# Surface tension of graphene/Fe3O4 water-based hybrid nanofluids

Soulayma Gal, David Cabaleiro, Walid Hassen, Ludivine Rault, Housseinou Ba, Patrice Estellé

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Soulayma Gal, David Cabaleiro, Walid Hassen, Ludivine Rault, Housseinou Ba, et al.. Surface tension of graphene/Fe3O4 water-based hybrid nanofluids. Journal of Molecular Liquids, 2025, 417, pp.126630. 10.1016/j.molliq.2024.126630. hal-04822760

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Submitted on 29 Sep 2025

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# Surface tension of graphene/Fe₃O₄ water-based hybrid nanofluids

Soulayma Gal<sup>a,b</sup>, David Cabaleiro<sup>c</sup>, Walid Hassen<sup>b</sup>, Ludivine Rault<sup>d</sup>, Housseinou Ba<sup>e</sup>,
Patrice Estellé<sup>a,w</sup>

## ARTICLE INFO

**Keywords:**

Graphene

Iron oxide

Hybrid nanofluids

Surface tension

Concentration influence

## ABSTRACT

Advanced hybrid nanofluids have been engineered through the synthesis of aqueous suspensions containing graphene sheets and iron oxide (Fe₃O₄) nanoparticles at a graphene-Fe₃O₄ mass ratio of 70:30. Karaya gum and cocoamidopropyl betaine (CAPB) were selected as surfactants given their good affinity with dispersed nano-materials. Graphene sheets with Fe₃O₄ nanoparticles as well as the prepared dispersions were first characterized in terms of morphology, chemical composition and stability using various techniques, including electron microscopy, UV-visible spectroscopy and Zeta potential analyses. Given the crucial role that surface tension (ST) plays in boiling/condensation processes or micro-flow applications, this physical property was investigated at nanoadditive mass concentrations of 0.005–0.100 % and temperatures of 283.15–313.15 K using the pendant drop method. As an entry parameter for ST evaluation, the density of these hybrid nanofluids was also measured at the same temperature and concentration ranges. Experimental studies revealed that ST of water reduces with the addition of surfactant and increasing temperature. Graphene-Fe₃O₄ nanoparticles were also found to further reduce the ST (thus enhancing the effect of the surfactant mixture) by up to 42.7 % on average at 0.1 %wt. compared to water in the tested temperature range. This may be potentially interesting for improving boiling heat transfer performance and optimizing bubble flow pattern.

## 1. Introduction

Nanofluids, suspensions of nanoparticles in conventional fluids such as water, glycols, and oils, represent a significant advancement in nanotechnology and heat transfer since they first appeared in the early 1990s. Incorporating metallic nanoparticles, carbides, oxides, or carbon materials imparts these fluids with superior thermophysical properties compared to conventional fluids. Notable advantages include enhanced thermal conductivity, higher heat transfer coefficients, and increased critical heat flux. These exceptional characteristics have facilitated the development of a wide range of practical applications, including microchannel cooling in integrated circuits, chemical and pharmaceutical processes [1–4], nuclear reactors [5], and solar energy concentration systems [6]. Among the different types of nanofluids, those based on graphene and iron oxide (Fe₃O₄) are particularly noteworthy. Graphene possesses exceptional properties, including high electrical and thermal conductivity, high Young's modulus, and remarkable fracture

toughness, making it an ideal additive for nanofluids as demonstrated in different studies [7–11]. Fe₃O₄ nanoparticles are one of the most suitable materials for nanofluids due to their availability, enhanced stability, high thermal conductivity, and magnetic properties enabling controlled cooling. They are stable, corrosion-resistant, easy to synthesize, and also used in biomedicine for magnetic hyperthermia [12–14].

Research on nanofluids often focuses on the characterization of thermal conductivity and dynamic viscosity, both of which are critical for optimizing heat transfer performance as highlighted in the following studies [15–18]. However, experimental data on other physical and interfacial parameters is essential for making appropriate decisions in the design of heat transfer and energy storage systems. Surface tension (ST) refers to the energy required to increase the surface area of a liquid due to intermolecular forces, which significantly influences heat transfer and the interaction of surface fluids. In boiling and condensation processes, ST plays a crucial role in the formation and detachment of bubbles, as well as in the development of a liquid film. Variations in ST

<footnote><sup>a</sup> LGCGM, Univ Rennes, Rennes, France</footnote>

<footnote><sup>b</sup> LMES, Université de Monastir, Monastir, Tunisia</footnote>

<footnote><sup>c</sup> Dept. Applied Physics, Universidad de Vigo, Vigo, Spain</footnote>

<footnote><sup>d</sup> ScanMAT, Univ Rennes, Rennes, France</footnote>

<footnote><sup>e</sup> BLACKLEAF SAS, Strasbourg, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: patrice.estelle@univ-rennes.fr (P. Estellé).</footnote>
can either enhance or hinder the thermal performance of nanofluids. A comprehensive understanding of ST is essential for the effective design and improvement of nanofluids, particularly in micro-flow applications where precise management of fluidic interactions is paramount [19–21]. Although graphene and Fe₃O₄ nanoparticles suspended in the base fluid have been extensively studied for their thermal and rheological properties, their surface tension has been rarely examined. The primary findings from the existing literature are summarized below. Du et al. [22] studied the ST of a graphene-based aqueous nanofluid and its effects on heat transfer. They observed a decrease in ST with increasing dispersant concentration and temperature, noting a reduction from 24.6 % to 0.6 wt% of graphene compared to water. The incorporation of graphene improved the contact angle of water with stainless steel and polypropylene random plate materials, thereby reducing resistance to heat transfer. This reduction in ST also improved boiling heat transfer performance and optimized the bubble flow pattern, while offsetting the increase in frictional resistance. In a recent study, Liu et al. [23] examined the ST of nanofluids composed of distilled water and graphene oxide, with mass concentrations ranging from 0.02 to 0.12 wt%, using an acoustic levitator. They observed an increase in ST with higher mass concentration and a decrease with higher temperature. For nanoparticle concentrations below 0.08 wt%, surface tension increased progressively, while for higher concentrations, significant differences were noted between supercooled and non-supercooled states. Non-contact measurement techniques enabled precise measurements without contamination. Ilyas et al. [24] studied the ST behavior of saline nanofluids composed of graphene nanoplatelets and saline fluid at a concentration of 30 parts per thousand. Their measurements covered graphene nanoplatelet concentrations ranging from 0 to 0.25 wt% and a temperature range from 298.15 to 338.15 K. The study revealed a significant 21 % reduction in ST with increasing nanoplatelet concentration and temperature. Cabaleiro et al. [25] investigated the impact of chemical reduction of graphene oxide on the surface tension of aqueous nanofluids at 293.15 K. Graphene oxide (GO) was synthesized from commercial synthetic graphite using a modified Hummers method, while reduced graphene oxides (rGOs) were produced through the chemical reduction of GO. Three series of aqueous nanofluids were prepared using both GO and rGOs without surfactants, covering volume fractions ranging from 0.0005 to 0.1 %. The results showed a decrease in surface tension proportional to the increase in graphene concentration, with maximum reductions of 3 % observed at the highest concentration (0.1 %), without significant impact from the chemical reduction process. Tian et al. [26] studied the ST of functionalized graphene nanofluids. Their findings indicated that the incorporation of graphene nanosheets led to a reduction in ST by up to 13.9 % in ethylene glycol. Although there was an increase in bond strength, this reduction was not fully compensated. In addition, the ST of the base fluid decreased by 8.3 % with rising temperature, whereas the 5 wt% nanofluid demonstrated a lesser decrease of 3.86 %, suggesting a reduced sensitivity to temperature due to the presence of nanoparticles. Ahammed et al. [27] used sodium dodecyl benzene sulfonate (SDBS) as a surfactant in the synthesis of graphene-containing nanofluids. They investigated the impact of varying graphene concentrations and temperatures, specifically within the range of 283.15–363.15 K on the surface tension of the nanofluids. The results indicated a tendency to decrease as graphene concentration and temperature increased, indicating a negative correlation with these parameters. Notably, at a temperature of 323.15 K and a graphene concentration of 0.15 vol%, ST was reduced by 18.7 % compared to water. The study revealed that the effect of graphene concentration on ST was more significant than that of temperature. Kujawska et al. [28] explored the surface tension of a graphene oxide (GO) water-based nanofluid both prior to and following a boiling cycle within a thermosyphon. The authors conducted a comparative analysis of GO nanofluids with and without the incorporation of sodium dodecyl sulfate (SDS) surfactant to distinguish the effects of GO flakes from those of the surfactant. The results showed that even a minimal concentration of SDS

(0.01 g/L) reduces the surface tension by approximately 2 % when compared to pure water. However, in the presence of GO, the effect of SDS is attenuated, as surfactant molecules tend to adsorb onto the GO flakes, reducing the free SDS concentration in the fluid and leading to an increase in the surface tension relative to a solution containing only the surfactant. Hamze et al. [15] examined the surface tension of nanofluids using Triton X-100, Pluronic P-123, and gum Arabic as dispersants across a temperature range of 283.15 to 323.15 K. The study evaluated both the individual effects of the surfactants and graphene particles on ST, as well as their combined interactions. The results indicated that gum Arabic did not exert a measurable effect on the ST of water, whereas the presence of graphene resulted in a 21.5 % increase in ST, independent of graphene concentration. Additionally, the incorporation of Triton X-100 into Tyfocor® LS led to a reduction in ST, with a decrease of 10.8 % observed at a concentration of 0.1 wt% and a temperature of 283.15 K, and a reduction of 0.4 % at 323.15 K. Similarly, the introduction of Pluronic® P-123 into Tyfocor® LS resulted in a decrease in ST, ranging from 14.8 % to 11.4 % as the temperature increased from 283.15 to 323.15 K, with no significant variations observed with respect to concentration. These findings highlight the significant influence of surfactant selection and temperature on the control of the surface tension in nanofluids. Banisharif et al. [29] studied the ST of Fe₃O₄ nanoparticles dispersed in a water/ethylene glycol mixture at concentrations ranging from 0 to 1.0 vol%. This investigation was carried out over a temperature range of 253.15–293.15 K, with a focus on cooling applications. The results showed that ST decreased with the addition of surfactant to the base fluid, then increased with Fe₃O₄ concentration, achieving an increase of nearly 38 % at 253.15 K and 33 % at 293.15 K for a nanoparticle concentration of 0.1 vol%. To enhance the understanding of the influence of Fe₃O₄ nanoparticles on the ST of aqueous nanofluids, Chicea and Goncea [30] investigated the impact of Fe₃O₄ and its functionalization. Their findings indicated a reduction in the surface tension value as the concentration of nanoparticles increased. Jiang et al. [31] studied the ST of nanofluids containing iron(II) oxide and light crude oil. The authors found that the ST was minimized at a nanoparticle concentration of 2.0 wt% at a temperature of 343.15 K. ST decreased significantly between 298.15 K and 343.15 K, but increased at higher temperatures. In a separate investigation, Saptoro et al. [32] used a non-chemical method based on microwave irradiation to modify the ST of Fe₃O₄ nanoparticles dispersed in water. Their findings indicated a reduction in ST of 7.0 % at a nanoparticle mass concentration of 0.05 wt %, 11.6 % at 0.1 wt%, and 12.5 % at 0.5 wt%, in comparison to pure water. Additional results concerning various types of nanoparticles are compiled in Refs. [33,34] which also emphasize the importance of ST in heat transfer processes.

Recently, hybrid nanofluids have captured growing interest due to their ability to combine different types of nanoparticles, thereby leveraging the synergistic benefits of each constituent. These nanofluids exhibit the potential for enhanced thermal performance, opening up new prospects for more efficient industrial and technological applications, such as solar cooling systems and nuclear reactors, thereby augmenting their overall efficiency and reliability. However, research on the ST of these hybrid nanofluids remains limited, with only a few studies conducted in this field. In this context, Huminic et al. [35] investigated the ST of hybrid nanofluids composed of either water (W) or a water + ethylene glycol mixture (W+EG) that were loaded with reduced graphene oxide decorated with silver nanoparticles (Ag NPs-rGO). The incorporation of surfactants reduced the ST by 8.66 % for water and 4.63 % for the water + ethylene glycol mixture at 293.15 K. Furthermore, an increase in the concentration of Ag NPs-rGO led to an increase in ST by 7.48 % for Ag NPs-rGO/water and 9.50 % for Ag NPs-rGO/W+EG at 293.15 K and 0.10 wt%. Additionally, an increase in temperature was associated with a decrease in ST, more pronounced effect observed for Ag NPs-rGO/water compared to Ag NPs-rGO/W + EG. Nayebpashaee et al. [36] prepared hybrid nanofluids by combining water and ethylene glycol (W + EG in a 50:50 vol% ratio at 298.15 K)
with surfactants containing oleic acid and sodium dodecylsulfonate. They measured the surface tension of the graphene-Al₂O₃/ethylene glycol-water hybrid nanofluid at temperatures ranging from 253.15 to 293.15 K and at different nanoparticle volume fractions (0.05%–2.5%). The addition of surfactant initially resulted in a decrease in surface tension, which then subsequently increased with nanoparticle concentration, reaching rises in this property around 47.84% (268.15 K) and 54.30% (283.15 K) for 2 vol% sample and around 48.25% (258.15 K) for 2.5 vol% concentration. Overall, surface tension exhibited a decreasing trend with increasing temperature.

Owing to the importance of surface tension and density in understanding the thermal and fluid-dynamic characteristics of hybrid nanofluids, the lack of significant investigations on those parameters needs to be filled with more literature on the matter. Our comprehensive literature review, as referenced in studies [33,34], indicates a lack of research focused on the ST of hybrid nanofluids containing graphene and Fe₃O₄ nanostructures. Consequently, this study presents novel findings regarding the synthesis of such hybrid nanofluids and their ST characterization. In the following, as shown in Section 2, the hybrid nanofluids consist of graphene nanosheets with few layers which were prepared through the liquid-phase exfoliation of graphite in water with the aid of surfactants. Additionally, magnetic Fe₃O₄ particles were incorporated into the nanofluids at a graphene-Fe₃O₄ mass ratio of 70:30. The structural and morphological characteristics of selected nanoparticles were analyzed and the stability of the prepared hybrid nanofluids was assessed using UV-visible spectroscopy and zeta potential measurements, as detailed in Section 3. In the same section, the density and surface tension were experimentally evaluated by varying the temperature, ranging from 283.15 K to 313.15 K, and nanoparticle concentration from 0.005 to 0.100 wt%. Finally, a correlation was established among surface tension, temperature and the mass fraction of graphene-Fe₃O₄ nanoparticles, providing practical data to guide their future application across various industrial fields.

## 2. Materials and methods

### 2.1. Hybrid nanofluid preparation

Hybrid nanofluids were produced in two successive steps. Initially, a suspension of graphene was generated using an optimized liquid-phase exfoliation technique, akin to the method reported in [37]. To enhance the exfoliation process, karaya gum (Thermo Scientific Chemicals, USA) was used. Additionally, cocoamidopropyl betaine (CAPB) (Microbialtec, USA) was incorporated as co-surfactant. Karaya gum was chosen as surfactant due to its natural emulsifying and dispersion-stabilizing properties, which are essential for the long-term stability of nanofluids. Studies have shown previously that polysaccharides like karaya gum are effective in stabilizing nanoparticle suspensions in aqueous fluids [38]. Cocoamidopropyl betaine (CAPB), an amphoteric surfactant, was selected as the co-surfactant for its strong affinity with iron oxide (Fe₃O₄) nanoparticles, preventing agglomeration and promoting uniform dispersion in the base fluid. This karaya gum/CAPB combination achieves a stable suspension, as shown later, while maximizing the specific surface area of exfoliated graphene, which is crucial for thermal applications of nanofluids.

In practice, 1.0 g of high-purity graphite (Imerys, France) was mixed with 0.1 g of both surfactant/co-surfactant with ratio 1:1 blend in a 1000 mL volumetric flask containing doubly-distilled water, ensuring a controlled environment. This mixture was subjected to sonication using a probe-type sonicator SFX550 Sonifier (Branson, USA) operating at a frequency of 50/60 Hz, with an 80-watt power setting for 2 h, under continuous mechanical stirring to achieve thorough graphite exfoliation. Following the exfoliation process, spherical Fe₃O₄ particles, purchased from Nanographi (Turkey) and with properties gathered in Table 1, were introduced into the suspension at a graphene/Fe₃O₄ ratio of 70:30 and agitated for an additional 30 min. These parameters are

<table><caption>**Table 1**

Manufacturer data of Fe₃O₄ nanoparticles [41].</caption><tr><td>Purity (%)</td><td>>98.45</td></tr><tr><td>Color</td><td>Dark Brown</td></tr><tr><td>Average Particle Size (nm)</td><td>18–28</td></tr><tr><td>Morphology</td><td>Spherical</td></tr><tr><td>Specific Surface Area (m²/g)</td><td>>55</td></tr><tr><td>Bulk density (kg/m³)</td><td>900</td></tr><tr><td>True density (kg/m³)</td><td>5100</td></tr><tr><td>Element Analysis (%)</td><td>Ca: 0.023; Cr: 0.0016; K: 0.0012; Mn: 0.086; SiO₂: 0.14</td></tr></table>

optimal for exfoliating graphite into graphene while ensuring effective dispersion of Fe₃O₄ nanoparticles. Studies have shown that such settings minimize agglomeration and maintain a homogeneous suspension over extended periods [39], a key criterion for ensuring the stability of hybrid nanofluids. To prevent excessive temperature increase during the 2-hour ultrasonication, the beaker containing the suspension was placed in a double-walled reservoir connected to a chiller circulating a water-glycol coolant. This setup maintains a stable ambient temperature, ensuring the thermal stability of the suspension and preventing any changes to the nanofluid's properties during preparation. Temperature control is particularly crucial, as high temperatures during ultrasonication can lead to instability and aggregation of nanoparticles [40].

Then, this primary solution underwent meticulous dilutions to ensure its suitability for subsequent characterization evaluations. As a result, five distinct samples were prepared, with particle mass contents ranging from 0.100 to 0.005 wt%.

### 2.2. Characterization methods

The morphology of graphene-Fe₃O₄ nanostructures was investigated using conventional and high-resolution transmission electron microscopy (TEM and HRTEM) with a JEM 2100 HR (JEOL, Ltd., Tokyo, Japan). Conventional TEM micrographs were acquired with a Gatan Orius SC200D camera, high resolution images were captured with a Gatan UltraScan 1000XP camera. Elemental analysis was conducted using an EDX Oxford X-Max 80T detector. A small aliquot of the sample suspension was diluted with ultrapure water. Subsequently, a droplet of the diluted suspension was placed on a holey carbon-coated 300 mesh copper grid and allowed to dry at room temperature.

The temporal stability of graphene-Fe₃O₄ nanofluids was evaluated at a temperature of 298.15 K utilizing UV-visible spectroscopy and Zeta Potential analyses. The UV-vis measurements were conducted using an HP-8453 diode array spectrophotometer (Agilent Technologies, Inc., California, USA), which was equipped with a cell carrier maintained at a constant temperature by an external water cooler (Julabo, F12-ED, Germany). Dispersions at concentrations of 0.050 wt% and 0.100 wt% were diluted one hundred times with Milli-Q water and subjected to sonication for 5 min in a low-energy ultrasonic bath (200 W, 40 kHz, JP Selecta SA, Spain). These dilutions were then transferred into 10 mm-path-length quartz cuvettes and maintained under static conditions for a duration of 24 days. Absorbance spectra were periodically recorded over a wavelength range of λ = 200–800 nm. Zeta potential (ζ-potential) measurements were conducted by means of a Zetasizer Nano ZS device (Malvern Instruments Ltd., UK). The five developed dispersions were analyzed with a 4-mW helium-neon laser source emitting at 632.8 nm, with a detection angle of 13° (forward scattering). To ensure that the recorded signal remained within the optimal sensitivity range of the instrument, samples were also diluted 100 times in Milli-Q water. Then, fluids were filled into electrophoresis cells (DTS 1070 from Malvern) and were kept in a static state for 23 days.

Density ρ determinations were performed by means of a vibrating quartz U-tube densimeter, the DMA 501 manufactured by Anton Paar (Austria). This experimental apparatus is equipped with a Peltier
thermostat, which facilitates temperature control within the range of 288.15 to 313.15 K, achieving an accuracy of ±0.03 K (with a repeatability: ±0.01 K). The expanded uncertainty associated with the density measurements is estimated to be less than 0.1 % [15].

The surface tension (ST) measurements were performed using a DSA-30 drop shape analyzer manufactured by KRÜSS GmbH (Hamburg, Germany). Sample droplets were generated using a 15-gauge needle (outer diameter 1.835 mm), with both the flow rate and volume meticulously controlled. The experimental methodology employed has been comprehensively detailed in Ref. [42]. Based on the suspended drop technique, ST was calculated from the density of each sample and the analysis of the droplet shape suspended at the needle tip, in accordance with the Young-Laplace equation. In the following, each ST value has been obtained from the average of at least sixty measurements. Additionally, the ST of distilled water was also measured in the temperature range of 283.15 to 313.15 K. Samples were equilibrated at least for 10 mins at required temperature using a TC40 environmental chamber, where the temperature is regulated by a Peltier system (with an accuracy of ±0.2 K) and monitored via a PT100 probe. To validate the experimental method and evaluate uncertainty in ST, Fig. 1 shows the experimental results for distilled water alongside reference data from Vargaftik et al. [43]. The comparison demonstrates a strong correlation, with the ST values deviating by an AAD of 1.4 % from the reference values [43] within the examined temperature range.

# 3. Results & discussion

## 3.1. Nanostructures morphology

TEM analyses were performed for evaluating the liquid phase exfoliation process in synthesizing graphene sheets with few layers, evaluating their average dimension, and confirming the morphological properties of Fe₃O₄ nanoparticles and their chemical species, in comparison to manufacturer data previously reported in Table 1. As shown by Fig. 2a to 2c, the average lateral dimensions of graphene sheets are between 5 and 10 µm on average. These values are similar to the ones reported in [37] where a similar liquid exfoliation process was used. However, it appears here that graphene sheets thickness is higher, reaching 14 nm in average, as illustrated by Fig. 2d to 2f. Consequently, graphene sheets are here composed of higher number of layers, between 35 and 40. This can be probably explained by the mixture of surfactants used, karaya gum and CAPB, that are less effective in exfoliate graphite sheets that karaya gum alone [37], and by the presence of Fe₃O₄ nanoparticles. It should also be noted that graphene sheets exhibit many folds and folded regions, which are characteristic for this nanostructure.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Surface tension of distilled water as a function of temperature – Experimental data versus reference data [43]. Error bars stand for experimental uncertainty.</figcaption></figure>

With regards of Fe₃O₄ nanoparticles characteristics, TEM analysis shown in Fig. 2g evidences that the sizes of nanoparticles are within the range given by the manufacturer, e.g. 18–28 nm, but the nanoparticles are not well spherical in shape rather in polygon form. Chemical species of these nanoparticles are reported in Fig. 2i. This latter figure highlights the presence of Fe, O, and C as expected. Some other species like Ca and Si are found, in agreement of species reported in Table 1. However, additional impurities are also present, like Na, Al, and Cl. Several other spectra analyses were performed, providing the same results.

## 3.2. Stability of hybrid nanofluids

As per Beer-Lambert's law, the amount of light absorbed by a colloidal suspension depends upon the concentration of dispersed particles. Thus, nanofluid stability can be investigated by monitoring the evolution of sample absorbance. Fig. 3.a shows several representative UV-vis spectra recorded for 1:100 dilutions of the dispersions loaded with 0.050 wt% and 0.100 wt% of graphene-Fe₃O₄. As can be observed, nanofluids exhibit a maximum peak at wavelengths around λ = 260–270 nm. Graphene nanostructures have been reported to present maximum peaks in the wavelength range between 230 and 300 nm, which correspond to π → π* transitions of aromatic C—C bonds [44,45]. Thus, in this work, the stability of the dispersions was evaluated by averaging the absorbance in the range λ = 260–270 nm and monitoring that value over time. Comparing Fig. 3a and b, it can be observed that, as expected, the higher the graphene concentration, the higher is the extinction coefficient. As shown in Fig. 3.b, recorded absorbance reduced mainly during the first week in the case of the dispersion loaded with 0.050 wt% and during the first two weeks in the case of the 0.100 wt% nanofluid. After then, reductions in absorbance value were considerably lower. This means that at first sight, the tested hybrid nanofluids are subjected to some aggregation phenomena during few days after their preparation, as shown by the decrease in the extinction coefficient values during the first few days. Then, the values remained practically constant, with only minor changes observed, indicating equilibrium state of the nanofluids [46]. This equilibrium is reached quickly with the sample containing the least graphene, as evidenced by Fig. 3b.

In colloidal dispersions, Zeta potential (ζ-potential) is an important physical-chemical parameter since it provides valuable information regarding the magnitude of electrostatic interaction between interfaces. High Zeta potentials are usually an indication of electrostatic charges strong enough to prevent aggregation or agglomeration of dispersed particles. Therefore, ζ-values greater than ±30 mV are generally considered a criterion for judging nanofluids to be stable [47]. Table 2 summarizes the results obtained for 1:100 dilutions of the five developed dispersions. All samples showed ζ-potentials in the range from ±40 mV to ±60 mV, which are an indication of good stability [48]. As shown in Table 2, recorded values did not considerably change in the investigated timeframe.

## 3.3. Density of hybrid nanofluids

Density ρ was experimentally investigated at 5 K steps covering the temperature interval between 288.15 and 313.15 K. Fig. 4 depicts the temperature dependence of ρ results for distilled water (used as base fluid) and the five prepared graphene-Fe₃O₄ hybrid nanofluids. In the investigated temperature range, all samples exhibit a similar ρ(T) trend, with average reductions of 0.27 % for every 10 K increase in temperature. Experimental data were also correlated as a function of temperature (in Kelvin) by means of a second-order polynomial (i.e. ρ(T) = a₀ + a₁·T + a₂·T²). Table 3 presents the obtained aᵢ fitting parameters together with the standard deviations of the adjustments. The density of the nanofluids at temperatures of 283.15 K, necessary for surface tension analyses, were calculated using those correlations. In addition, the coefficients of isobaric thermal expansion (i.e. αₚ = -(1/ρ)·(∂ρ/∂T)ₚ), were
<figure><img src="image_5.png" /><figcaption>Fig. 2. Characterization by TEM of various graphene sheets with Fe₃O₄ nanoparticles. (a), (b), (c) TEM micrographs show the average lateral dimensions of graphene sheets, (d), (e), (f) HRTEM images show the average thickness of graphene sheets, (g) TEM micrograph shows the size and the shape of Fe₃O₄ nanoparticles, (h) TEM micrograph of graphene sheets with Fe₃O₄ nanoparticles and the location of the EDX spectrum (i) with corresponding peaks for Fe (yellow).</figcaption></figure>

also obtained analytically by differentiating the $\rho(T)$ fittings. Within the studied temperature range, $\alpha_p$ coefficients take values ranging from $2.0 \cdot 10^{-4}$ K⁻¹ (at 293.15 K) to $3.4 \cdot 10^{-4}$ K⁻¹ (at 308.15 K). Nanofluids showed slight lower coefficients of thermal expansion, even if the maximum differences between studied fluids were lower than $0.1$ K⁻¹.

As for the influence of graphene-Fe₃O₄ addition, density increases with the addition of the nanoparticles. Rises in $\rho$ regarding the base fluid are similar for all investigated temperatures and reach the 0.10% for the 0.100 wt% sample. Based on the classical theory for mixtures of ideal gases, Pak and Cho [49] proposed a mixing rule to predict the effective density of nanofluids. Such equation can be expressed as a function of nanoparticle mass fraction $\varphi$ as follows:

$$ \frac{1}{\rho_{nf}} = \frac{\varphi}{\rho_{np}} + \frac{1 - \varphi}{\rho_{bf}} \qquad (1) $$

where nf, np and bf subscripts stand for nanofluid, nanoparticles and base fluid (typically water here), respectively. In this case, the density of the dispersed nanoparticles was calculated using:

$$ \frac{1}{\rho_{np}} = \frac{\varphi_{graphene}}{\rho_{graphene}} + \frac{\varphi_{Fe3O4}}{\rho_{Fe3O4}} \qquad (2) $$

Considering that hybrid particles consisted of a mixture of graphene and Fe₃O₄ at a mass ratio of 70:30 and taking the density values of $\rho_{graphene} = 1820$ kg·m⁻³ for graphene [15] and $\rho_{Fe3O4} = 5100$ kg·m⁻³ for iron oxide (see Table 1, in agreement with reference [50]), a value of $\rho_{np} = 2255$ kg·m⁻³ was estimated by means of Eq. (2). Even if, in general, nanofluid experimental densities were slightly larger than expected according to Eq. (1), the maximum deviations were here lower than the experimental uncertainty. It is worst noting that density of both
<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) Representative absorbance spectra recorded for 1:100 dilutions of (a₁) 0.050 wt% and (a₂) 0.100 wt% graphene-Fe₃O₄ dispersions. (b) Temporal evolution of the absorbance (averaged values in the region of λ = 260–270 nm).</figcaption></figure>

<table><caption>**Table 2**
Temporal evolution of Zeta Potential.</caption><thead><tr><th rowspan="2">Samples (1:100 diluted)</th><th colspan="4">ζ-potential (mV)</th></tr><tr><th>1st day</th><th>8th day</th><th>16th day</th><th>23rd day</th></tr></thead><tbody><tr><td>graphene-Fe<sub>3</sub>O<sub>4</sub> 0.005</td><td>-47.0 ±</td><td>-49.2 ±</td><td>-45.5 ±</td><td>-44.0 ±</td></tr><tr><td>wt%</td><td>1.9</td><td>1.0</td><td>1.2</td><td>1.8</td></tr><tr><td>graphene-Fe<sub>3</sub>O<sub>4</sub> 0.010</td><td>-45.2 ±</td><td>-47.2 ±</td><td>-45.9 ±</td><td>-43.6 ±</td></tr><tr><td>wt%</td><td>1.1</td><td>1.3</td><td>1.2</td><td>1.9</td></tr><tr><td>graphene-Fe<sub>3</sub>O<sub>4</sub> 0.025</td><td>-45.7 ±</td><td>-44.4 ±</td><td>-42.7 ±</td><td>-46.2 ±</td></tr><tr><td>wt%</td><td>0.9</td><td>0.6</td><td>1.2</td><td>1.0</td></tr><tr><td>graphene-Fe<sub>3</sub>O<sub>4</sub> 0.050</td><td>-47.6 ±</td><td>-46.1 ±</td><td>-45.9 ±</td><td>-47.1 ±</td></tr><tr><td>wt%</td><td>0.8</td><td>0.8</td><td>0.8</td><td>0.6</td></tr><tr><td>graphene-Fe<sub>3</sub>O<sub>4</sub> 0.100</td><td>-49.1 ±</td><td>-45.2 ±</td><td>-46.6 ±</td><td>-46.2 ±</td></tr><tr><td>wt%</td><td>1.6</td><td>1.1</td><td>0.3</td><td>0.5</td></tr></tbody></table>

surfactants, respectively karaya gum and CAPB, was not explicitly include in Eq.2 due to values similar to the one of water [37].

### 3.4. Surface tension of hybrid nanofluids

The study of ST properties provides insight into the mechanism of heat transfer enhancement and the interaction of surface fluids [51–53]. During the boiling process, part of the liquid vaporizes and forms bubbles, and ST plays an important role in bubble formation and detachment. The results are particularly contradictory concerning changes in ST following the addition of nanoparticles [26,45–49,54–57]. It is difficult to predict whether ST decreases or increases with the increase in nanoparticle mass fraction, and the causes of such behavior is not generalized as well. However, from a practical point of view, a decrease in ST is mostly favorable for heat transfer and heat flux improvement [33]. The present section aims to clarify this issue with the currently

<figure><img src="image_7.png" /><figcaption>Fig. 4. Obtained densities for the graphene-Fe₃O₄ nanofluid set at various temperatures.</figcaption></figure>

<table><caption>**Table 3**
Second-order polynomial adjustments of graphene-Fe₃O₄ nanofluid densities.</caption><thead><tr><th rowspan="2"></th><th colspan="5">Graphene-Fe<sub>3</sub>O<sub>4</sub> mass concentration</th></tr><tr><th>0.005 wt %</th><th>0.010 wt %</th><th>0.020 wt %</th><th>0.050 wt %</th><th>0.100 wt %</th></tr></thead><tbody><tr><td>a<sub>0</sub>, kg/m<sup>3</sup></td><td>631.6</td><td>657.3</td><td>657.4</td><td>632.0</td><td>658.4</td></tr><tr><td>a<sub>1</sub>, kg/(m<sup>3</sup>·K)</td><td>2.70</td><td>2.52</td><td>2.52</td><td>2.70</td><td>2.52</td></tr><tr><td>-10<sup>3</sup>a<sub>2</sub>, kg/(m<sup>3</sup>·K<sup>2</sup>)</td><td>-4.93</td><td>-4.64</td><td>-4.64</td><td>-4.93</td><td>-4.64</td></tr><tr><td>10<sup>2</sup>·s, kg/m<sup>3</sup></td><td>3.2</td><td>1.6</td><td>1.6</td><td>3.2</td><td>5.1</td></tr></tbody></table>
studied hybrid nanofluids. The ST of water, as a reference and yet reported in Fig. 1, mixture of water and surfactants at initial content, and the hybrid nanofluids composed of graphene and Fe₃O₄, with mass fractions of 0.005, 0.010, 0.025, 0.050, and 0.100 wt% was experimentally evaluated at temperatures ranging from 283.15 to 313.15 K. All these experimental data are gathered in Fig. 5.

First, Fig. 5 shows that the presence of the mixture of both surfactants, karaya gum and CAPB respectively, significantly reduces the ST of water by 29.3 % at 283.15 K, 30.2 % at 293.15 K, 35.0 % at 303.15 K and 37.0 % at 313.15 K. These results are generally expected with low viscous and polar fluid like water. Actually, as surfactant molecules are governed by Gibbs adsorption phenomena, they try to form monolayers at the interface and diminish the cohesive forces between liquid molecules, that results in the reduction of ST of the system. These findings agree also with those of Huminic et al. [35], who studied the influence of sodium carboxymethyl cellulose (CMCNa) surfactant on the ST of AgNP-rGO/water and AgNP-rGO/water + ethylene glycol nanofluids, and found that the presence of CMCNa significantly decreased the ST of the base fluid. Du et al. [22] also investigated the modification of the ST of a graphene-based aqueous nanofluid and its effects on the heat transfer process, focusing on the surfactants xanthan-gum (XTG), sodium carboxymethylcellulose (SCMC), and polyvinyl oxide (PEO). Their study demonstrated that, at a concentration of 0.5 %, the dispersant reduced the surface tension by 30.2 % (XTG), 19.9 % (SCMC), and 21.8 % (PEO) in the three systems compared to water. Ahammed et al. [27] have shown that the presence of surfactants also has an effect on the ST of graphene-based nanofluids in the temperature range from 283.15 to 363.15 K, and that the ST of nanofluids decreases in the presence of the surfactant SDBS (5 % vol.). Here, the decrease in ST of the mixture of surfactants and water is larger than in these previous works, and it is sensitive to temperature increase.

The interaction between nanoparticles and surfactants is complex due to the variety of possible involved phenomena and contributions [33]. The Fig. 5 shows the variation in surface tension for graphene-Fe₃O₄/water nanofluids at five nanoparticle concentrations (0.005, 0.010, 0.025, 0.050 and 0.100 wt%). Hence, it is clearly shown that the ST of the graphene-Fe₃O₄ water hybrid dispersions decreases with mass concentration in nanoparticles. In particular, compared to the initial distilled water mixture at 293.15 K, the surfactant results in a 30.2 % reduction. The hybrid solutions demonstrate similarly significant reductions, ranging from 27.1 % for 0.005 wt%, 29.5 % for 0.010 wt%, 33.3 % for 0.025 wt%, 35.4 % for 0.050 wt%, and reaching 41.7 % for 0.100 wt%.

Some theoretical models for liquid and nanofluids surface tension as well as empirical correlations were developed in the past as reported in

<figure><img src="image_8.png" /><figcaption>Fig. 5. Surface tension of distilled water, mixture of distilled water and surfactants, and hybrid graphene-Fe₃O₄ nanofluids in function of temperature. Error bars stand for standard deviation.</figcaption></figure>

[26,27,33,34,58,59]. However, only two correlations refer to graphene nanofluids. The first one was developed by Tian et al. [26] for predicting the surface tension of a dispersion made of commercial graphene nanosheets (thickness 18–20 nm) within ethylene glycol. This correlation, depicted by Eq. (3), has been established for graphene mass content between 0.005 and 5 %, and temperature T (in °C) between 25 and 70 °C. In this equation, the ST is initially expressed in N/m.

$$ \tau_{nf} = 0.0503869 - 0.000228T - 0.0108072\varphi + 3.365 \times 10^{-5}\varphi T + 4.378 \\ \times 10^{-6}T^2 + 0.00568072T^2 + 2.58 \times 10^{-7}T^2\varphi - 9.942 \\ \times 10^{-6}T\varphi^2 - 3.668 \times 10^{-8}T^3 - 0.00073728\varphi^3 \quad (3) $$

The second one, given by the Eq. (4), was established by Ahammed et al. [27] for water based nanofluids containing commercial graphene (thickness 1–5 nm) and SDBS as surfactant. In this equation, T refers to the temperature in °C, and varies between 15 and 90 °C, T∞ is the ambient temperature, taken at 20 °C and φ, defined by Eq. (5), is the nanoparticle volume fraction with the following values 0.05, 0.10 and 0.15 %. It should be noted that here the volume fraction of hybrid nanoparticles is calculated by Eq. (5).

$$ \tau_{nf} = \tau_{bf} \times 0.493 \left(\frac{T_{\infty}}{T_{nf}}\right)^{0.163} \left(\frac{1}{\bar{\varphi}}\right)^{0.0884} \quad (4) $$

$$ \varphi = \frac{\varphi^{\frac{\rho_{bf}}{\rho_{np}}}}{\left(1 - \varphi\left(1 - \frac{\rho_{bf}}{\rho_{np}}\right)\right)} \quad (5) $$

Those correlations are compared to our experimental data in Fig. 6. It should be noted that here the volume fraction of hybrid nanoparticles varies between 0.0022 and 0.047 due to mass fraction considered in this study and density of hybrid nanostructures reported earlier in Section 3.3. It is evident from this figure that those correlations are unable to correctly predict our experimental data. The range of ST value provided by Eq. (3) does not agree with the experimental data, and the values from Eq. (4) are underpredicted. Several coupled reasons can explain such a great deviation, among them one can cite: different base fluid, use of hybrid graphene nanofluid rather than simple graphene nanofluid, dissimilarities in graphene type, dimensions, and structural quality, presence of surfactant, range of nanoparticle content, ...

Consequently, in absence of relevant equations, we propose here a new correlation based on the experimental results of ST of graphene-Fe₃O₄/water hybrid nanofluids. A simple linear regression (LR) for predicting ST ratio for these nanofluids is used. The LR model was developed using a backward elimination approach, considering temperature and nanoparticle mass fraction as significant variables. Such a

<figure><img src="image_9.png" /><figcaption>Fig. 6. Comparison between experimental surface tension data of graphene-Fe₃O₄ aqueous nanofluid and empirical prediction from Eq. (3) [26] and Eq. (4) [27].</figcaption></figure>
correlation is expressed by Eq. (6):

$$ \frac{\tau_{nf}}{\tau_{bf}} = 1.3168 - 0.002 \times T - 1.345 \times \varphi \quad (6) $$

where $\tau_{nf}$ and $\tau_{bf}$ are the surface tension of the hybrid nanofluids and base fluid -namely water-, respectively. T is the nanofluid temperature in Kelvin and $\varphi$ is the nanoparticle mass fraction.

The accuracy of Eq. (6) was evaluated by the deviation margin following the Eq. (7). In this equation, the subscripts Exp. and Pred. represent the experimental and predicted values, respectively.

$$ \text{Deviation margin (\%)} = \left[ \frac{\left( \frac{\tau_{nf}}{\tau_{bf}} \right)_{\text{Exp}} - \left( \frac{\tau_{nf}}{\tau_{bf}} \right)_{\text{Pred}}}{\left( \frac{\tau_{nf}}{\tau_{bf}} \right)_{\text{Pred}}} \right] \quad (7) $$

Fig. 7 compares the results of the proposed equation with the experimental data over a temperature range of 283.15 to 313.15 K and for all nanoparticle contents. Most of the data points lie near or on the bisector, indicating a minimal difference between the experimental surface tension ratio and the values predicted by the Linear regression model (LR). The correlation well predicts surface tension ratio values with an absolute average deviation (AAD) of 2.48 % within the experimental conditions tested. In addition to deviation margin and AAD calculation, Fig. 8a displays both experimental and predicted values of surface tension ratio in function of temperatures and nanoparticle mass content. It is also observed a good accuracy of the proposed equation, the larger deviation being observed at lower nanoparticles content. Finally, as shown in Fig. 8b, the distribution of studentized residuals is expressed in function of predicted surface tension ratio. It is noticed that most of the residuals are centered around the “0” reference line. This indicates that the developed correlation is valid and adequately captures the trend of the data. Additionally, the figure demonstrates a fairly random distribution of residuals with respect to the run order, suggesting that the model effectively considers the temporal aspect of the data.

## 4. Conclusion

Aqueous hybrid nanofluids were synthesized as dispersions of graphene, which were initially obtained through the liquid phase exfoliation of graphite assisted by ultrasonication and the use of a mixture of surfactants, specifically karaya gum and cocoamidopropyl betaine. Additionally, commercial iron oxide nanoparticles were incorporated in a ratio 70/30. The morphologies and dimensions, as well as chemical species of both graphene and iron oxide nanostructures were characterized using transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDX). The stability of these hybrid

<figure><img src="image_10.png" /><figcaption>Fig. 7. Comparison between experimental and predicted surface tension ratio of graphene-Fe₃O₄ aqueous nanofluid.</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. (a) Evaluation of linear regression methodology accuracy by comparing predicted and experimental values of surface tension ratio of hybrid nanofluids at different temperatures; (b) residuals expressed in function of predicted surface tension ratio of hybrid nanofluids.</figcaption></figure>

nanofluids was assessed through ultraviolet–visible (UV–Vis) spectrometry and zeta potential measurement, demonstrating significant colloidal stability. Then, as a preliminary parameter for surface tension measurement, the density of the graphene-Fe₃O₄/water hybrid nanofluids was measured at temperatures ranging from 283.15 to 313.15 K and at various mass fractions of nanoparticles, including 0.005, 0.010, 0.025, 0.050, and 0.100 wt%. The density of all samples exhibited a consistent decrease with increasing temperature, averaging a reduction of 0.27 % for every 10 K increase. The incorporation of graphene-Fe₃O₄ nanoparticles only increased the nanofluid density by 0.10 % at a concentration of 0.100 wt%. The experimental density data were well-represented by a second-order polynomial, enabling the calculation of densities at specific temperatures for further analysis. The surface tension of these hybrid nanofluids were evaluated within the same concentration and temperature ranges. A significant reduction in surface tension was observed with the presence of nanoparticles, which enhanced the effectiveness of the surfactants. At the highest mass concentration of 0.100 wt%, reductions of 39.7 % at 283.15 K, 41.7 % at 293.15 K, 45.0 % at 303.15 K, and 44.1 % at 313.15 K was highlighted. Finally, a linear empirical model was proposed to predict the experimental data with a mean deviation of 2.5 %. These findings provide a foundational basis for investigating the impact of graphene-Fe₃O₄ nanofluids on heat transfer performance across different heat exchanger configurations, from both experimental and numerical aspects. Future work will aim to complement these findings with an examination of the thermal and rheological properties of these hybrid nanofluids, and potential influence of magnetic field on those properties.

## CRediT authorship contribution statement

Soulayma Gal: Writing – original draft, Visualization, Validation,
Investigation, Formal analysis, Data curation. **David Cabaleiro:** Writing – original draft, Visualization, Validation, Investigation, Formal analysis, Data curation. **Walid Hassen:** Writing – review & editing, Supervision, Project administration, Funding acquisition. **Ludivine Raul:** Writing – review & editing, Visualization, Investigation, Formal analysis. **Housseinou Ba:** Writing – review & editing, Visualization, Resources. **Patrice Estellé:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Soulayma Gal, Walid Hassen and Patrice Estellé gratefully acknowledge the financial support of CMCU and Campus France through the grant n°23G1111 from the PHC Utique. Soulayma Gal also acknowledges Rennes Métropole for its financial support through the PhD student incoming mobility grants received in 2022 and 2023. David Cabaleiro is a recipient of a "Juan de la Cierva" contract (Reference IJC2020-043779-I) funded by MICIU/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR.

Data availability

Data will be made available on request.

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