The Impact of Silicon Dioxide Nanoparticle Size on the Viscosity and Stability of Nanofluids: A Comprehensive Study

This study investigated the impact of silicon dioxide nanoparticle size on the viscosity and stability of nanofluids. A comprehensive study was conducted, including the synthesis and characterization of silicon dioxide nanoparticles of varying sizes, as well as the preparation and testing of nanofluids with different nanoparticle concentrations. The results show that nanoparticle size has a significant effect on both the viscosity and stability of nanofluids, with smaller nanoparticles leading to higher viscosity and improved stability. Silicon dioxide nanoparticles were dispersed in deionized water at mass fractions of 0.5% and 3% and average particle diameters of 12 nm and 40 nm using an ultrasonic disperser. The rheological properties of the obtained nanofluids at 304 K were studied depending on the mass concentration and linear size of nanoparticles in the liquid. An analysis of the results showed that the viscosity of the nanofluids increased with decreasing linear size of the nanoparticles. These findings have important implications for the development and optimization of nanofluid-based applications in various industries, such as electronics, energy, and biomedical engineering.

Nanofluids, which are liquids containing nanoparticles, have become increasingly popular due to their potential to enhance heat transfer and improve the performance of various applications. 1 Silicon dioxide nanoparticles are among the most widely used particles for nanofluids due to their excellent thermal and mechanical properties. 2 However, the impact of silicon dioxide nanoparticle size on the viscosity and stability of nanofluids remains a topic of great interest and debate. Nanofluids are a two-phase system consisting of a carrier fluid and nanoparticles. [1][2][3][4][5][6][7][8] They are used in various chemical reactors and plants, including the development of new systems for cooling, heat generation, and transportation of various devices, biotechnology, nanotechnology, and microelectromechanical systems. In addition to the above purposes, they are widely used in the design of new drugs and cosmetics, supply of drugs, detection of various pollutants, development of air and water treatment systems, production of new lubricants, paints, varnishes, building materials, and other areas. [9][10][11][12][13][14][15] The proper use of the application potential of nanofluids depends on the methods of nanofluid preparation.
There are two main methods of preparing nanofluids: one-step and two-step preparation methods. [10][11][12][13][14] The one-step process consists of simultaneously making and dispersing the particles in the fluid. In this method, the processes of drying, storage, transportation, and dispersion of nanoparticles are avoided, so the agglomeration of nanoparticles is minimized, and the stability of fluids is increased. The one-step processes can prepare uniformly dispersed nanoparticles, and the particles can be stably suspended in the base fluid. The two-step method is the most widely used method for preparing nanofluids. The nanoparticles used in this method are first commercially available dry powders with nanoparticles by chemical or physical methods. Then, the nanosized powder will be dispersed into a fluid in the second processing step with the help of intensive magnetic force agitation, ultrasonic agitation, high-shear mixing, homogenization, and ball milling. 7 Usually, ultrasonic dispersants are used to disperse nanoparticles in a liquid to reduce their agglomeration compared to other methods.
Stable dispersion is a major problem associated with this experimental practice because of the strong van der Waals force between nanoparticles and other effects, and the powder is easily coagulated. To enhance the stability of a nanofluid and prevent particles from clustering together, surfactants and stabilizers can be added to the formulation. The surfactant and stabilizer chosen will depend on the characteristics of the nanoparticles and the carrier fluid, as well as the intended use of the nanofluid. Notably, the addition of these substances can alter the viscosity and other physical properties of the nanofluid. The size and concentration of the nanoparticles also affect the properties of the nanofluid. Smaller nanoparticles tend to interact better with the carrier fluid and disperse more easily, but increasing their concentration can lead to instability and higher viscosity. 10 The shape of the nanoparticles can also play a role in the stability of the nanofluid, with spherical nanoparticles generally being more stable than nonspherical nanoparticles. 2,4 Therefore, optimizing the design of a nanofluid requires a comprehensive understanding of how nanoparticles interact with the carrier fluid, including the proper selection of surfactants, stabilizers, particle size, concentration, and shape, all of which can greatly enhance the stability, viscosity, and overall performance of the nanofluid in a variety of applications.
In this study, we investigate the effect of nanoparticle size on the viscosity and stability of nanofluids, providing valuable insights into the design and optimization of nanofluids for various applications. We begin by introducing the concept of nanofluids and their potential applications, with a focus on silicon dioxide nanoparticles due to their desirable thermal and mechanical properties. We then discuss the importance of understanding the effect of nanoparticle size on nanofluid behavior and how this knowledge can inform the design and optimization of nanofluids for various applications. We also provide an overview of the two main methods for preparing nanofluids, namely, one-step and two-step preparation methods, and z E-mail: anand@ms.xjb.ac.cn highlight the challenges associated with achieving stable nanoparticle dispersion. Overall, this study aims to contribute to the growing body of research on nanofluids and provide valuable insights into the design and optimization of these materials for various applications.
Despite such shortcomings, dispersants are the best method for the formation and production of nanofluids. Due to their tendency to coagulate, nanofluids can lose their heat transfer properties. It is, therefore, important to obtain nanofluids that are sustainable over the long term. Sustainability is a major problem that can alter the physical properties of nanofluids. Thus, in this study, it is important to analyze and compare the methods for studying the stability of nanofluids. These methods include ζ-potential analysis, spectral analysis, electron microscopy, dynamic scattering of light, and visual observation.
ζ Potential Analysis Method The ζ potential has great importance in assessing the stability of nanofluids. A schematic representation of the ζ potential is shown in Fig. 1a. According to the analysis of the literature, at high absolute values of the ζ potential, nanofluids maintain a stable state for a longer period 2,16 ( Fig. 1b). In this method, the ability to determine the stability of high-viscosity nanofluids by measuring their ζ potential is limited.
Spectral analysis method.-According to Beer-Lambert's law, the absorption of a solution is directly proportional to the concentration of light-absorbing nanomaterial present in the solution and the wavelength of light. This quantitative method was used to determine the concentration of nanoparticles present in a nanofluid. 17 In this method, the maximum light absorption wavelength was recorded, which was then used to record the light absorption rate of nanofluids of a certain concentration. The absorption rate of light helps to determine the unknown concentration of this nanofluid. The spectral light absorption method can be widely used to evaluate the stability of nanofluids. 18 With this method, it is possible to assess the stability of only highly concentrated nanofluids. 19,20 Electron microscopy method.-Electron microscopy produces images called micrographs, which can provide a clear conclusion about the size distribution of nanoparticles in a liquid base. To achieve this, the method uses a stream of electrons passing through the sample. Unlike optical microscopes, electron microscopes can easily detect materials with a sample thickness of less than 0.5 μm down to the nanoscale. Figure 2 shows a transmission electron microscopy (TEM) micrograph of 0.1% alumina nanoparticle liquid. 21 The most popular methods of electron microscopy are TEM and scanning electron microscopy. The disadvantages of these methods are that the sample must be prepared for study by freezing it to cryogenic temperatures and that the research must be carried out in a vacuum environment. During the sample preparation process, the structure of the sample may change significantly.
Dynamic light scattering method.-Dynamic light scattering (also called photon correlation spectroscopy or quasielastic scattering of light) is an important method for determining and measuring the agglomeration state of nanoparticles. 22,23 When laser light interacts with small particles, a time-dependent change in scattering intensity is observed. The fluctuation of the intensity is primarily because small particles are in Brownian motion, so the distance between the light scatterers in the solution changes over time. The scattered light is observed to be constructive or disruptive interference by surrounding particles, and information on the time scale of the motion of scattering particles in these intensity fluctuations is available. Particle dynamics data are obtained from the autocorrelation of the intensity value table recorded during the experiment. By analyzing the results of the exponential autocorrelation function, the average hydrodynamic measurement of a particle called the Z-average is calculated based on the intensity using the Stokes-Einstein equation. Using this method, the polydispersity index can also be used to determine the distribution of particles by size. Although the method is simple, the reliability of the result depends on parameters such as the optical properties and viscosity of the sample. Sometimes it is necessary to dilute it using a base liquid  to reduce the nanoparticle concentration in the sample for analysis. Therefore, it is very important to analyze the stability or to carefully analyze the object of study before using this method to determine the size of different particles (e.g., to determine the upper limit for particle concentration). When the nanoparticle concentration is high, the phenomenon of multiple scattering results in large systematic errors.
Visual observation method.-The visual observation method is the most common, easiest, and cheapest method of assessing the stability of nanofluids. Although this method depends only on visual observations and requires a certain amount of time, it is the commonly used method among researchers working with nanofluids. Stokes's law for spherical particles (Eq. 1) explains that the sinking rate is lower for small diameter (D np ) particles.
In this case, g is the acceleration of free fall, ρ np is the density of nanoparticles, and ρ f and η f are the density and viscosity of the base fluid, respectively. Although the effect of gravity on nanosized particles is very small, their tendency to agglomerate makes them sensitive to such forces, so sediment is also formed at the bottom (Fig. 3). The study of the sedimentation process involves recording the spontaneous agglomeration of the nanofluid stored in the solution without external influences. We can conclude about the stability of nanofluids according to the volume occupied by the sediment particles in the nanofluid. Sedimentary types in nanofluid systems are divided into flocculated sediments, dispersed sediments, and mixed sediments. 23 To assess the stability of the nanofluid, the next classification of the sedimentation process is evaluated by taking a sediment photograph. [24][25][26] The use of a camera has proven to be a suitable device for taking sedimentation photographs in monitoring the stability of nanofluids. 27,28 The concentration of nanoparticles in nanofluids was considered stable if they were constant over time. It was stated that the photographs taken during the observation to obtain stable nanofluids were related to the effective use of the method. We have seen that in all of the methods analyzed above, there are different limitations for the study of nanoparticles (nanoparticle concentration, complex processes in preparing the sample for study, viscosity, and optical transparency due to its relatively long time). On the other hand, many inconsistencies in the results of different research groups have been noticed during the literature review even for the same nanofluid, 10 which could be due to the effect of preparation and dispersion techniques, particle shape and size, measuring techniques, agglomeration, shear rate, etc.
The fact that nanofluids have a limited time to stay in a stable state requires the development of research methods that are free from the abovementioned limitations in their diagnosis.

Methodology
Amorphous and hydrophilic SiO 2 nanoparticles were used in this study. Nanoparticles are a white powder provided by AEROSIL ® Fumed Silica (Germany) with an average linear size of 12 nm and 40 nm, with a purity of 98%. Ultra-pure deionized water was used as the base liquid.
To obtain a stable dispersion, the suspensions were dispersed in an ultrasonic disperser (ultrasonic disintegrator type UD-11   3-thermostatically controlled jacket where water with a constant temperature is circulated; 4-thermostat with a digital control system; 5-rheometer head with a pneumatic rotation system; 6-compressor; 7-table with pneumatic vertical movement for adjustment; 8-computer with RHEOWIN software for controlling the measurement process and data processing. automatic, Poland) operating at 100 W and 22 kHz for 20 min to prevent initial agglomeration of nanoparticles in deionized water (Fig. 4).
The rheological properties of the sample under study were studied on a RheoStress 600 device from Haake (Germany). The experimental uncertainty of the dynamic viscosity measurements was 0.4%. The block diagram of the automated measuring device is shown in Fig. 5.
Using this equipment, the dependence of the viscosity of nanofluids on the shear rate was studied. Measurements were performed in the range of 900 s −1 to 2000 s −1 with a shear rate. For the measurement of shear rate range measurements, each viscosity spectrum was determined at 600 s. The minimum value of shear stress was from 0.00523 Pa to 1.536 Pa. The sample temperature was maintained at a constant temperature of 304 ± 0.1 K using an external thermostat.
Since almost all applications of nanofluids are related to readability, viscosity is a decisive factor in their use. This factor has prompted many research groups in different countries to conduct research in recent years to study the viscosity of nanofluids. [29][30][31] It was found that the viscosity of nanofluids depends not only on the concentration of nanoparticles but also on their linear size.
Obtaining experimental data on the viscosity of nanofluids is complicated by several factors: difficulties in forming monodisperse suspensions, particle concentration, uniformity of linear size distribution, various methodological problems of accurate measurement of agglomerated particle formation, etc, analyzed in literature. [32][33][34][35][36] Results and Discussion In this study, the temperature of the sample was at room temperature (295 K) during the preparation of the nanofluids. SiO 2 nanoparticles with average diameters of 12 nm and 40 nm were added to deionized water in 0.5% and 3% mass fractions, waited 5 min for the particles to completely sink into the water, and then the obtained mixture was dispersed. The first task we performed in the preparation of nanofluids was to find the optimal exposure time of the ultrasonic dispersant to the suspension. At the same time, the linear dimension of the aggregates changed with the change in the dispersion time in the preparation of nanofluids; as a result, it was shown that this change also affects the rheology of the nanofluids. 35 According to the results of a previous study 37 the dispersing time of the dispersant sample was assumed to be 20 min. The obtained nanofluids were placed in glass containers to study the sedimentation process (Fig. 6). Over 35 d, changes in the samples were observed. According to the results of this visual observation, the linear size of the nanoparticles resulted in more precipitation in 40 nm nanofluids. For example, a nanofluid (with a mass fraction of 0.5%) of silicon dioxide nanoparticles with a linear dimension of 40 nm had a volume of 15 ml in a bottle. After 35 d, 1 ml of sediment was formed as a result of nanoparticle aggregation and gravity in the liquid. Our conclusions from these observations are as follows: it is important to find the optimal time for the dispersion effect on the sample during the preparation of a nanofluid consisting of SiO 2 nanoparticles, i.e., when working with dispersants; in nanoparticle preparation, the smaller the linear size of the nanoparticles, the slower the sedimentation process.
The viscosity of a Newtonian liquid is normally measured by a relative technique in an instrument calibrated using a liquid of known viscosity. The common practice is to calibrate viscometers by a step-up technique using a series of instruments and test fluids based on the viscosity of water. To calibrate the equipment, the viscosity of deionized water was measured at a temperature of 304 K  before measuring the viscosity coefficient of the silicon dioxide nanofluid. The measured values of viscosity for pure water were closely related to the values given in the literature. 38 Studies 39 have shown that the addition of nanoparticles changes the viscosity of the base liquid to a Newtonian or non-Newtonian property. Therefore, the first task of the study was to determine the Newtonian or non-Newtonian properties of the nanofluid (Fig. 7). The equation representing the Newtonian property of a fluid has the following form: In this equation, t-shear stress, η-viscosity coefficient, and Ashear rate. Based on the results obtained, we concluded that the dynamic viscosity of the nanofluid has a constant value at any value of the shear rate (see Fig. 7). The nanofluids studied in the study (both at 0.5% and 3% concentrations) obey Newton's laws.
In summary, the analysis of the experimental results showed that the linear dimension of the nanoparticles is important for the viscosity of the nanofluid. As the linear size of the particles decreases, the viscosity increases. The results, which depend on the viscosity of the liquid in this study, made it possible to estimate the size of the nanoparticles in the liquid. To confirm this conclusion, the viscosity of each sample studied was repeated 5 times. Their average values are shown in the histograms in Figs. 8 and 9. However, it can be seen from these images that the absolute value of the nanofluid viscosity also depends on the mass concentration of the nanoparticles in it. For example, when comparing the viscosity of 12 nm particle samples, we can see that the viscosity of the sample with a mass fraction of 3% increased by 39% relative to the viscosity of the sample with a mass fraction of 0.5%.
The research revealed that the size of silicon dioxide nanoparticles has a notable effect on the viscosity and stability of nanofluids. Specifically, an increase in nanoparticle size results in an increase in nanofluid viscosity and a decrease in its stability. These outcomes hold significant implications for the development and optimization of nanofluids for various applications, including thermal management in electronic devices and industrial heat exchangers. To achieve optimal performance, it is vital to carefully consider the nanoparticle size selection. The study offers insights into the underlying mechanisms that cause changes in viscosity and stability. According to the authors, these changes are caused by larger nanoparticles increasing interparticle interactions and agglomeration, resulting in increased resistance to flow and reduced stability.
The study emphasizes the importance of comprehending the connection between nanoparticle size and nanofluid properties. It provides valuable insights for creating next-generation nanofluids that have enhanced performance and stability.

Conclusions
Based on the results obtained in this study, it can be inferred that the coefficient of viscosity of a nanofluid is influenced by the size of the nanoparticles, with smaller nanoparticles resulting in higher dynamic viscosity coefficients. The use of SiO 2 nanoparticles in the study demonstrated the applicability of Stokes' law for spherical particles in nanofluids, as the increased surface area of interaction between solid particles and liquid caused by the presence of nanoparticles led to an increase in viscosity. The study also revealed that stability is an important factor to consider when working with nanofluids, as precipitation was observed in a 40-nm-sized nanofluid after 35 d of visual observation. By simultaneously studying the viscosity and stability of a silicon dioxide nanofluid, the study allowed for quick and accurate conclusions to be drawn about the linear size of nanoparticles and the stability of a nanofluid. The findings suggest that small-sized nanoparticles can be effectively utilized in controlling the rheological properties of nanofluids. However, to fully comprehend the mechanisms behind the changes in the viscosity coefficient depending on nanoparticle size, further research is required that focuses on the surface properties of nanoparticles. Overall, this study emphasizes the potential of nanofluids in enhancing the rheological properties of liquids and highlights the need for continued research in this field.  . Dependence of the dynamic viscosity of nanofluids on particle size (for a mass fraction of 0.5%) at 304 K. Figure 9. Dependence of the dynamic viscosity of nanofluids on particle size (for a mass fraction of 3%) at 304 K.