Enhancement of SiO2 based nanofluid stability and thermophysical properties using surface active ionic liquids
Elaheh Janbezar, Hemayat Shekaari, Mohammed Taghi Zafarani-Moattar
TL;DR
This study shows that using a specific ionic liquid, THEA-Ole, significantly improves the long-term stability and performance of SiO2 nanofluids.
Contribution
THEA-Ole is shown to stabilize SiO2 nanofluids for over 60 days, surpassing conventional surfactants and typical stability limits.
Findings
THEA-Ole provides minimal sedimentation and optimal dispersity in SiO2 nanofluids.
THEA-Ole nanofluids exhibit high zeta potential and stable viscosity trends.
PC-SAFT model confirms strong SiO2 interactions with THEA-Ole.
Abstract
This study addresses the challenge of achieving long-term colloidal stability in SiO2 nanofluids, a critical barrier for their practical applications, by investigating the stabilizing effects of surface-active ionic liquids (SAILs) on aqueous SiO2 nanoparticle dispersions. The purpose is to evaluate how SAILs specifically (2-hydroxyethyl)ammonium oleate (HEA-Ole), bis(2-hydroxyethyl)ammonium oleate (BHEA-Ole), and tris(2-hydroxyethyl)ammonium oleate (THEA-Ole) can enhance SiO2 stability beyond typical literature reports of less than 20 days. The stability was assessed through excess molar volume (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…
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Taxonomy
TopicsIonic liquids properties and applications · Nanofluid Flow and Heat Transfer · Enhanced Oil Recovery Techniques
Introduction
The increasing heat generation in modern energy, electronics, and power generation systems presents a major challenge for maintaining efficiency and system reliability. High heat fluxes can reduce the performance of conventional cooling methods, accelerate material degradation, and shorten component lifespan. This has created a strong need for fluids with improved heat transfer properties [1]. In this context, nanofluids are a suspension of nanoparticles (1–100 nm) in base liquids have emerged as a promising solution. The high specific surface area of nanoparticles, combined with their unique phonon and electron transport characteristics and strong particle fluid interactions, enables significant enhancement of thermal conductivity and convective heat transfer [2]. Moreover, the thermal performance can be optimized by controlling particle size, shape, and concentration, which directly influence Brownian motion, micro convection, and phonon scattering within the fluid [3].
Considering these benefits, the stability of colloids remains a significant challenge in practical applications. Interparticle forces, including van der Waals attractions, may induce aggregation and sedimentation, affecting particle uniformity and impacting thermal performance. Various strategies have been employed to address this challenge, including surface functionalization of nanoparticles, polymer coatings, and the incorporation of surfactants [4]. Particle stability is also affected by environmental factors of temperature, pH, and ionic strength, emphasizing the importance of selecting effective stabilizing agents appropriate to operating conditions [5].
Surfactants' low cost, convenience of use, and capacity to stabilize nanoparticles at low concentrations make them very beneficial. Surfactants prevent aggregation and sedimentation by reducing interfacial tension and generating electrostatic or steric repulsive forces at the particle–fluid interface [6]. The choice of surfactant, its chain length, surface charge, and thermal stability are key determinants of overall nanofluid performance. Latest research indicate that surfactants can provide synergistic steric and electrostatic stabilization when combined with polymeric additives or surface-active ionic liquids, particularly in high-temperature or high-salinity conditions [7–10]. The selection of (2-hydroxyethyl) ammonium oleate (HEA-Ole), bis(2-hydroxyethyl) ammonium oleate (BHEA-Ole), and tris(2-hydroxyethyl) ammonium oleate (THEA-Ole) was motivated by their tunable amphiphilic structures and strong surface activity. These SAILs share a common oleate anion, which provides a long hydrophobic chain promoting adsorption onto the SiO_2_ surface, while the cationic moieties contain one, two, or three hydroxyethyl groups, respectively. The progressive increase in hydroxyethyl substitution enhances hydrophilicity, hydrogen-bonding capability, and electrostatic stabilization in aqueous media. This structural tunability enables systematic evaluation of how cation architecture influences micellization behavior, interfacial properties, and nanoparticle dispersion stability. Moreover, compared with conventional surfactants, these SAILs offer higher thermal stability, reduced volatility, and multifunctional stabilization mechanisms, making them particularly attractive for advanced nanofluid formulations [7–10].
Among the various nanoparticles, silicon dioxide (SiO_2_) is widely employed due to its abundance, low cost, chemical stability, and biocompatibility. Hydroxyl groups on the SiO_2_ surface allow chemical modification and strong interaction with surfactants, enhancing particle dispersion, prolonging colloidal stability, and reducing undesirable reactions under operating conditions [11]. Furthermore, the tunable surface chemistry of SiO_2_ allows functionalization for targeted thermal pathways, interaction with other additives, and optimization of viscosity and rheological properties for specific applications [12, 13].
While oxide-based nanofluids have demonstrated significant improvements in heat transfer performance, detailed investigations into surfactant adsorption mechanisms on SiO_2_ surfaces, their influence on the stability of dilute nanofluids, and their effects on thermodynamic and rheological properties are still limited. Therefore, systematic studies are essential to advance understanding of stability mechanisms and to guide the rational design of high-performance nanofluids for industrial applications [14].
In this study, nanofluid systems including silicon oxide (SiO_2_) nanoparticles dispersed in aqueous solutions, with (2-hydroxyethyl) ammonium oleate (HEA-Ole), bis(2-hydroxyethyl) ammonium oleate (BHEA-Ole), and tris(2-hydroxyethyl) ammonium oleate (THEA-Ole) surface-active ionic liquids (SAILs) as base fluids, were examined. The thermodynamic performance and intermolecular interactions within these systems were comprehensively evaluated. The particle size change for investigated nanofluids were investigated by dynamic light scattering and zeta potential. The density, viscosity and surface tension of nanofluids including SiO_2_ nanoparticles have been measured at three distinct concentrations namely the before-CMC, in CMC and after-CMC of the SAILs in water at a temperature range of T = 298.15.15 K. In order to clarify the interactions within biphasic heterogeneous colloidal systems, the excess molar volume ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} ) was identified as an appropriate parameter for this analysis. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} values were analyzed through correlation with the Redlich–Kister, polynomial and Ott equations to effectively model the observed interactions. The PC-SAFT equation of state was used to achieve a suitable approach in microscopic scale from the studied systems. The Eyring-mNRF and Eyring-NRTL model has been successfully used to correlate the viscosity reported data. Lastly, we employ the Einstein, Batchelor, Brinkman, and Lundgren models to predict the viscosity data. The COSMO results provided valuable information such as the sigma profile (σ-profile), cavity surface area (A), total cavity volume (V), dielectric solvation energies, and HOMOLUMO levels were derived.
Material and methods
Materials
The materials utilized in this study including SiO_2_ nanoparticles (CAS no. 7631-86-9) with an average diameter of 20 nm and molar mass of 60.08 g mol^−1^, 2-hydroxyethylamine (CAS no. 141-43-5) with molar mass of 61.08 g mol^−1^, bis(2-hydroxyethyl) amine (CAS no. 111-42-2) with molar mass of 105.14 g mol^−1^, tris(2-hydroxyethyl) amine (CAS no. 102-71-6) with molar mass of 149.19 g mol^−1^, oleic acid (CAS no. 112-80-1) with molar mass of 318.13 g mol^−1^, was obtained from Merck with purity of > 99% (The related SiO_2_ XRD parameters along with its peak have been provided respectfully within Table S1 and Fig. S1) (2-hydroxyethyl)ammonium oleate with molar mass of 343.55 g mol^−1^, bis(2-hydroxyethyl)ammonium oleate with molar mass of 387.33 g mol^−1^ and tris(2-hydroxyethyl)ammonium oleate with molar mass of 431.66 g mol^−1^ were synthesized as surface active ionic liquids (SAILs). Double distilled, deionized water was used in preparation of nanofluids.
Preparation of SAILs and nanofluids
Surface-active ionic liquids (SAILs) were synthesized via acid–base neutralization of oleic acid with 2-hydroxyethylamine (2-HEA), bis(2-hydroxyethyl)amine (BHEA), and tris(2-hydroxyethyl)amine (THEA) in equimolar (1:1) ratios, yielding HEA-Ole, BHEA-Ole, and THEA-Ole, respectively. Initially, oleic acid was introduced into a reaction vessel and heated to 323–333 K under continuous stirring to obtain a homogeneous liquid phase. The corresponding ethanolamine was then added dropwise while maintaining constant agitation. The neutralization reaction was exothermic; therefore, careful temperature control was applied to prevent overheating, with the reaction temperature maintained below 343 K. Following complete addition of the ethanolamine, the reaction mixture was further stirred at 333–343 K for 2–4 h to ensure completion. During the reaction, a gradual color change from yellow to light brown and a notable increase in viscosity were observed. The physicochemical characteristics of the resulting SAILs depended on the ethanolamine structure: HEA-Ole exhibited moderate viscosity, BHEA-Ole formed a more viscous liquid with enhanced surface activity, and THEA-Ole demonstrated pronounced emulsifying behavior. After completion, the products were subjected to vacuum drying and heated at 313–323 K to remove residual volatiles. Structural integrity and purity (> 98%) were confirmed by FT-IR and FT-NMR spectroscopy (Figs. S2–S7).
For Preparation of the Nanofluids, SiO_2_ nanoparticles were dispersed in base fluids consisting of water combined with HEA-Ole, BHEA-Ole, or THEA-Ole at different molal concentrations (before, at and after the critical micelle concentration range of the studied SAILs in water). The SAILs were used at three concentrations namely the before CMC, at CMC, and after CMC, determined via surface tension and electrical conductivity measurements. The mixtures were accurately weighed and sonicated for one hour using an ultrasonic bath to ensure uniform dispersion and stability.
Determination of critical micelle concentration (CMC)
The critical micelle concentrations (CMC) of the SAILs were obtained from complementary measurements of electrical conductivity and surface tension analysis. In the electrical conductivity method, increasing surfactant concentration raises solution specific conductivity until micelle formation reduces the slope. The CMC values for aqueous nanofluids of HEA-Ole, BHEA-Ole, and THEA-Ole were 0.001323, 0.001264, and 0.001009 mol kg^−1^, respectively. The differences are related to molecular structure: HEA-Ole, with one hydroxyl group, forms micelles at higher concentration, whereas THEA-Ole, with three hydroxyl groups, forms micelles at lower concentrations due to enhanced hydrophilicity and hydrogen bonding (Fig. S9) [15, 16].
In surface tension method, increasing surfactant concentration decreases surface tension until the interface becomes saturated. Beyond this point, additional surfactant molecules enter the bulk, forming micelles, and the surface tension decline slows or stops. Extrapolating two linear regions of the surface tension curve provided CMC values consistent with the electrical conductivity method (Fig. S10). Using both methods together improves the reliability of CMC determination [8, 17].
Instruments and process
Visual observation
Nanofluid stability was assessed visually by monitoring turbidity and particle sedimentation over time. Samples were stored in transparent containers and observed periodically, typically every few days. This simple, rapid method provides an initial evaluation of stability and allows comparison between different nanofluids or the effects of stabilizing agents.
Density measurements
Nanofluids densities were determined using a digital vibrating U-tube densitometer (KYOTO ELECTRONICS DA210) with a resolution of ± 1 × 10^−5^ g cm^−3^. Measurements were performed at ambient pressure (0.087 MPa) with an uncertainty of ± 4 × 10^−4^ g cm^−3^. The instrument was calibrated beforehand using distilled water following the standard air–water calibration procedure.
Viscosity
The dynamic viscosity of SiO_2_ nanofluids was measured using an Ubbelohde-type capillary viscometer (Julabo, MD-18 V, Germany). Measurements were performed at 298.15 K with temperature controlled to ± 0.005 K using a built-in Peltier thermostat. Flow times were recorded with a stopwatch (accuracy 0.01 s), and each measurement was repeated at least five times. The viscometer constants were determined by calibrating with deionized water at different temperatures. The viscosity (η) were obtained by the following expression and the definitions of its parameters have given by:
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\eta }{\rho }=Lt-\frac{K}{t}$$\end{document}where L and K are the viscometer constants in Eq. (1). L, represents the pre-exponential factor related to molecular mobility, and K denotes the energy-related parameter associated with viscous flow. Also, ρ and t represents the density, and the flow time of the solution. For determining viscometer constants (L and K), deionized water viscosity and flow time of measured at different temperatures and fitting the experimental data.
Surface tension measurement
The surface tension measurements of the studied nanofluids were performed at 298.15 K utilizing a KRÜSS EasyDyne K20 tensiometer (KRÜSS GmbH, Germany) operating with the Wilhelmy plate technique. The measurement uncertainty was ± 0.01 mN m^−1^. The plate was carefully cleaned before each experiment using ultrapure water, acetone, and heating to red-hot. The CMC of the SAILs was determined from the inflection point of the surface tension versus molality curve.
Dynamic light scattering studies (DLS) and zeta potential
Nanofluids particle size distribution and zeta potential were measured using a Nanotrac Wave dynamic light scattering (DLS) instrument to evaluate nanoparticle stability. A laser beam illuminated the samples, and scattered light fluctuations were detected at a 90° angle. All measurements were performed under isothermal conditions at 298.15 K, with the temperature regulated to within ± 0.1 K.
Results and discussion
Experimental findings
Visual observation results
In this study, nanofluids containing silicon dioxide (SiO_2_) nanoparticles were prepared using different base fluids consisting of HEA-Ole, BHEA-Ole, THEA-Ole SAILs at three concentration regions: before CMC, at CMC, and after CMC. After one hour of ultrasonication, their stability was systematically monitored over a period of 60 days. Since SiO_2_, due to its wide band gap and dielectric nature, exhibits no distinct absorption in the UV–Vis region, direct evaluation of nanofluid stability by UV–Vis spectroscopy was not feasible. Therefore, interpretation required a complementary approach involving visual observation and other techniques.
Direct observations (Fig. S8) indicated that, in the initial storage period, most nanofluids remained visually uniform and turbid, with no obvious signs of nanoparticle sedimentation. Over time, however, this apparent equilibrium gradually deteriorated, and the particles progressively migrated out of suspension and settled. Among the investigated systems, SiO_2_-based nanofluids exhibited the highest stability when triethanolamine oleate was employed as the SAILs after the CMC concentrations. This behavior can be attributed to the surface chemistry of SiO_2_, particularly the presence of silanol groups, which are capable of forming extended hydrogen-bonding networks with the hydroxyl groups of the triethanolamine cation. In combination with the formation of stable micellar structures at higher concentrations, these interactions enhanced nanoparticle surface coverage, prevented secondary aggregation, and facilitated a more homogeneous dispersion [18–21].
In contrast, nanofluids lacking SAILs (SiO_2_–water systems) demonstrated very poor stability, maintaining dispersion for less than 48 h. This highlights the intrinsic inability of such systems to establish a protective interfacial layer around the nanoparticles to counteract van der Waals attractions and particle agglomeration, and therefore they were not further discussed [22–24].
The findings emphasize that nanofluid stability is governed by the interplay of three key factors: (1) the type and structure of the ionic liquid cation, (2) the surface chemistry of the nanoparticles, and (3) the concentration region of the surfactant relative to the CMC. The synergistic effect of these parameters particularly evident in the case of SiO_2_ plays a decisive role in modulating interparticle interactions, preventing sedimentation, and prolonging colloidal stability. These insights must be carefully considered in the rational design and optimization of nanofluid systems [25–28].
Density results
From the measured density data (presented in Table S5) of the studied systems at 298.15 K, the excess molar volume \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} , apparent molar volume Vφ have been obtained through the utilization of the Redlich-Kistler an Redlich-Mayer equations at ranges of before CMC, at CMC and after CMC of the studied aqueous nanofluid SAILs. Additionally, the density data has been further assessed by the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) [29, 30]. The superior performance of the THEA-Ole SAIL can be attributed to its higher hydrophilicity and enhanced hydrogen-bonding capability, arising from the presence of three hydroxyl groups on the tris(2-hydroxyethyl)ammonium cation. These functional groups promote strong hydrogen-bond interactions with both the oleate anion and the surface hydroxyl groups of SiO_2_ nanoparticles, leading to improved dispersion stability, stronger solvation, and more structured interfacial layers. This molecular feature underpins the trends observed in density, excess molar volume, viscosity, surface tension, and colloidal stability throughout this work [26, 27].
Excess molar volume (\documentclass[12pt]{minimal}
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In this work, the excess molar volume ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} **) **of the nanofluids was investigated and correlated using the Redlich–Kister equation (Eq. 2), the Ott et al. model (Eq. 3), and a polynomial equation (Eq. 4) at 298.15 K [31].
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V_{m}^{E} = x_{1} x_{2} \sum\limits_{h \ge 0} {A_{h} (x_{1} - x_{2} )^{h} } $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V_{m}^{E} = x_{2} (1 - x_{2} )\left[ {\exp ( - \gamma x_{2} )\sum\limits_{I = 0}^{1} {B_{I} } (1 - 2x_{2} )^{I} + (1 - \exp ( - \gamma x_{2} ))\sum\limits_{I = 0}^{3} {C_{I} } (1 - 2x_{2} )^{I} } \right] $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V_{m}^{E} = \sum\limits_{h \ge 0} {x_{1} x_{2} A_{h} (x_{1} )^{h} } $$\end{document}The standard deviations of the fittings for excess molar volume and density are reported in Table 1.Table 1. The Standard deviations ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document} ) from fitting the excess molar volume ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} ) values in equations Redlish-Kistler, polynomial and Ott for SiO_2_ nanofluids at 298.15 KRedlish-KistlerPolynomialOttTimeMethod 1Method 2Method 1Method 2Method 1Method 2σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ (d)/g cm^−3^σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ (d)/g cm^−3^σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ (d)/g cm^−3^σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ (d)/g cm^−3^σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ s (d)/g cm^−3^σ ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{e}$$\end{document} )/cm^3^ mol^−1^σ (d)/g cm^−3^SiO2-HEA-Ole30 min0.04780.05200.0008310.042630.008400.040900.000400.042600.008250.001060.002730.042502880 min0.12790.06300.0035320.0426230.012800.062500.000400.042600.008390.001090.002840.042495760 min0.12760.02200.0035250.0426410.012800.062500.000400.042600.008540.001110.002940.0424710,080 min0.13720.16300.0005610.0426330.012800.062500.000600.042600.008680.001140.003040.0424514,400 min0.57300.02600.0005820.042630.012800.062500.000100.042600.008830.001160.003150.0424428,800 min0.02770.02500.0005390.0426310.004200.062500.000400.042600.008970.001190.003250.0424236,000 min0.20000.07100.0000110.0419380.012400.061500.000000.042900.009120.001220.003360.0424143,200 min0.18520.04700.0002080.0419380.012400.061500.000100.042900.009260.001240.003460.0423950,400 min0.13680.05500.0002560.0419380.828300.061500.000100.042900.009410.001270.003570.0423740 Day0.03440.06200.0000140.0419380.126000.061500.000000.042900.009550.001290.003670.0423660 Day0.15550.0546− 0.000610.041800.329460.06562-0.000040.042960.009700.001320.003780.04234Overall0.15930.05820.000850.042300.124760.060450.000220.042740.008970.001190.003250.04242SiO2* -BHEA-Ole30 min0.17660.06350.00030.04330.00060.04160.00020.04330.010860.001530.004610.042222880 min0.17720.06350.00390.04330.00090.06350.00020.04330.011010.001550.004710.042205760 min0.17710.06350.00100.04330.00090.06350.00040.04330.011150.001580.004820.0421810,080 min0.10750.06350.00030.04330.00090.06350.00040.04330.011300.001610.004920.0421714,400 min0.11040.06350.00030.04330.00090.06350.00040.04330.011440.001630.005020.0421528,800 min0.17650.06350.00040.04330.00910.06350.00030.04330.011590.001660.005130.0421436,000 min0.17070.06320.05460.04310.15850.06320.05250.04340.011730.001680.005230.0421243,200 min0.20820.06320.05420.04310.15850.06320.05250.04340.011880.001710.005340.0421050,400 min0.21020.06320.05420.04310.15850.06320.05250.04340.012020.001740.005440.0420940 Day0.11600.06250.00070.04260.00180.06250.00060.04360.012170.001760.005550.0420760 Day0.17660.06350.00030.04330.00060.04160.00020.04330.012310.001790.005650.04206Overall0.1706110.0630110.0323220.0429640.0964290.0590290.0317020.0434530.0124570.0018150.0057550.04204SiO_2_ -THEA-Ole*30 min0.21570.06450.00120.044030.00080.04220.00010.0440.01090.00150.00460.04222880 min0.17420.06450.00560.044010.00130.06450.00010.0440.01100.00160.00470.04225760 min0.21570.06450.00350.044030.00130.06450.00010.0440.01120.00160.00480.042210,080 min0.21580.06450.00150.044020.00130.06450.00020.0440.01130.00160.00490.042214,400 min0.18460.06450.00060.044020.00130.06450.00060.0440.01140.00160.00500.042228,800 min0.21570.06450.00070.044020.00130.06450.00020.0440.01160.00170.00510.042136,000 min0.21580.06450.00060.044020.00210.06450.00010.0440.01170.00170.00520.042143,200 min0.21570.06450.00060.044020.00130.06450.00010.0440.01190.00170.00530.042150,400 min0.21580.06450.00070.044020.00130.06450.00010.0440.01200.00170.00540.042140 Day0.19880.06450.00050.044020.21700.06450.00020.0440.01220.00180.00550.042160 Day0.21570.06450.00120.044030.00080.04220.00010.0440.01230.00180.00560.0421Overall0.2075910.06450.0015180.0440220.0208910.0604450.0001730.0440.0115910.0016640.00510.0421
For the SiO_2_-based nanofluids, the polynomial equation (Eq. 3) exhibited the lowest standard deviation, confirming its superior accuracy in correlating excess molar volume and density data compared to the Redlich–Kister, Ott and Polynomial models. The corresponding fitting parameters are summarized in Tables (S2–S4). The fitting coefficients and standard deviations obtained from the Redlich–Kister, Ott, and polynomial correlations are summarized in Tables S2–S4. As shown in these tables, the polynomial model yields the lowest standard deviations for all SiO_2_–SAIL systems, confirming its superior ability to represent the ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} **) **data.
Analysis of excess molar volume data (Tables S2–S4) revealed that the negative values of ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} ) in most cases indicate dominant attractive interactions between unlike species (nanoparticle–SAILs, nanoparticle–water, and SAILs–water), leading to structural compactness of the solution and enhanced colloidal stability. These interactions primarily involve hydrogen bonding, electrostatic interactions, and the formation of stable micelles [32–35].
For the SiO_2_– THEA-Ole system after CMC, ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} ) values became more negative over time and remained stable during the 60-day period. This behavior is attributed to strong hydrogen-bonding interactions between the silanol groups (Si–OH) of SiO_2_ and the tri-hydroxylated [TEA]^+^ cation. Such interactions facilitate the formation of compact micellar structures with strong hydrophilic shells, which effectively encapsulate the nanoparticles and maintain a uniform dispersion. In contrast, in the SiO_2_– HEA-Ole and SiO_2_– BHEA-Ole systems after the CMC, ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{m}^{E}$$\end{document} ) values gradually became less negative (more positive), suggesting weakened unlike interactions, destabilization of micelles due to lower hydrophilicity, and increased nanoparticle aggregation [36–39].
The results indicates that the choice of SAILs plays a decisive role in nanofluid stability depending on the nanoparticle surface chemistry. Among the investigated systems, SiO_2_– THEA-Ole in the concentration range of after CMC demonstrated the highest colloidal stability due to strong hydrogen-bonding interactions and the formation of robust micellar structures [40–43].
Apparent molar volume
The apparent molar volume, Vφ (Eq. 5) [44], is a key parameter in these systems as it reflects structural changes in the solution in the presence of nanoparticles and SAILs, and it helps to better understand the colloidal stability and reduction of nanoparticle aggregation. The results of the apparent molar volume measurements are presented in Table S5. The apparent molar volume values of the investigated nanofluids are reported in Table S5. The more negative and stable Vφ values observed for the SiO_2_–THEA-Ole system indicates a compact solution structure and strong nanoparticle–SAIL interactions, consistent with enhanced colloidal stability.
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V\varphi = \frac{M}{d} - \left[ {\frac{{(d - d_{0} )}}{{mdd_{0} }}} \right] $$\end{document}Studies indicate that Vφ is crucial for assessing the effect of SAILs on the density and dispersion of nanoparticles and can be used to predict the long-term stability of the system. The apparent molar volume is also used to interpret interactions between system components, including surfactant adsorption on the nanoparticle surface, micelle formation, and hydrogen bonding or electrostatic interactions with the aqueous solvent. Negative Vφ values indicate a compact solution structure, resulting from strong adsorption interactions and reduced free molecular volume due to the organization of micelles and adsorbed layers [45].
In the studied systems, the Vφ data (shown in Table S5) for SiO_2_–THEA-Ole exhibit more negative and stable values, reflecting strong hydrogen bonding between the silanol groups on the SiO_2_ surface and the hydroxyl groups of THEA-Ole, as well as the formation of robust micelles, confirming the superior stability of this system [46–49]. Contrary, in systems such as SiO_2_–HEA-Ole and SiO_2_–BHEA-Ole, the increase in Vφ over time indicates weakened interactions and predominance of aggregation or sedimentation due to less stable micelles. The negative Vφ values in all systems indicate a compact solution structure and strong adsorption interactions, which are enhanced in the after CMC region due to surfactant migration into the aqueous phase and confinement of nanoparticles, thereby increasing colloidal stability [39].
PC-SAFT
The perturbed chain statistical associating fluid theory (PC-SAFT) models fluids as chains of spherical segments, enabling the accurate representation of chain-like molecules and self-associating systems (such as those involving hydrogen bonding) through second-order perturbation theory. Within the canonical ensemble framework (constant temperature, volume, and number of particles), the Helmholtz free energy expression serves as a fundamental basis for deriving the thermodynamic properties of such complex fluids [30, 50].
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ a = a^{hc} + a^{disp} + a^{assoc} $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ a^{hc} = ma^{hs} - \sum\limits_{i} {x_{i} } (m_{i} - 1)\ln (g^{hs} (\sigma )) $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ a^{disp} = - 2\pi I_{1} \overline{{m^{2} \varepsilon \sigma^{3} }} - \pi \rho mC_{1} I_{2} \overline{{m^{2} \varepsilon^{2} \sigma^{3} }} $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ a^{assoc} = \sum\limits_{i} {x_{i} } \left[ {\sum\limits_{{A_{i} }} {\left( {\ln X^{{A_{i} }} - \frac{{X^{{A_{i} }} }}{2}} \right)} + \frac{1}{2}M_{i} } \right] $$\end{document}Here, the superscripts hc and disp denote the hard-chain and dispersion contributions, respectively, while the term assoc represents the association contribution, which is evaluated using the standard SAFT equations [51–53]. The components of the equations are described in detail in the original references cited in the literature. The density can be determined using the following equation through iterative calculation with respect to pressure [54–56]:
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Z = 1 + \rho \left( {\frac{{\partial (a/K_{B} T)}}{\partial \rho }} \right) $$\end{document}where, ρ and Z are the number density and compressibility factor, respectively. The main parameters of this equation of state are segment number, m, segment diameter, σ, dispersion energy, u0/KB, association energy, εAB/K_B_, and effective association volume, κ_AB_. These parameters commonly obtained from the experimental vapor pressure or density data at different pressures and temperatures (P,T). However, there is some indirect methods to obtain these parameters. Recently, a new methodology has been introduced that could be used to predict these parameters with density functional theory results. This approach enables the theoretical estimation of equation-of-state parameters without reliance on experimental data. Researchers have utilized this relationship to derive the segment diameter an essential parameter from the cavity and surface area outputs of the complementary model [54–57].
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sigma = \frac{6V}{A} $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ m = \frac{A}{{\pi \sigma^{2} }} $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{{u_{0} }}{{K_{B} }} = \frac{a}{{\sigma^{6} }} + b $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{{\varepsilon^{AB} }}{{K_{B} }} = \frac{c}{{\sigma^{6} }} + d $$\end{document}Here, V denotes the cavity volume and A represents the corresponding cavity surface area. The parameters a, b, c, and d are obtained from the correlation of dispersion and association energies with literature data. The remaining symbols correspond to the standard PC-SAFT parameters. For the studied systems, the 2B association scheme was applied for SAILs, while the 4C scheme was used for water. The dipole term reflects the contribution of the components’ permanent dipole moments to the overall polar interactions within the system. The employed parameters segment number (m), segment diameter (σ), dispersion energy (ε/k_B_), association energy (εAiBi/k_B_), and effective association volume (κAiBi)—are listed in Table S6. The average relative deviation percentage (ARD%) represents the mean deviation between the predicted and experimental densities (Table S7), where lower ARD% values indicate higher predictive accuracy. For SiO_2_ in aqueous SAIL nanofluids, the PC-SAFT model yields ARD% values in the range of 1–4%, demonstrating satisfactory predictive performance. The ARD% values were lowest for SiO_2_ nanoparticles in the presence of the aqueous THEA-Ole nanofluids solutions [54–57]. Additionally, the results have been provided for the SiO_2_ in the aqueous SAILs nanofluids at the after CMC concentration range in Fig. S11. The PC-SAFT pure-component parameters and association schemes used in this work are listed in Table S6, while the corresponding average relative deviations (ARD%) between experimental and calculated densities are provided in Table S7. The low ARD% values (1–4%) demonstrate the good predictive capability of the PC-SAFT model, particularly for the SiO_2_–THEA-Ole nanofluids.
Viscosity results
Viscosity changes in nanofluids can serve as an indirect indicator of nanoparticle stability. Stable viscosity over time reflects uniform particle dispersion and minimal sedimentation, whereas a gradual decline indicates aggregation and reduced stability. Monitoring viscosity at different concentrations (before CMC, at CMC, and after CMC) provides insight into dynamic nanofluid behavior. For SiO_2_-based nanofluids, THEA-Ole-containing systems showed stable, nearly linear viscosity profiles over 60 days, especially after CMC, indicating uniform dispersion. In contrast, HEA-Ole systems exhibited significant viscosity decline, while BHEA-Ole showed intermediate behavior. These differences arise from surfactant micelle structure and interactions with SiO_2_ surfaces: THEA-Ole forms micelles with strong hydrophilic shells that stabilize particles, HEA-Ole forms weaker micelles, and BHEA-Ole provides moderate stability. Increasing the number of hydroxyethyl groups and surfactant molecular weight enhances micelle stability, maintaining uniform dispersion and long-term viscosity [58].
Modeling
The nanofluid viscosity data fitting while simultaneously considering both concentration and temperature dependence is of critical importance. Many traditional models account for only temperature dependence, while concentration-dependent correlations are often used to predict viscosity at individual temperatures. Models that incorporate both temperature and concentration dependencies generally involve numerous parameters and are relatively rare [59]. For clarity, only the essential expressions of the Eyring–mNRF and Eyring–NRTL models required for physical interpretation and performance comparison are presented here; detailed mathematical derivations are provided in the supplementary information.
Recently, the Eyring–NRTL model has shown excellent capability in accurately correlating viscosity data [60]. The present study, showcases the applicability of the Eyring–NRTL model (Eqs. 15–17) and the newly proposed Eyring–mNRF model (Eqs. 18–24) in correlating the viscosity data of nanofluids was evaluated. The fitting parameters of the Eyring–mNRF model, along with the corresponding standard deviations, as well as the comparative results obtained from the Eyring–NRTL model, are summarized in Table 2 for nanofluids containing SiO_2_ nanoparticles. The Eyring-NRTL equation is as follows [31]:
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n(\eta V) = \sum\limits_{I = 1}^{n} {\phi_{I} \ln (\eta_{I} V_{I} )} + \sum\limits_{I = 1}^{n} {\phi_{I} \frac{{\sum\nolimits_{J = 1}^{n} {\phi_{J} A_{JI} G_{JI} } }}{{\sum\nolimits_{J = 1}^{n} {\phi_{J} G_{JI} } }}} $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ A_{JI} = a_{JI} + b_{JI} T $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ G_{JI} = \exp \left( { - \frac{{\alpha A_{JI} }}{RT}} \right) $$\end{document}Table 2. Eyring-mNRF and Eyring-NRTL model parameters along with standard deviation ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document} ) of SiO_2_ in aqueous solutions of HEA-Ole, BHEA-Ole and [THEA] [Ole] at 298.15 KEyring-mNRFSystemTime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{1sss}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{11s1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{1sss}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{11s1}$$\end{document} 10^3^ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{{\sigma \left( {\eta /mPa.s} \right)}}$$\end{document} SiO_2_—HEA-Ole30 min− 104,152.882− 1,188,318,467.5920.050− 3,096,404,187.1960.802880 min− 115,788.178− 22,549,892,872.655254.943− 3,096,404,187.1960.105760 min− 12,714.505− 104,482.42660,942.173− 1,548,202,093.5980.0610,080 min− 16,790.796− 6,687,675,280.2141,660,344.924− 1,548,202,093.5980.1114,400 min− 15,545.240− 4,643,020,085.5261,660,344.924− 1,548,202,093.5980.3028,800 min− 16,177.500− 5,678,781,824.5641,660,344.924− 1,548,202,093.5980.5036,000 min− 16,535.860− 6,264,898,228.5461,660,344.924− 1,548,202,093.5980.8543,200 min− 16,440.679− 6,105,315,587.6151,660,344.924− 1,548,202,093.5980.6050,400 min− 17,750.832− 6,953,787,868.98723,122.394− 1,548,202,093.5980.3640 days− 15,629.225− 4,769,106,537.1911,620,184.277− 774,101,046.7990.2560 days14,063.297− 4,929,018,247.2211,758,580.978− 722,494,310.3460.30 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{1sss}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{11s1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{1sss}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{11s1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\eta /mPa.s} \right)$$\end{document} SiO_2_—BHEA-Ole30 min− 12,701.569− 29,609,264.0241,515,639.598− 3,865,595.6171.02880 min− 12,684.709− 7620.08657,236.923− 966,398.9041.05760 min− 12,686.062− 31.297193,906.501− 4906.7910.210,080 min− 12,789.197− 1.29627,999.995− 49.7921.014,400 min− 12,686.354− 0.324190,020.954− 12.4481.028,800 min− 13,429.4570.04423,095.38554,294.0001.036,000 min− 12,686.1350.011117,365.40513,573.5051.043,200 min− 12,685.9550.01190,137.3271357.5051.050,400 min− 12,845.1580.71127,032.8871357.5050.540 days− 12,695.1190.178180,426.521339.3761.060 days− 12,838.9215,922,871.200− 179,247.889913,202.7550.6SiO_2_—THEA-Ole30 min− 12,650.080− 48,954.472185,157.3279.8440.32880 min− 12,653.195− 87,343.042185,157.3279.8501.05760 min− 12,648.307− 1894.24657,381.767800.3100.210,080 min− 13,914.568− 1,605,879.541248,987.8151,416,219.5800.314,400 min− 17,273.527− 5,922,658.30362,248.793708,109.7901.028,800 min− 12,648.392203.31871,253.650− 280.6630.436,000 min− 12,648.566101.659180,114.948− 140.3310.243,200 min− 12,648.1545332.43248,323.662− 70.1650.450,400 min− 12,690.40426.76130,225.371114,735.0821.040 days− 12,830.0676693.39226,665.5103688.7960.160 days− 13,042.407− 369,125.27117,756.47386,787.0300.2Eyring-NRTLSystemTimea_12_a_21_b_12_b_21_10^3^ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma \left( {\eta /mPa.s} \right)$$\end{document} SiO_2_—HEA-Ole30 min− 1.0013751.2570.800434.3860.022880 min− 1.0043745.6810.182432.0710.535760 min− 10.199375.675− 0.083442.2720.5810,080 min− 0.33614.477− 0.258442.9570.0614,400 min− 0.2203.619− 0.453442.2760.4228,800 min29.3331068.595666.6089.1330.6936,000 min0.1120.020− 0.449442.3060.2143,200 min344.6432497.969300.375436.3910.1650,400 min7057.7024619.1982101.069− 2.7760.0840 days1764.4223858.3191050.532− 0.2240.0960 days3155.1742617.1891289.25160.5490.14SiO_2_—BHEA-Ole30 min1764.4223703.6051050.530− 0.2240.062880 min44.0841109.09211.630− 0.3990.185760 min43.9963736.3111000.002− 0.3340.2810,080 min44.0212282.780139.272− 0.3370.0914,400 min43.5412211.5125.748− 0.3370.0428,800 min2.721160.82527,775.00011.6590.0736,000 min555.057154.597454.46311.6720.0643,200 min138.69838.647165.027459.5440.0150,400 min63.0463470.685275.8180.1960.0240 days45.11351.834− 0.307445.1620.5160 days3155.1742617.1891289.25160.5490.63SiO_2_—THEA-Ole30 min154.652100.753− 50.315189.0350.792880 min2.5350.098− 0.366446.3350.265760 min277.500116.6501260.003447.3740.3510,080 min252.042253.707205.3849.4370.4814,400 min62.54912.9548.3894.6960.0828,800 min0.2205.8290.04811.6670.0536,000 min0.0010.066251.05511.1360.3243,200 min2.17331.033− 0.01111.6340.6050,400 min0.034− 0.48217.0310.4250.0540 days37.500− 0.1081810.00011.7350.2360 days− 29.978− 18.215706.562− 115.1090.11
The V and VI denote the molar volumes of the nanofluid and component I, respectively. The term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi_{I}$$\end{document} is the volume fraction of component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I$$\end{document} , which is equivalent to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{x_{I} V_{I} }}{{\sum\nolimits_{J = 1}^{3} {(x_{J} V_{J} )} }}$$\end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{I}$$\end{document} is the component I mole fraction. The T illustrates the temperature and R is the universal constant of gases; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{JJ}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{JJ}$$\end{document} are empirical parameters of the Eyring-NRTL model. The non-randomness factor in this study has been shown by the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a$$\end{document} and has been set to 0.2. The Eyring–mNRF model has been computed through the referenced expressions provided within the supplementary information.
Furthermore, the performance of the Eyring-mNRF model was also evaluated without including energy correction parameters, and the results are summarized in the tables below. These comparisons highlight the effectiveness of the Eyring-mNRF model for accurately describing the simultaneous concentration and temperature dependence of nanofluid viscosity.
Figure 1 illustrates the fitted viscosity data for SiO_2_-based nanofluid systems using the Eyring-mNRF and Eyring-NRTL models, respectively. As shown in Fig. 1, the experimental viscosity data for the investigated systems were successfully correlated using the Eyring–NRTL and Eyring–mNRF models, both of which exhibited an excellent agreement with the experimental results. Nanofluid viscosity can also be predicted using classical models such as Einstein (Eq. 16), Brinkman (Eq. 17), Batchelor (Eq. 18), and the Lundgren (Eq. 19) [31].
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta = \eta_{2} (1 + 2.5\varphi_{1} ) $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta = \eta_{2} (1 + 2.5\varphi_{1} + 6.2\varphi_{1}^{2} ) $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta = \eta_{2} \left( {\frac{1}{{1 - \varphi_{1}^{2.5} }}} \right) $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta = \eta_{2} \left( {1 + 2.5\varphi_{1} + \frac{25}{4}\varphi_{1}^{2} + f\left( {\varphi_{1}^{3} } \right)} \right) $$\end{document}Fig. 1. The viscosity behavior of SiO_2_ was investigated in the presence of the studied nanofluid solutions at concentrations below, at, and after the CMC, including A, D SiO_2_ in aqueous HEA-Ole, B, E SiO_2_ in aqueous BHEA-Ole, and C, F) SiO_2_ in aqueous THEA-Ole at T = 298.15 K, with comparisons made to the predicted values from both the Eyring-mNRF and Eyring-NRTL equation
The results of these predictions are presented in Table 3.Table 3. Standard deviations ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma \left( {\eta /mPa.s} \right)$$\end{document} ) and absolute average relative deviations (AARD) obtained from prediction of viscosity values of nanofluid of SiO_2_ in aqueous solutions of HEA-Ole, SiO_2_ in aqueous solutions of BHEA-Ole and SiO_2_ in aqueous solutions of THEA-Ole with Einstein (Eq. 16), Batchelor (Eq. 17), Brinkman (18) and Lungren (19) modelsTimeEinsteinBatchelorBrinkmanLundgren \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\eta /mPa.s} \right)$$\end{document} AARD×100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\eta /mPa.s} \right)$$\end{document} AARD×100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\eta /mPa.s} \right)$$\end{document} AARD×100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\eta /mPa.s} \right)$$\end{document} AARD×100SiO2—HEA-Ole30 min5.3395.9073.3563.6782.081.496.9265.0392880 min4.8815.3712.9003.1531.7821.2656.6264.7965760 min5.1335.6403.1663.4161.7821.2656.7834.91810,080 min5.0745.5913.0953.3681.911.3576.754.89514,400 min5.0955.6353.1053.4111.9151.3766.7714.91528,800 min5.1345.6683.1513.4441.9151.3856.7924.9336,000 min5.2635.8173.2803.5901.9461.3896.8764.99843,200 min5.3395.9073.3563.6782.031.4526.9265.03950,400 min5.4576.0453.4733.8132.081.495.0034.10140 days6.1186.7834.1554.5362.1571.5474.4224.43560 days4.9203.2573.8923.5212.6051.8564.0053.852SiO2—BHEA-Ole30 min3.8894.2351.912.0411.1350.7894.9794.2822880 min3.9314.2841.9512.0891.1620.8105.0074.3055760 min3.9794.3411.9972.1551.1910.8344.0393.33010,080 min3.8724.2161.8891.9511.1850.8753.9683.27414,400 min4.0064.3542.0392.1581.1250.7815.054.33628,800 min3.9914.3562.0062.161.2210.8395.0474.33736,000 min4.014.3792.0242.1821.1970.845.064.34843,200 min4.0044.3722.0192.1751.2080.855.0564.34450,400 min4.114.4972.122.298.151.2050.8474.1274.40140 days4.4014.8282.4142.6211.2710.8994.3164.5560 days4.2524.6922.1511.8571.4631.0384.3593.851SiO2—THEA-Ole30 min2.5662.7310.6840.5690.3650.163.1053.6022880 min2.5432.7020.6740.5400.3620.1473.0883.5895760 min2.5112.6720.6320.5110.5440.3493.0702.57510,080 min2.9573.1830.9981.0120.3550.1354.3683.80714,400 min2.9573.1830.9981.0180.5440.3493.0253.80728,800 min2.5142.6760.6350.5150.3770.1363.0722.55736,000 min2.5142.6830.6120.5210.3160.1393.0752.2543,200 min2.5132.6650.6610.5040.3590.1323.0672.57250,400 min2.4752.6240.6260.4640.3400.1153.0433.55440 days2.5432.7160.6360.5540.3280.1533.0942.59560 days2.1132.0280.6000.4820.2580.1432.9982.872
Table 3 illustrates the strong predictive capability of the evaluated models, particularly the Brinkman model, in estimating the viscosity of nanofluid systems containing SiO_2_ nanoparticles dispersed in HEA-Ole, BHEA-Ole, and THEA-Ole SAILs.
Surface tension results
The surface tension of nanofluids containing SiO_2_ nanoparticles in HEA-Ole, BHEA-Ole, THEA-Ole was monitored over time to evaluate nanoparticle stability before CMC, at CMC, and after CMC concentrations. SiO_2_ nanoparticles, due to their semi-metallic nature, exhibited behaviors distinctly different from metallic nanoparticles in similar systems [37].
Based on the data (Table S8 and Fig. 2), aqueous SiO_2_ nanofluids in THEA-Ole, particularly at concentrations after CMC, showed the most stable surface tension over a 60-day period. This stability is indicated by a nearly constant slope in the surface tension profiles, reflecting uniform nanoparticle dispersion and minimal aggregation or sedimentation. In contrast, HEA-Ole and BHEA-Ole systems exhibited significant increases in surface tension over time, indicating lower stability and greater nanoparticle sedimentation. These differences are attributed to the micellar structures of the SAILs and their interactions with the SiO_2_ surface [61].Fig. 2. The time-dependent surface tension of SiO_2_ nanofluids stabilized with a HEA-Ole b BHEA-Ole c THEA-Ole within their varied concentration ranges of before CMC, at CMC and after CMC, at 298.15 K
Surface tension was measured at 298.15 K as an indicator of interfacial behavior and micellar stability. The amphiphilic SAILs, with hydrophilic ammonium cations containing hydroxyl groups and hydrophobic oleate chains, accumulate at the water–air interface, reducing the surface tension of water (~ 72 mN/m). At concentrations after CMC, micelle formation enhances this reduction, as SAIL molecules migrate into the bulk phase and form stable micelles that encapsulate SiO_2_ nanoparticles. THEA-Ole, with the [TEA]^+^ cation containing three hydroxyl groups, maintained stable surface tension, consistent with high viscosity and density stability in this system. In contrast, HEA-Ole and BHEA-Ole, with weaker hydrophilicity, formed micelles with less effective hydrophilic layers, leading to nanoparticle aggregation and increasing surface tension over time [62, 63].
From a physicochemical perspective, surface tension behavior depends on the interactions between SiO_2_ nanoparticle surfaces and the micellar structures of the SAILs. The SiO_2_ surface, bearing silanol groups (Si–OH) and a negative charge (isoelectric point ~ 2–3), exhibits lower polarity than water due to semi-metallic covalent Si–O–Si bonds. This allows the hydrophobic tails of SAILs to adsorb onto the SiO_2_ surface, while the hydrophilic ammonium headgroups orient toward the aqueous phase, forming conventional micelles. In THEA-Ole, the highly hydrophilic [TEA]^+^ cations create strong hydrophilic layers around micelles, effectively encapsulating SiO_2_ nanoparticles and preventing aggregation and sedimentation. Conversely, the lower hydrophilicity of [HEA]^+^ results in weaker micelles that inadequately stabilize nanoparticles, causing sedimentation and surface tension increases. BHEA-Ole shows intermediate behavior [63].
Increasing the number of hydroxyl groups from HEA-Ole to THEA-Ole enhances hydrophilicity and lowers CMC, facilitating micelle formation via stronger hydrogen bonding with water. However, long-term surface tension stability in THEA-Ole indicates that the quality of micelles (strong hydrophilic layer) is more critical than CMC in maintaining nanoparticle dispersion. The rising surface tension in HEA-Ole and BHEA-Ole is attributed to sedimentation of micelles and nanoparticles, disrupting the equilibrium between surface-bound and bulk SAIL molecules. This process, accompanied by migration of SAIL molecules from the surface to the bulk, reduces surface concentration and strengthens hydrogen bonding in water, shifting surface tension toward higher values, especially in HEA-Ole [62].
From a fluid dynamics standpoint, stable surface tension in THEA-Ole indicates resistance to structural changes at the nanofluid interface, consistent with uniform nanoparticle dispersion and minimal sedimentation. In contrast, the increase in surface tension in HEA-Ole and BHEA-Ole indicates gradual nanoparticle aggregation and reduced surface coverage by SAILs, confirming lower stability. These findings highlight the key role of cation hydrophilicity in stabilizing nanofluids, positioning THEA-Ole as the optimal choice for thermal management applications [28].
Key parameters, including ΔG°ads (Gibbs free energy of adsorption; negative values indicate spontaneous adsorption) and Π (surface pressure, γ_0_ − γ, indicating surface tension reduction and interfacial stability), were also evaluated over 30 min to 60 days. SiO_2_ nanoparticles in THEA-Ole after CMC demonstrated the highest long-term stability, consistent with previous studies showing that hydroxyl-rich surfactants form strong hydrogen bonds with metal oxide surfaces. The results are reported in Table S9 and they provide a reliable criterion for the design of stable nanofluids [17, 64]. Thermodynamic parameters related to adsorption, including the ΔG°ads and surface pressure (Π), are summarized in Table S9. The more negative ΔG°ads values for THEA-Ole indicate spontaneous and strong adsorption of SAIL molecules on the SiO_2_ surface, supporting the observed superior stability of this system.
Dynamic light scattering studies (DLS) and zeta potential
DLS and zeta potential analyses revealed distinct stability behaviors of SiO_2_ nanofluids in HEA-Ole, BHEA-Ole, and THEA-Ole systems. Although the smallest particle size was observed in BHEA-Ole (17.45 nm), its high PDI (60.98) indicated poor dispersion uniformity. In contrast, THEA-Ole, despite a slightly larger particle size (24.20 nm), exhibited lower PDI (42.84) and a remarkably high zeta potential (106.4 mV), far exceeding the ± 30 mV threshold for colloidal stability. This strong electrostatic repulsion effectively suppressed aggregation, which was consistent with negligible sedimentation over 60 days [65]. The PDI values reported in this work are expressed in percentage form, as provided by the instrument software.
The superior performance of THEA-Ole can be attributed to strong hydrogen bonding and electrostatic interactions between the highly hydrophilic [TEA]^+^ cation and the negatively charged silanol groups on SiO_2_ (IEP ~ 2–3). The resulting thick and stable micro solubilization layer prevented nanoparticle aggregation, whereas BHEA-Ole and HEA-Ole, with fewer hydroxyl groups, formed weaker interfacial coatings that led to aggregation and precipitation. These findings highlight that stability assessment requires simultaneous consideration of particle size, PDI, and zeta potential. THEA-Ole provided the most stable SiO_2_ nanofluid, making it a promising medium for energy and heat transfer applications where long-term colloidal stability is essential. The stability of SiO_2_ nanoparticles in aqueous nanofluids containing the HEA-Ole, BHEA-Ole, THEA-Ole are presented in Fig. 3 [66].Fig. 3. Recorded particle size distributions via DLS measuurement for the SiO_2_ nanofluid in the presence of a HEA-Ole b BHEA-Ole c THEA-Ole SAILs
The enhanced stability of SiO_2_ nanoparticles in SAIL-based biphasic systems can be attributed to a combination of interfacial interactions at the solid–liquid interface. The oleate anion, possessing a long hydrophobic alkyl chain, adsorbs onto the SiO_2_ surface through van der Waals interactions and surface affinity, while the ammonium cations interact electrostatically with the negatively charged silica surface. The hydroxyethyl substituents on the cation further strengthen interfacial binding via hydrogen bonding with surface silanol groups and surrounding water molecules. This multi-interaction adsorption layer provides both electrostatic repulsion and steric hindrance, effectively preventing particle–particle aggregation. Moreover, at concentrations near and above the CMC, micelle-assisted structuring of the interfacial region enhances dispersion uniformity and long-term colloidal stability [66].
Conductor like screening model (COSMO) results
The theoretical framework of this study is based on density functional theory (DFT) calculations performed using the DMol^3^ module implemented in Materials Studio (BIOVIA, 2023). Solvent effects were incorporated through the COSMO implicit solvation model, with water selected as the solvent medium. To ensure computational reliability, the generalized gradient approximation (GGA) with the VWN–BP exchange–correlation functional was employed, following the recommendations of the DMol^3^ developers. Geometry optimization and subsequent energy minimization were conducted using the GGA VWN–BP functional in combination with the DND (3.5) basis set. One of the principal thermodynamic descriptors obtained from COSMO analysis is the σ-profile, which represents the surface charge density distribution and serves as a molecular fingerprint for assessing intermolecular interactions. The σ-profile provides valuable insight into the spatial distribution of electronic charge across molecular surfaces and is particularly useful for interpreting the interaction propensity of surface-active ionic liquids (SAILs) with zirconium oxide and silica-based nanoparticle interfaces. These profiles are derived from quantum chemical DFT calculations, which enable accurate descriptions of molecular electron density; however, the computational cost associated with such methods remains a practical limitation for large-scale or high-throughput simulations [17].
The σ-profiles of the investigated SAILs exhibit broadened charge density peaks spanning approximately − 0.02 to + 0.02 e Å^−2^ (Fig. S12), indicating a delocalized electronic environment characteristic of amphiphilic ionic systems. This delocalization originates primarily from pronounced charge separation between the cationic and anionic moieties, leading to extensive electrostatic interactions that govern the physicochemical behavior of the SAILs. The presence of flexible alkyl chains and multiple hydroxyl functional groups further promotes charge delocalization, stabilizes charge-separated species, and enhances interactions with polar environments. COSMO-derived σ-profiles, optimized molecular geometries, dielectric solvation energies, surface cavity areas (A), surface cavity volumes (V), and frontier molecular orbital energies (HOMO and LUMO) for the studied SAILs and SiO_2_ are presented in Fig. S12 and Table S10 (Supplementary Information). Analysis of the σ-profile peak intensities reveals a clear trend in electron density accumulation, with THEA-Ole exhibiting the highest peak intensity, followed by BHEA-Ole and HEA-Ole. This trend reflects the increasing number of hydroxyethyl groups in the cationic structure, which enhances charge delocalization and electrostatic interaction capability. The broader and more intense σ-profile of THEA-Ole suggests stronger interactions with polar solvents and charged interfaces, theoretically implying improved solubility and interfacial affinity. Despite these theoretical predictions, experimental observations indicate that HEA-Ole provides superior stability under the investigated conditions [65]. In particular, the dielectric solvation energy of HEA-Ole is the most negative among the studied systems, signifying enhanced solubility and more favorable interactions in aqueous media. This behavior correlates with the observed superior stability of SiO_2_ nanoparticles dispersed in HEA-Ole-based nanofluids. The enhanced stability of HEA-Ole is attributed to its relatively simpler molecular architecture, which facilitates improved molecular packing, reduced steric hindrance, and more efficient formation of stable ion pairs. Moreover, HEA-Ole demonstrates a strong tendency to participate in hydrogen bonding and electrostatic interactions, promoting the formation of a dynamic yet thermodynamically stable structural network. This balance reduces excessive ionic mobility and contributes to enhanced colloidal stability. In contrast, while THEA-Ole benefits from increased charge accumulation and stronger hydrogen-bonding interactions, its more complex molecular structure may limit optimal packing and adaptability under the experimental conditions employed. Overall, these findings highlight that, although COSMO and DFT analyses predict enhanced interfacial interaction capability for more hydroxyl-rich SAILs, experimental stability is governed by a balance between molecular complexity, hydrogen bonding regulation, electrostatic interactions, and structural adaptability. Consequently, HEA-Ole demonstrates superior stability compared to more structurally complex SAILs such as THEA-Ole under the studied conditions, emphasizing the critical role of molecular architecture in the design of stable SAIL-based nanofluids [17].
Comparison with previous studies
To further strengthen this study's findings, a comparative analysis is conducted with prior research on oxide-based nanofluid stability in aqueous media, emphasizing surfactant effects. Three key studies are examined: Ordóñez et al. [67], on ZrO_2_ nanofluids, Tian et al. [68], on modified SiO_2_ for enhanced oil recovery (EOR), and Zhao et al. [69], on hydrophobic SiO_2_ nanofluids. These comparisons highlight similarities in nanoparticle type, base fluid, and stabilization strategies while underscoring differences in methodology, agents, and outcomes.
Ordóñez et al. [67], synthesized ZrO_2_ nanoparticles (59.9 ± 13.5 nm) via sol–gel and dispersed them at 0.1 wt% in deionized water with anionic (SDBS), cationic (CTAB), or non-ionic (PVP) surfactants at 0.01–0.05 wt%. Stability was assessed over 20 days using dynamic light scattering (DLS), zeta potential, pH, visual inspection, and UV–Vis spectroscopy. PVP outperformed SDBS and CTAB by reducing agglomeration through steric hindrance, yielding stable nanofluids at a final 0.01 wt% concentration, with shifts in zeta potential and isoelectric point.
In contrast, this study disperses unmodified SiO_2_ nanoparticles in aqueous solutions of surface-active ionic liquids (SAILs: HEA-Ole, BHEA-Ole, THEA-Ole) at concentrations before, at, and after their critical micelle concentrations (CMCs). SAILs provide enhanced electrostatic and steric stabilization via micelle formation, diverging from the conventional surfactants in Ordóñez et al. [67]. Notably, THEA-Ole after CMC achieved 60-day stability three times longer than the 20 days for PVP-stabilized ZrO_2_ evidenced by minimal sedimentation, stable viscosity and density, low polydispersity index (PDI: 42.84), and high zeta potential (106.4 mV).
Extending the analysis to SiO_2_-specific work, Tian et al. [68] l. modified hydrophilic SiO_2_ nanoparticles (~ 78 nm initial size) with KH570 silane (optimal 5 wt%), shifting wettability to hydrophobic (contact angle 79.8°) and reducing sedimentation (40% after 24 h). Compounding 0.2 wt% modified SiO_2_ with 0.3 wt% petroleum sulfonate (PS) lowered oil/water interfacial tension (IFT), with salinity tolerance up to 10,000 mg/L NaCl and emulsion stability (Turbiscan Stability Index: 2.23 after 120 min; zeta potential: − 54.8 mV) attributed to PS adsorption [68].
Unlike Tian et al. covalent modification [68], this study relies on micellar encapsulation and hydrogen bonding between SAIL cations particularly [THEA]^+^ and SiO_2_ silanol groups, yielding 60-day colloidal stability far exceeding their 120-min assessment. Metrics include smaller hydrodynamic sizes, lower PDI, and higher zeta potential, with stable thermophysical properties (viscosity, density, surface tension) and computational insights (PC-SAFT ARD%: 1–4%; COSMO confirming strong interactions). While Tian et al. [68]. prioritized IFT for EOR, this work focuses on thermal management.
For deeper insight into SAIL superiority over nonionic agents, Zhao et al. [69], stabilized hydrophobic SiO_2_ nanoparticles with Triton X-100 (TX-100) at 0.05–0.5 wt% and pH 2–12 (optimal: 0.1 wt% SiO_2_/TX-100 at pH 10), achieving minimal effective diameters and zeta potentials (> 30 mV absolute value) via electrostatic and steric effects. Alkaline pH (> 9) reduced aggregation, but long-term stability was unquantified, emphasizing short-term dispersion for EOR and heat transfer.
This study, however, uses CMC-driven SAILs without pH adjustment or modification, leveraging THEA-Ole’s tri-hydroxyl structure for robust hydrophilic shells and 60-day stability, with negligible sedimentation, stable properties, and ultra-high zeta potential. Methodologically, both employ DLS and zeta potential, but this extends to 60-day monitoring, excess molar volume,viscosity modeling (Eyring-mNRF/NRTL), and PC-SAFT/COSMO for superior SiO_2_-SAIL interactions. Zhao et al.'s pH dependence contrasts with our approach, yielding smaller sizes and better anti-aggregation, though their system may suit hydrophobicity-tuned EOR.
Overall, these comparisons underscore SAILs' advantages for prolonged (60-days) oxide nanofluid stability without pH tuning or modification, outperforming traditional surfactants in dispersion uniformity and thermal applications.
Model assumptions and applicability
The PC-SAFT equation of state was employed assuming transferable segment parameters and temperature-independent binary interaction parameters, which is a common and well-established approach for associating ionic liquid systems. The improved performance of PC-SAFT for THEA-Ole based systems, reflected by lower ARD% values, can be attributed to the higher symmetry and increased number of hydroxyl functional groups in the THEA cation, which enhances hydrogen-bonding representation within the association term of the model.
The COSMO-based predictions exhibited good qualitative agreement with experimental trends, particularly in capturing relative changes in thermophysical properties among the investigated SAILs. Minor quantitative deviations are expected due to the implicit treatment of long-range ionic correlations and nanoparticle–interface effects, which are not explicitly accounted for in COSMO calculations. Overall, the combined use of PC-SAFT and COSMO provides a consistent and complementary framework for interpreting the experimental data.
Limitations of the study
The present study focuses on the experimental characterization of SiO_2_-based nanofluids stabilized by hydroxyl-functionalized surface-active ionic liquids under ambient and static conditions. Particle size distribution was primarily evaluated using dynamic light scattering, which provides ensemble-averaged information for heterogeneous systems. While the observed stability trends are robust and supported by zeta potential and long-term sedimentation results, further investigation under dynamic flow or elevated temperature conditions, as well as complementary microscopic or molecular-level analyses, may provide additional insight and are suggested for future work. From an economic perspective, the cost of SAILs remains higher than that of conventional heat transfer fluids, which may limit large-scale implementation. However, the low volatility, high thermal stability, and tunable molecular structure of SAILs offer opportunities for performance optimization at relatively low additive concentrations, potentially mitigating cost-related concerns.
Conclusions
In this study, the stability of silicon dioxide (SiO_2_) nanoparticles in aqueous solutions containing HEA-Ole, BHEA-Ole, THEA-Ole SAILs, at three concentrations (before CMC, at CMC, after CMC) was evaluated over a 60 day period at 298.15 K. Stability was assessed using various techniques, including visual observation, viscosity and density measurements, zeta potential, DLS, and surface tension analysis. Overall, the consistently superior behavior of THEA-Ole across all measured properties reflects the dominant role of its hydroxylethyl-rich cation structure in strengthening intermolecular and interfacial interactions. Key results revealed that SiO_2_ exhibited the highest stability in THEA-Ole, particularly at after CMC concentration. Viscosity data were correlated with the Eyring-mNRF and Eyring-NRTL models, and the low average relative deviation (ARD%) confirmed their excellent agreement with experimental data. Among viscosity models, the Brinkman model showed the best performance with the lowest ARD% compared to the Einstein, Lundgren, and Batchelor models. Moreover, density data were used to calculate apparent and excess molar volumes, which were analyzed using the Redlich–Mayer and Redlich–Kister equations. Excess molar volume fitting was further performed with Ott, Redlich–Kister, and polynomial equations, among which the polynomial model yielded the lowest ARD%. Advanced computational methods, including COSMO-based thermodynamic and PC-SAFT, provided robust predictions of molecular interactions and solution properties. These findings highlight the importance of the chemical structure of SAILs and their interactions with nanoparticles in designing stable nanofluids for thermal management applications. The stability of SiO_2_ is attributed to its semi-metallic nature, which promotes the adsorption of the hydrophobic tails of SAILs, thereby emphasizing the key role of cation hydrophilicity.
Supplementary Information
Supplementary Material 1
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