizadeh.

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Zareei, M., Yoozbashizadeh, H. & Madaah Hosseini, H.R. The effect of pH and ionic strength on the transport of alumina nanofluids in water-saturated porous media. J Therm Anal Calorim 137, 1169–1179 (2019). https://doi.org/10.1007/s10973-018-08002-w

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