Abstract
Shear-thickening fluids (STFs), especially nanofluids, are one of the key research areas in the world at the present time because of their ability to increase viscosity in response to specific shear conditions. This transition in viscosity is of great interest in various fields, including mechanical platforms and smart structures to advanced protective fabrics and armor. This increase in viscosity under applied shear conditions can be of great interest in the development of enhanced geothermal systems (EGSs). However, there is currently less research on the potential application of these shear-thickening nanofluids in EGS reservoirs. In this comprehensive review, the basic mechanisms of shear-thickening behavior in nanofluids are explained, while the effects of nanoparticle concentration, size, and temperature on this mechanism have been discussed in detail. This comprehensive review highlights how such factors can be optimized to adjust the rheological properties of nanofluids in order to improve their performance in fluid flow in highly fractured EGS reservoirs. An in-depth review of existing literature indicated that the combination of hydrolusters formation and the thermal properties of the shear-thickening nanofluids can be optimized to provide a potential solution to some of the EGS challenges such as thermal short-circuiting and low thermal energy extraction efficiency. Despite the huge potential of STF nanofluids in EGS development, extensive experimental and numerical investigations are needed to realize the effectiveness of these fluids further.
1 Introduction
Geothermal energy is swiftly becoming a critical component of the global energy transition to a sustainable future. It is a reliable, abundant, and natural renewable energy source that can significantly reduce the world's reliance on fossil fuels. Currently, the energy sector is dominated by fossil fuels, especially coal, oil, and gas. However, the combination of stringent environmental regulations and the continuous depletion of fossil fuel resources have paved the way for other types of energy resources, including renewable energy sources. Renewable energy systems, such as solar and wind are gradually replacing fossil fuels in the development of a new, carbon-free, and sustainable energy landmark [1,2]. Geothermal energy offers a consistent and constant energy supply compared with solar and wind, and unlike the periodic nature of solar and wind energy that is strongly influenced by seasons, geothermal energy supplies energy 24/7 all year round [3,4]. The potential of geothermal energy is attributed to the thermal gradient in the earth's subsurface. The earth maintains a high temperature deep within its interior due to the impact of many different natural processes. For this reason, there is a stable thermal gradient that extends from the interior to the surface of the earth [3,5]. Geothermal has been characterized by an exceedingly high-capacity factor of above 72% over the past decade [3,4]. Geothermal energy is highly versatile, with applications ranging from direct uses such as food processing, fish farming, greenhouse climate control, and space heating, to electricity generation. The diverse nature of geothermal resources allows for categorization into three main types: (1) geothermal heat pump systems, (2) hydrothermal resources, and (3) enhanced geothermal systems (EGSs) [5]. In contrast to geothermal heat pumps and hydrothermal resources that harness heat from shallow to medium–depth reservoirs, EGS technology targets the extraction of heat from hot, dry rock at significantly greater depth. EGS technology gains the advantage over conventional geothermal physics by creating novel subsurface fractures where heat can be extracted and fluid can flow. Such geoengineering is possible in areas with hot and dry rocks where conventional geothermal reservoirs cannot be established. Activating pre-existing faults and crack systems in the solid rock, and artificially creating new permeable paths in dry rock formations, EGS technology opens a window to the vast amounts of thermal energy stored [4,6].
EGS represents a cutting-edge approach to renewable energy production, offering the ability to tap into the earth's vast geothermal resources in regions where conventional hydrothermal reservoirs are inadequate or nonexistent. Unlike traditional geothermal systems, which rely on naturally occurring hydrothermal reservoirs, EGS can be deployed in a wider range of geological settings by artificially stimulating or creating permeability in hot, dry rock formations deep beneath the earth's surface [6,7]. In other words, EGS enables the exploitation of huge geothermal energy within interconnected fractures, albeit on a much bigger scale than systems exploiting hydrothermal reservoirs. However, the development of EGS is still significantly limited by many challenges. Kumari and Ranjith [8] observed that geothermal technologies like EGS are still at the demonstration and development stage; thus, they present technological, economic, and environmental hurdles that impede the widespread commercial use of this energy. Addressing these challenges is imperative to maximize the potential of alternative geothermal resources as a clean and sustainable energy source. One of the most critical technical challenges is thermal short-circuiting [6,9]. Thermal short-circuiting occurs when the working fluid, typically water or brine, flows preferentially through high-permeability fractures within the EGS reservoir, thus preventing the fluid from reaching zones with low fracture conductivity where the thermal output could be higher. These fractures with high aperture offer less resistance to fluid flow. As a result, the fluid–rock thermal interaction is greatly reduced, leading to suboptimal heat transfer and efficiency of the geothermal system [6,10]. This issue is compounded by the complexity of subsurface conditions in EGS reservoirs, where natural and induced fractures can create unpredictable flow paths. Managing and optimizing the fluid flow through these fractured networks is crucial to maximizing the thermal output of the system. Advanced techniques such as hydraulic fracturing, chemical stimulation, and the use of shear-thickening fluids (STFs) are being explored to mitigate thermal short-circuiting by enhancing the connectivity of low-permeability zones and controlling the flow pathways within the reservoir by altering the permeability through an increase in viscosity or gelation [6,10].
Among these potential solutions, the application of STFs, such as nanofluids, is gaining significant interest. These fluids are particular because of their rheological behavior where the viscosity shows a sharp increase under applied shear conditions. At small shear rates, STFs behave like any fluid as they undergo large deformations under the action of small stresses and, thus, flow. However, beyond a given critical shear rate, STFs undergo a rapid increase in resistance to flow and transition to a solid-like behavior due to the formation of particle aggregates known as “hydroclusters” [11–13]. Shear-thickening behavior could occur through multiple mechanisms, including the order–disorder mechanism, the hydrocluster mechanism, and the role of contact angle [14]. The hydrocluster theory, in particular, has indicated that increasing shear rate causes particle collisions in the fluid until a cluster of particles, known as a hydrocluster is formed. These dense clusters drastically increase the nanofluid's resistance to flow. This sharp increase in viscosity under shear conditions can be harnessed to control fluid flow dynamics in EGS reservoirs. Applying the principles of shear-thickening nanofluids (STNFs) to the heart of EGS operations enables optimization of thermal energy extraction by retaining the working fluid in contact with the reservoir's hot zones, rather than letting it pass by through relatively high-permeability fractures.
This comprehensive review offers an in-depth overview of shear-thickening fluids, with special emphasis on nanofluids, and discusses the role that shear-thickening nanofluids could play in developing next-generation geothermal energy technologies such as EGS. The review introduced the special features of shear-thickening nanofluids, described the underlying mechanisms of shear-thickening effects, and explained how the shear-thickening phenomenon of the nanofluids can be leveraged for EGS applications through providing flowrate control and optimizing thermal energy extraction efficiency.
2 Shear-Thickening Behavior in Nanofluids
Nanofluids are special kinds of colloidal suspensions where nanoparticles are suspended in a base fluid or carrier fluid. These are specially designed to take advantage of the unique properties of the nanoparticles to obtain enhanced thermal, electrical, and rheological behaviors as compared to conventional fluids. One of the most obvious characteristics of the nanofluids is their shear-thickening response at a higher shear rate.
Shear thickening, often called dilatant fluidity and also categorized as a non-Newtonian behavior, reflects an increase in viscosity as the applied shear rate exceeds a critical value [11,12]. At a certain critical shear condition, the viscosity of a shear-thickening fluid increases sharply. This viscosity trend contradicts the Newtonian fluid profile in which the viscosity remains constant regardless of shear rates. Shear-thickening fluids under stress increasingly resist flow, which is usually associated with the formation of hydroclusters, known as temporary, localized, dense agglomerates that form under high shear conditions [15,16]. Figure 1 shows the profile of a shear-thickening fluid. Under the same shear stress, fluid viscosity sharply increases as the shear rate increases past a critical value, reflecting the onset of shear thickening.
2.1 Mechanism of Shear Thickening in Nanofluids.
Shear-thickening behavior in nanofluids can be an extremely complex and intriguing rheological phenomenon where the fluids' viscosity increases when subjected to an applied shear rate. Unlike conventional Newtonian fluids, non-Newtonian behavior is observed in various nanofluids, and this behavior is primarily attributed to the interactions between dispersed nanoparticles and the carrier fluid under varying shear conditions. Understanding the mechanisms behind shear thickening is critical for optimizing nanofluid formulation for industrial and engineering applications, such as enhanced geothermal systems, protective materials, and shock absorbers. Several self-consistent mechanical mechanisms in terms of particle–particle interaction and particle–solvent interaction, which mainly include the order–disorder transition (ODT), hydroclustering, jamming, and friction contact theory [12,17].
2.1.1 Order–Disorder Transition.
The ODT was proposed as a key mechanism to explain the shear-thickening behavior in nanofluids and other shear-thickening fluids in 1974 by Hoffman [12]. His studies laid the foundation for understanding the micromechanical structure of shear-thickening fluids. These studies highlighted the crucial role of particle organization within suspensions, forming the basis of the ODT theory. According to this theory, at shear rates below a critical value, the nanoparticles in suspension adopt a layered, ordered structure, allowing for relatively smooth flow. However, as the shear rate increases beyond a critical threshold, the hydrodynamic forces acting on the particles intensify, disrupting the layered arrangement. This disruption leads to a transition from an ordered to a disordered state, resulting in a sharp increase in suspension viscosity [12,18]. Hoffman's work demonstrated that at low shear rates, the ordered particle layers are able to move past each other easily, resulting in shear-thinning behavior. In the shear-thinning region, repulsive particle–particle interactions, such as electrostatic forces, maintain the particles in a minimum disrupted state. However, as the shear rate increases, the shear forces become more dominant over the repulsive forces, causing the particles to lose their equilibrium position. As a result, the particle configuration is disordered, which dramatically increases the viscosity of the suspension, leading to shear-thickening behavior [19,20]. The ODT model (Fig. 2) shows that the transition from order to disorder is responsible for the shear-thickening phenomenon, particularly when particles are arranged in layers. At low shear rates, the ordered particles interact less strongly, leading to smooth, low-viscosity flow. Once the critical shear rate is surpassed, the particles collide more frequently, and their movements become increasingly chaotic, contributing to an increase in viscosity. This transition is what Hoffman described as the core of the shear-thickening mechanism. Several studies have supported and expanded upon these theories of shear thickening in nanofluids. Bender and Wagner [19] provided experimental evidence for the ODT mechanism by showing that suspensions of colloidal particles exhibited shear-thickening behavior consistent with the transition from ordered to disordered states. Their work confirmed Hoffman's hypothesis that ordered particle arrangements at low shear rates gave way to disordered, high-viscosity structures as the shear rate increased. Similarly, Selim et al. [20] conducted rheological studies on various nanoparticle suspensions, confirming that particle disorganization at high shear rates was a key factor in the observed shear-thickening behavior.
![Order–disorder transition shear-thickening mechanism (adapted from Selim et al. [20])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f002.png?Expires=1740397584&Signature=CcKODqw7brGX3bIdb-jRM4Yv6J5iFzwX9JtKMGRHC8wrXlGRHYfWhFgYi3UWQHU059bsMMhqcH0gLsoa3JGrRigGVjso7QQy3rzGcgmeqSEoNcUfEitwNX2Mr0SvYGA2Z-S6k9eXs5mlqj4vwlx5lZxxj0sSssvlJqAcuxLfblqPJq2DJHsJ1yXPvzNy7YO1wZi1aIZ4cNYXzRjQU1BipNgbpN3jWzZsWj~uSATyMgnx8Oa~QVVo5P22tIDhsDr7GLbTuF-6CzjhT27N1TaPsGN3n7feTPljzukGuRFE2lyweF1XLwtzwSZtSH3K0l0vqpBjKpOr7EhZrkdhRWz0fQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Order–disorder transition shear-thickening mechanism (adapted from Selim et al. [20])
![Order–disorder transition shear-thickening mechanism (adapted from Selim et al. [20])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f002.png?Expires=1740397584&Signature=CcKODqw7brGX3bIdb-jRM4Yv6J5iFzwX9JtKMGRHC8wrXlGRHYfWhFgYi3UWQHU059bsMMhqcH0gLsoa3JGrRigGVjso7QQy3rzGcgmeqSEoNcUfEitwNX2Mr0SvYGA2Z-S6k9eXs5mlqj4vwlx5lZxxj0sSssvlJqAcuxLfblqPJq2DJHsJ1yXPvzNy7YO1wZi1aIZ4cNYXzRjQU1BipNgbpN3jWzZsWj~uSATyMgnx8Oa~QVVo5P22tIDhsDr7GLbTuF-6CzjhT27N1TaPsGN3n7feTPljzukGuRFE2lyweF1XLwtzwSZtSH3K0l0vqpBjKpOr7EhZrkdhRWz0fQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Order–disorder transition shear-thickening mechanism (adapted from Selim et al. [20])
2.1.2 Hydroclustering Theory.
While the ODT mechanism provided a critical early understanding of shear thickening, subsequent research has revealed that it is not the sole mechanism responsible for this phenomenon. Initially, Hoffman's work proposed that shear thickening arises from an order to a disorder transition in which the particles in a suspension transition from an ordered, layered state to a disordered one under increasing shear rates. This disruption in particle layering was thought to impede flow and cause a rise in viscosity. However, more recent studies have demonstrated that shear thickening can also occur in systems that do not exhibit any discernible ordered structure. In 1989, Bossis and Brady [21] significantly expanded upon Hoffman's work by introducing the concept of hydroclustering as an alternative or complementary mechanism for shear thickening. They demonstrated that shear-thickening behavior is not entirely dependent on the existence of an ordered structure. Instead, it can occur even when particle clusters form in various orientations under high shear conditions [21]. Hydroclustering (as illustrated in Fig. 3) describes the formation of transient, stress-bearing clusters of particles as the shear rate increases. These clusters, known as hydroclusters, emerge when hydrodynamic forces dominate the suspension, overcoming the repulsive interactions—such as electrostatic or steric repulsions—that normally keep the particles apart. Unlike the ODT model, where the ordered particle arrangement is essential for shear thickening, hydroclustering occurs irrespective of the initial particle arrangement and structure. At low shear rates, the suspension flows relatively easily because the weak hydrodynamic forces allow the particles to remain in a stable, dispersed state. In this regime, Brownian motion, electrostatic repulsion, and interparticle forces maintain the separation between particles. However, as the shear rate increases, hydrodynamic interactions begin to dominate, forcing the particles closer together and inducing the formation of hydroclusters. The emergence of these hydroclusters leads to a significant rise in viscosity, resulting in the characteristic shear-thickening response [21]. Neutron scattering experiments and rheo-optical techniques have confirmed the formation of these clusters in real-time under high shear rates [11]. In these studies, it was observed that as the shear rate exceeds a certain critical threshold, the hydrodynamic forces overcome the stabilizing interparticle repulsions, compressing the particles into tightly packed clusters. These hydroclusters act as barriers to the flow of the suspension, dramatically increasing its viscosity and resulting in shear thickening. The hydroclustering theory has since become the most widely accepted mechanism for explaining shear-thickening behavior in fluids including nanofluids. Nanofluids, which are colloidal suspensions of nanoparticles, show similar shear-thickening properties to those observed in larger particle systems. However, the smaller particle size and higher surface area-to-volume ratio in nanofluids can amplify the effects of interparticle interactions, making hydroclustering even more prominent. At elevated shear rates beyond a critical point, the combination of interparticle forces such as Van der Waals forces, hydrodynamic interactions, and electrostatic repulsions cause nanoparticles to draw closer together, leading to the formation of clusters. The formation of these hydroclusters increases the effective volume fraction of the dispersed phase, which, in turn, results in a significant rise in viscosity [11,14]. Selim et al. [20] conducted a detailed study that supports this theory, showing that beyond the critical shear rate, the hydrodynamic forces in the suspension begin to dominate, suppressing the repulsive forces between particles. This suppression leads to the formation of stress-bearing particle clusters, which impede flow and cause shear thickening. Their experiments, combining rheological measurements and numerical simulations, showed that as particles aggregate into hydroclusters, the interparticle gaps shrink dramatically, leading to the significant viscosity increase that defines shear-thickening behavior. The hydroclustering theory has been substantiated through a combination of experimental and numerical approaches. Techniques such as neutron scattering, rheological testing, and rheo-optical methods have provided direct evidence of the formation of hydroclusters under shear. These experiments have visualized the structural changes occurring within suspensions as the shear rate increases, providing real-time insight into the dynamics of cluster formation. In addition, computer simulations have played a key role in confirming the hydrocluster theory. Numerical models, including Stokesian dynamics and DPD, have been used to simulate the behavior of colloidal suspensions and nanofluids under varying shear conditions. These simulations have consistently shown the formation of transient clusters at critical shear rates, confirming that hydroclustering is a primary driver of shear thickening [21,23]. Moreover, experimental work by Raghavan and Khan [14] revealed that the effective volume fraction of a suspension increases significantly when particles aggregate into hydroclusters, explaining the dramatic rise in viscosity. This phenomenon occurs because the hydroclusters behave as larger entities within the fluid, taking up more space and increasing the resistance to flow.
![Illustration of hydrocluster theory explains the shear-thickening mechanism in nanofluids (adapted from Zarei and Aalaie [22])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f003.png?Expires=1740397584&Signature=JwWhRLQrADyZiBbXm8zZ01Hc3KHjHFu8qlHkur1pi0NdojHMTAr4WKsN0v4KxIi9sAhQpOWwDGnx3AfYNna7uXcXMealqxRYr4e2piSzqWMrCZyDCMyfby9eHgiVUHY9kXOR9FYMdTkOSwvI6BVx5nkLR2IYQZdUU-qqKx-S07AHaCaJpgx7hgX8g99luObEoPGuYI5T3HNZSPKZMh6-M73roTkMv2g1hvNcxBvPsqH64RGUMgbCQ9GM98fASPozkU2VGY75iomrkt1RrRkkPCrT~YLkKS6pW2BvJ00hp1DzXp3IZCtyr~uMvZO4IYQCDzpJEMPuJqs3QRDRTq8nOw__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Illustration of hydrocluster theory explains the shear-thickening mechanism in nanofluids (adapted from Zarei and Aalaie [22])
![Illustration of hydrocluster theory explains the shear-thickening mechanism in nanofluids (adapted from Zarei and Aalaie [22])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f003.png?Expires=1740397584&Signature=JwWhRLQrADyZiBbXm8zZ01Hc3KHjHFu8qlHkur1pi0NdojHMTAr4WKsN0v4KxIi9sAhQpOWwDGnx3AfYNna7uXcXMealqxRYr4e2piSzqWMrCZyDCMyfby9eHgiVUHY9kXOR9FYMdTkOSwvI6BVx5nkLR2IYQZdUU-qqKx-S07AHaCaJpgx7hgX8g99luObEoPGuYI5T3HNZSPKZMh6-M73roTkMv2g1hvNcxBvPsqH64RGUMgbCQ9GM98fASPozkU2VGY75iomrkt1RrRkkPCrT~YLkKS6pW2BvJ00hp1DzXp3IZCtyr~uMvZO4IYQCDzpJEMPuJqs3QRDRTq8nOw__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Illustration of hydrocluster theory explains the shear-thickening mechanism in nanofluids (adapted from Zarei and Aalaie [22])
2.1.3 Jamming Transition Theory.
In addition to the order–disorder transition and hydrocluster theory, the jamming transition theory is another mechanism that plays a significant role in explaining the shear-thickening behavior observed in nanofluids. The jamming transition shares similarities with the hydroclustering mechanism, yet it operates on a more macroscopic scale. While hydroclustering refers to the formation of dense, transient particle clusters under increasing shear stress, the jamming transition occurs when these particle–particle interactions become so dominant that they reach a critical threshold where the particles “jam,” leading to a substantial increase in viscosity and resistance to flow. The jamming transition is typically observed in concentrated colloidal suspensions and granular materials. As the applied shear stress increases, the particles in the fluid become more closely packed, and the lubricating layer between them diminishes. This leads to an increase in frictional interactions and interparticle forces, resulting in a loss of fluidity. At a critical point, the particles are so densely packed that the system forms a solid-like network or matrix within the fluid, which significantly impedes movement and causes a dramatic rise in viscosity. This solid-like behavior is characteristic of a jamming transition, in which the system transforms from a flowing, liquid-like state to a jammed, solid-like state. Brown and Jaeger [24] highlighted that this transition occurs when the system is pushed beyond a critical shear rate, causing a structural change that results in the fluid behaving more like an amorphous solid. Unlike typical solids, the structure formed during jamming is disordered, with particles locked in place due to the overwhelming contact forces that arise under high stress. This leads to what is often referred to as a “dynamically arrested” state, where particle mobility is significantly restricted. In the context of nanofluids, the jamming transition is particularly relevant because the presence of nanoparticles significantly alters the flow dynamics compared to traditional fluids or colloidal suspensions. Nanoparticles tend to form complex interaction networks due to their high surface area-to-volume ratio and the strong interparticle forces they experience, such as van der Waals forces and electrostatic interactions. As shear stress increases, these particles experience progressively stronger interparticle interactions, which drive the system toward a jamming transition. Nanofluids, especially those with high concentrations of nanoparticles, can reach this jamming state more readily because of the tighter packing of nanoparticles and their ability to form interconnected networks. As Barnes [25] explained, in concentrated suspensions, the balance between hydrodynamic and contact forces determines whether shear thickening (and potentially jamming) will occur. In nanofluids, the presence of strong, short-range forces between particles enhances the likelihood of this jamming transition under high shear rates. Experimental studies have provided substantial evidence for the jamming transition in nanofluids. For example, Fall et al. [26] demonstrated that suspensions with high particle concentrations exhibit a sharp increase in viscosity at a critical shear rate, corresponding to the onset of jamming. This observation was consistent with both theoretical predictions and simulations of jamming transitions, further supporting the idea that such transitions are central to the shear-thickening behavior seen in nanofluids. Additionally, Cates et al. [27] emphasized that the shear thickening caused by jamming is a robust phenomenon across a wide range of systems, including both colloidal and non-colloidal suspensions. In nanofluids, the addition of nanoparticles not only increases the viscosity but also shifts the critical shear rate at which jamming occurs, due to the unique properties of nanoscale interactions. While both the hydrocluster and jamming transition theories explain shear-thickening behavior, they differ in the scale and nature of particle interactions. Hydroclustering involves the formation of dense particle aggregates due to hydrodynamic forces under shear, but the particles retain some degree of fluidity within the clusters. In contrast, jamming represents a more severe form of crowding where particles lose mobility entirely and behave like a solid. According to Wagner and Brady [11], the transition from hydroclustering to jamming can be viewed as a continuum. At low shear rates, shear thickening is dominated by hydrocluster formation, where particles temporarily form clusters that resist flow. As the shear rate increases and these clusters grow denser, the system may cross into a jamming regime, where the particles effectively “jam” and the suspension behaves like a solid. This progression highlights the interconnected nature of these mechanisms in explaining the complex rheological behavior of shear-thickening fluids.
2.1.4 Friction Contact Theory.
The frictional contact theory was introduced to bridge the gap between the jamming and hydrocluster theories by considering the transition from fluid lubrication-dominated interactions to solid friction-dominated contacts between particles. This theory proposes that when the normal contact forces between particles are relatively small, the fluid lubrication forces dominate. These lubrication forces prevent direct particle–particle contact, allowing the suspension to flow with relatively low viscosity. However, as the shear rate increases and the normal contact forces between particles grow stronger, the lubrication film between particles breaks down. This leads to an increase in the contact angle between the particles thus, enhancing the particle–particle interaction where the frictional forces dominate. This increase in the particle–particle interaction causes the nanofluids to transition from a liquid-like state to a more solid-like state. Seto et al. [29] introduced the frictional contact model, showing that at high shear rates, particle surfaces come into direct contact, increasing friction between them. This frictional contact results in the significant viscosity rise characteristic of shear thickening. Their work demonstrated that adding friction to existing models of shear thickening provided a more comprehensive explanation, particularly for systems with both Brownian and non-Brownian particles. Similarly, Mari et al. [30] further confirmed that the transition to frictional contact explains why some suspensions exhibit DST. In these cases, a small increase in shear rate leads to a dramatic rise in viscosity due to the onset of friction-dominated contacts between particles. For Brownian suspensions, the hydrocluster mechanism is dominant at low to moderate shear rates, but at higher shear rates, the transition to frictional contacts drives the sharp increase in viscosity. In non-Brownian suspensions, the jamming theory provides a more accurate description of the behavior, where particle crowding and force chains are responsible for the shear-thickening response. Recent studies have shown that the frictional contact theory effectively unifies these two frameworks by introducing the role of contact forces. When lubrication forces fail to keep particles apart, the resulting frictional forces between particles lead to a dramatic increase in viscosity seen in both Brownian and non-Brownian suspensions. Hermes et al. [31] demonstrated that both jamming and hydrocluster theories could be viewed through the lens of frictional interactions. They observed that by controlling the lubrication and friction forces, they could replicate shear-thickening behavior across a wide range of particle sizes and suspension types, supporting the idea that frictional contacts are a universal mechanism for shear thickening.
2.2 Factors Influencing Shear-Thickening Behavior in Nanofluids.
Shear thickening is a non-Newtonian flow behavior characterized by a sharp increase in viscosity beyond a certain shear condition. In nanofluids, this phenomenon can be particularly pronounced due to the nature of the nanoparticles and is often predominately explained by the hydrocluster theory. According to this theory, under low to moderate shear rates, particles move relatively independently, and the fluid behaves in a Newtonian manner. However, at higher shear rates, particles form transient, densely packed clusters called hydroclusters due to hydrodynamic interactions. These clusters lead to a rapid increase in viscosity, which is characteristic of shear thickening. While hydrocluster theory provides a foundational understanding of shear thickening in nanofluids, several other factors significantly influence the onset and intensity of this behavior. The most critical parameters include nanoparticle concentration, particle size and shape, properties of the carrier fluid, and temperature. Each of these factors contributes to the dynamics of nanoparticle interaction, hydrocluster formation, and the overall rheological behavior of nanofluids under shear.
2.2.1 Nanoparticle Concentration.
The concentration of nanoparticles in a suspension plays a crucial role in determining the onset and extent of shear thickening in a nanofluid system. At low concentrations, nanoparticles are more dispersed, and the interactions between them are limited. However, as the concentration increases, the particles come into closer proximity, making it easier for hydroclusters to form under shear stress. This leads to an earlier onset of shear-thickening behavior and a more pronounced increase in viscosity. Wagner and Brady [11] indicated in their study that the viscosity of nanofluid suspensions increases non-linearly with nanoparticle concentration, where higher concentrations promote hydrocluster formation at low shear rates. They reported that suspensions with higher particle loading exhibited more dramatic shear-thickening behavior due to the increased probability of particle collisions and interaction under shear. Zarei and Aalaie [22] reported that an increase in particle volume fraction tends to lead to a decrease in the critical shear rate. This implies that at higher particle concentration suspensions, hydrodynamic forces enhance due to the decrease in distance between particles. As a result, a lesser shear rate can overcome repulsive forces. Their study highlighted that the shear-thickening behavior becomes stronger by increasing the volume fraction (Fig. 4) as the high particle volume fraction leads to confinement and limitations of particle motion in the suspension.
![Shear-thickening behavior of nanofluids at different volume fractions of nanoparticles (adapted from Zarei and Aalaie [22])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f004.png?Expires=1740397584&Signature=BqttQ~21widS8QjhXHIBcJjBzTWbp9VVrAaHJoIj1CKyPg1ag8pI1wbfUJLuGWPZe~T3qAjZbcov~6XlMaoM1XrAS~zF2YnKa6Lzi26-oHw2B6mBl7PwnUOHtMQpMdq9LF12Ck0nX-wKNKTA5lKn7hr08nwH6Nf9cvUTKrNjRYbAwGUMUry3i6KJPVsy6RnCgn27Td0m~cHFEtA5WazWcB2QyqA2eBqwBZeD774nmnYOjp6ZjfMYdmiClJ1PvgmrPJSRUq0Kzeb4eKz5mwaM6Oh4wvQIy1ZufstOCxt~X283aazd~F12JMFnDCu6DTIiLUzAebnGl9OP5dpEcOnCrA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Shear-thickening behavior of nanofluids at different volume fractions of nanoparticles (adapted from Zarei and Aalaie [22])
![Shear-thickening behavior of nanofluids at different volume fractions of nanoparticles (adapted from Zarei and Aalaie [22])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f004.png?Expires=1740397584&Signature=BqttQ~21widS8QjhXHIBcJjBzTWbp9VVrAaHJoIj1CKyPg1ag8pI1wbfUJLuGWPZe~T3qAjZbcov~6XlMaoM1XrAS~zF2YnKa6Lzi26-oHw2B6mBl7PwnUOHtMQpMdq9LF12Ck0nX-wKNKTA5lKn7hr08nwH6Nf9cvUTKrNjRYbAwGUMUry3i6KJPVsy6RnCgn27Td0m~cHFEtA5WazWcB2QyqA2eBqwBZeD774nmnYOjp6ZjfMYdmiClJ1PvgmrPJSRUq0Kzeb4eKz5mwaM6Oh4wvQIy1ZufstOCxt~X283aazd~F12JMFnDCu6DTIiLUzAebnGl9OP5dpEcOnCrA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Shear-thickening behavior of nanofluids at different volume fractions of nanoparticles (adapted from Zarei and Aalaie [22])
Prabhu and Singh [28] conducted a comprehensive study to investigate the impact of different concentrations of silica nanoparticles on the shear-thickening behavior of nanofluids. They experimentally investigated four silica concentrations and demonstrated a clear relationship between nanoparticle content and the rheological properties of the nanofluid. Their study found that increasing the weight fraction of silica nanoparticles led to a decrease in the critical shear rate, which is the point at which shear-thickening behavior is initiated, and a significant increase in the maximum viscosity during shear thickening as illustrated in Fig. 5. The observed decrease in the critical shear rate as the nanoparticle concentration is increased can be attributed to the increased likelihood of particle–particle interactions at higher concentrations. In nanofluids, as the concentration of nanoparticles increases, particles are positioned closer to one another, increasing the probability of particle interactions and the formation of hydroclusters under shear stress according to the hydrocluster theory [21]. These transient clusters, as explained by the hydrocluster theory, are responsible for the rapid increase in viscosity. The more concentrated the suspension, the earlier these hydroclusters form, leading to shear thickening at low shear rates. Furthermore, the increase in maximum viscosity with higher concentrations is linked to the stronger and more frequent particle–particle interactions as the nanoparticles come into closer contact under high shear conditions. The dense packing of particles in the suspension creates resistance to flow, contributing to the dramatic increase in viscosity that is characteristic of shear-thickening fluids. This is consistent with frictional contact theory, which suggests that at high shear rates, the fluid lubrication forces between particles are insufficient to keep them apart, leading to direct particle contact and frictional forces that significantly enhance the viscosity [29,30]. Wagner and Brady [11] provided a theoretical framework showing that the formation of hydroclusters in suspensions is directly influenced by particle concentration. Their study demonstrated that as the volume fraction of particles increases, the shear rate at which hydroclusters form decreases, resulting in an earlier onset of shear thickening. Wagner and Brady [11] indicated that the influence of nanoparticle concentration can be attributed to the formation of larger “particle clusters,” which increase the system's flow resistance, thereby intensifying the shear-thickening effect. As nanoparticle concentration rises, the shear thickening becomes progressively more pronounced.
![Suspension viscosity as a function of shear rate for different weight fractions of silica nanoparticles (adapted from Prabhu and Singh [28])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f005.png?Expires=1740397584&Signature=Z~7voYjEf1r9qAgLZTtzdR3H-2mxNCb7IZ07slxHU2m5W6lcrpmXC8kdgMrT~6dyLVmaJi3WfuRn2PH-XkizTDQYrZfq47tFh4Xuu8eIKeIBmzqRyOTJgeZXGO6u6PYEB8IJxOV8QAv2ecsO65AzZVawtryAI3MZ1viMCVsLq-h5qRQF~y2bSLZE0AZyELbbBbBI9aPi2MKQwnKvDOAUjKBlK5FktHAK9bBc916Rf5DBQPA~bQuW3nSkETAnj5HLKbvHCFWTtZoe2SjMqONmGcGjwltBKJ~SmUPawzGmi1Ul0ZMAUqhkPYiZw7n1mkU-nEqDrJY3AWy-r8BHVpijAQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Suspension viscosity as a function of shear rate for different weight fractions of silica nanoparticles (adapted from Prabhu and Singh [28])
![Suspension viscosity as a function of shear rate for different weight fractions of silica nanoparticles (adapted from Prabhu and Singh [28])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f005.png?Expires=1740397584&Signature=Z~7voYjEf1r9qAgLZTtzdR3H-2mxNCb7IZ07slxHU2m5W6lcrpmXC8kdgMrT~6dyLVmaJi3WfuRn2PH-XkizTDQYrZfq47tFh4Xuu8eIKeIBmzqRyOTJgeZXGO6u6PYEB8IJxOV8QAv2ecsO65AzZVawtryAI3MZ1viMCVsLq-h5qRQF~y2bSLZE0AZyELbbBbBI9aPi2MKQwnKvDOAUjKBlK5FktHAK9bBc916Rf5DBQPA~bQuW3nSkETAnj5HLKbvHCFWTtZoe2SjMqONmGcGjwltBKJ~SmUPawzGmi1Ul0ZMAUqhkPYiZw7n1mkU-nEqDrJY3AWy-r8BHVpijAQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Suspension viscosity as a function of shear rate for different weight fractions of silica nanoparticles (adapted from Prabhu and Singh [28])
2.2.2 Particles Size and Shape.
In addition to the concentration of nanoparticles, the size and shape of nanoparticles significantly influence the shear-thickening behavior of nanofluids. Nanoparticles come in various shapes and sizes. Some of the most common shapes include spheres, rods, plates, and grains. These shapes all have different impacts on the shear-thickening tendencies of associated nanofluids. Barnes [25] demonstrated that rod-shaped particles are more prone to aligning and forming complex structures under shear, which amplifies the thickening effect. This occurs because elongated particles, such as rods, contribute to larger and more stable hydroclusters, leading to a more pronounced increase in viscosity compared to spherical or plate-like particles. Further supporting this trend, Bossis and Brady [21] and Phung et al. [32] found that hydrodynamic stresses are proportional to the cube of the largest dimension of hydroclusters. This indicates that elongated particles, such as rods, generate greater resistance to flow than spherical particles, thus intensifying the shear-thickening behavior. Smaller nanoparticles with higher surface areas also play a role in forming more stable hydroclusters, which further enhances the shear-thickening response. Similarly to nanoparticle shape, particle size substantially impacts the shear-thickening behavior of nanofluids. Barnes [25] highlighted that smaller particles exhibit a low critical shear rate due to their larger surface area and higher interaction potential, making them more effective in inducing shear thickening (Fig. 6). These studies emphasize the significance of both particle shape and size in the shear-thickening behavior of nanofluids.
![Influence of particle size on the critical shear rate of a shear-thickening nanofluid (adapted from Barnes [25])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f006.png?Expires=1740397584&Signature=sRtvOsWg2WeG2ZtKyGoEsSpP~cAoJr1~GoUNrV4yx4tIhzLcktZFqQjyup3ZTorkMlud~pISGmWcJ5MmJGX~Wn7yLlXOdzNbcb5FqFPgRZLiFgC3yEbWXP0acxHk8Zxfpmu8g9OnTQHkLS7uZq1f~ZtvFL2uHR~JqC0sEO4bEdRntzHXm3GgUgQwjFdODb7VSVI9TJ3K9WpFy1HEtGlvlvdJuCLnwdgN8aZDD5u4LGHuwfEbACVcbwunvWxPbScrJkNCF64w0nZgV1OlbEC-k8kWGPqAsOpY7c8gclIE~K0Bep4dN3otDc2H8-dM10Yxb7lUaBnYzgaT0-baHYBIVQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Influence of particle size on the critical shear rate of a shear-thickening nanofluid (adapted from Barnes [25])
![Influence of particle size on the critical shear rate of a shear-thickening nanofluid (adapted from Barnes [25])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f006.png?Expires=1740397584&Signature=sRtvOsWg2WeG2ZtKyGoEsSpP~cAoJr1~GoUNrV4yx4tIhzLcktZFqQjyup3ZTorkMlud~pISGmWcJ5MmJGX~Wn7yLlXOdzNbcb5FqFPgRZLiFgC3yEbWXP0acxHk8Zxfpmu8g9OnTQHkLS7uZq1f~ZtvFL2uHR~JqC0sEO4bEdRntzHXm3GgUgQwjFdODb7VSVI9TJ3K9WpFy1HEtGlvlvdJuCLnwdgN8aZDD5u4LGHuwfEbACVcbwunvWxPbScrJkNCF64w0nZgV1OlbEC-k8kWGPqAsOpY7c8gclIE~K0Bep4dN3otDc2H8-dM10Yxb7lUaBnYzgaT0-baHYBIVQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Influence of particle size on the critical shear rate of a shear-thickening nanofluid (adapted from Barnes [25])
2.2.3 Properties of Carrier Fluid.
Carrier fluid or base fluid is another significant component that impacts the rheological properties and shear-thickening tendencies of nanofluids. The molecular weight, viscosity, and overall rheology of the carrier fluid directly influence the rheological response of nanofluids under shear stress. Boersma et al. [33] showed that an increase in carrier fluid viscosity enhances shear thickening at low shear rates because of restricted particle motions that promote cluster formation and subsequent thickening at reduced stresses. Additionally, carrier fluids with higher molecular weights have been shown to enhance shear-thickening behavior. This is because longer molecular chains create more resistance between fluid layers, leading to increased viscosity and stronger shear-thickening effects. For example, Shenoy and Wagner [34] demonstrated that nanofluids formulated with polyethylene glycol (PEG) exhibited a stronger shear-thickening response due to the higher molecular weight between nanoparticles and the longer length of polymer chains. Singh et al. [35] examined a range of fluid formulations using dispersing media with a molecular weight of 4600 g/mol, 6000 g/mol, and 10,000 g/mol. The results proved that a higher molecular weight dispersing medium significantly improves shear-thickening properties. The shear stress of polyethylene glycol with a molecular weight of 10,000 g/mol was the highest among the three, indicating the important role of higher molecular weight PEG in improving the shear-thickening response and acting as a suitable gel-forming agent that allows precise control of the rheological behavior of the nanofluid at very low concentrations.
These results stress the necessity of choosing the right carrier fluid while designing nanofluids for practical applications, as the molecular structure and viscosity of the carrier fluid have a primary role in determining the rheological behavior of the fluid and thereby its application potential, especially for EGS. The carrier fluid's properties, such as its viscosity and molecular interactions, have a significant impact on the generation of hydroclusters in nanofluids under shear conditions, which are ultimately responsible for modulating fluid flow and altering reservoir permeability in EGS. On one hand, an inappropriate choice of carrier fluid hinders the ability of nanofluid to form an adequate amount of hydroclusters and on the other hand, the misfit in the molecular interactions between particles and carrier prevents these flocs from forming stable hydroclusters, inhibiting fundamental rheological behaviors such as shear thickening. As a result, the fluid's capability to manage flow inside the geothermal reservoir is likely to suffer, ultimately compromising the fluid's potential to optimize the thermal energy extraction from the reservoir and control in situ fluid flow. Hence, the rationale behind choosing and formulating the right carrier fluid for the right nanofluid goes well beyond the standard benchmarking of only basic properties listed in the handbooks, requiring a thorough understanding of how these properties impact the interaction between nanoparticles and fluid molecules to achieve the desired rheological effects.
2.2.4 Temperature.
Temperature is a key parameter governing the development and performance of EGS since the reservoir temperature affects the energy output. In an ideal scenario, the higher the reservoir temperature, the more efficient the conversion of geothermal heat to usable energy via the working fluid. However, higher temperatures greatly impact the rheological properties of different fluid systems, particularly nanofluids used in EGS. Shear-thickening nanofluids, due to their ability to exhibit an increase in viscosity under applied shear conditions, can significantly influence the performance of EGS reservoirs. Therefore, the relationship between the reservoir temperature and the shear-thickening tendencies of nanofluids is crucial to optimizing the effectiveness of the nanofluids in EGS reservoirs. At low temperatures, the hydrodynamic lubrication forces between particles are sufficient to overcome repulsive interparticle forces, allowing hydroclusters to form more readily, thereby inducing shear thickening. However, as temperature increases, the behavior of nanofluids changes significantly. Previous studies have shown that at higher temperatures, the shear-thickening effect is often diminished or occurs only at high shear rates. This shift is due to several factors, including changes in the strength of interparticle interactions and the increasing influence of Brownian motion, which disperses particles and inhibits hydrocluster formation. At elevated temperatures, repulsive forces between nanoparticles, such as electrostatic and steric forces are typically enhanced. These forces prevent particles from coming into close proximity and forming the dense hydroclusters responsible for shear thickening [36]. As a result, these repulsive forces need to be overcome to induce shear-thickening behavior at higher temperatures. Liu et al. [36] investigated the effect of temperature on a fumed silica-based nanofluid, studying the behavior at three different temperatures (10 °C, 30 °C, and 60 °C) as illustrated in Fig. 7. Their results indicated that increasing the temperature resulted in a reduction in critical viscosity and an increase in the critical shear rate. This is attributed to two key effects: the weakening of hydrogen bonds between silica particles and the carrier fluid and the enhancement of Brownian motion. These changes lead to a more disordered particle structure, which hinders hydrocluster formation and diminishes the shear-thickening response. At higher temperatures, Brownian motion, which is the random thermal movement of particles, becomes more intense. This increased motion keeps nanoparticles dispersed within the fluid, preventing them from coming together to form the hydroclusters that cause shear thickening. In practical terms, this translates into an inability for nanoparticles to overcome the thermal fluctuations induced by Brownian motion, thus making it more difficult to form hydrodynamic clusters that cause an increase in viscosity [33,36]. Boersma et al. [33] in their study of the effect of temperature on the shear-thickening behavior in colloidal suspensions found that higher temperatures caused a shift in the shear-thickening profile of nanofluids. At elevated temperatures, the viscosity of the carrier fluid decreased, thus enhancing particle mobility, leading to earlier shear thickening at lower shear rates. However, the overall intensity of shear thickening was reduced, and the critical viscosity decreased, consistent with the findings of Liu et al. [36]. This highlights the importance of temperature control in managing the rheological behavior of nanofluids in EGS. In addition to Brownian motion, temperature affects the interparticle forces within the nanofluid, particularly through its impact on hydrogen bonding. Nanoparticles, such as fumed silica, often interact with the base fluid through hydrogen bonds, which contribute to the formation of a structured fluid network [36]. At higher temperatures, these bonds weaken, resulting in a less cohesive fluid structure and reduced particle aggregation.
![Impact of temperature on the shear-thickening behavior of fumed silica-based nanofluid (adapted from Liu et al. [36])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f007.png?Expires=1740397584&Signature=oLGELbs3Qq3qh9YuqFqubhnUM04GZD9wATyD8NnCDCOQcYVDzqdTLu4YYc7~VjB1hl7jwPQALvY1pYORTKVW9hI7M-MWaMBNCrV-H~qpbj4gMNnAol~PY3k60Ph7N8ICboGeQGUgDK1ZxdWIADW7y1ATetVv7gqtuf-oDuiKgfcQeqXxsMsit6415yxH~yDCTkZB1VtdGbNqaCIhn8bolsL5sTyV8NR2z0yjDY8dQDnL~Bwb7x5~nYrOvr7Q2nPky6Uxlny55bDjzzQL6h1kTPQsr45-utKV~LbuKXufAgnRgDcpV3BGiyfiLZ46dnR74OpHZdobGDDA8GFJKCosmA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Impact of temperature on the shear-thickening behavior of fumed silica-based nanofluid (adapted from Liu et al. [36])
![Impact of temperature on the shear-thickening behavior of fumed silica-based nanofluid (adapted from Liu et al. [36])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f007.png?Expires=1740397584&Signature=oLGELbs3Qq3qh9YuqFqubhnUM04GZD9wATyD8NnCDCOQcYVDzqdTLu4YYc7~VjB1hl7jwPQALvY1pYORTKVW9hI7M-MWaMBNCrV-H~qpbj4gMNnAol~PY3k60Ph7N8ICboGeQGUgDK1ZxdWIADW7y1ATetVv7gqtuf-oDuiKgfcQeqXxsMsit6415yxH~yDCTkZB1VtdGbNqaCIhn8bolsL5sTyV8NR2z0yjDY8dQDnL~Bwb7x5~nYrOvr7Q2nPky6Uxlny55bDjzzQL6h1kTPQsr45-utKV~LbuKXufAgnRgDcpV3BGiyfiLZ46dnR74OpHZdobGDDA8GFJKCosmA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Impact of temperature on the shear-thickening behavior of fumed silica-based nanofluid (adapted from Liu et al. [36])
3 Application of Shear-Thickening Nanofluids in Enhanced Geothermal Systems
EGS is a potentially important component of the renewable energy mix, with the aim to deliver large-scale baseload “green” energy. In contrast to traditional geothermal systems, EGS can be developed in a wide range of geological conditions, reflecting longer-term sustainability and making geothermal energy accessible for those areas of the world where this form of energy was previously considered infeasible. To secure full deployment and optimization of EGS, several critical challenges must be addressed including thermal short-circuiting, working fluid losses, and thermal depletion. Taking into consideration these phenomena, we discuss how STNFs can be a potential solution to some of the challenges and boost the EGS performance. Shear-thickening behavior is associated with increased viscosity of the fluid with applied shear rates. High shear viscosity can be beneficial to control the fluid flow in the reservoir.
3.1 Control of Fluid Flow
3.1.1 Mitigating Thermal Short-Circuiting.
Thermal short-circuiting occurs when the injected working fluid flows too rapidly through the reservoir, bypassing significant sections of the geothermal system. This premature fluid movement results in poor heat transport since the working fluid exits the system before it has sufficient time to pick up thermal energy from the host rock. The phenomenon of thermal short-circuiting is especially troublesome in fractured rock reservoirs, where fluid flow tends to be concentrated in highly permeable fractures. It can severely reduce the performance of geothermal systems, limiting the daily load that they can support, and thus significantly decreasing the heat recovery potential from the reservoir [6]. One of the most promising strategies to minimize this problem's impact is based on applying STNFs to EGS. STNFs show an intriguing property, in that their viscosity increases with high shear rates, such as those typically found in high-permeability fractures. This behavior enables STNFs to resist rapid flow through dominant fractures, effectively slowing down the fluid movement in these pathways. By increasing the viscosity, the fluid redistributes itself more uniformly throughout the reservoir, thereby enhancing heat absorption from less permeable rock sections and boosting the system's overall efficiency [25,35]. Furthermore, STNFs can alter the hydraulic conductivity of the reservoir. When introduced into large fractures, their viscosity increases, forming a gel-like structure. This phenomenon can sufficiently reduce the hydraulic conductivity in high-permeability zones, thereby “plugging” these dominant pathways. The plugging action redirects the working fluid toward regions of the reservoir with higher heat potential, facilitating a more effective heat transfer process [37]. Previous studies have also shown that the use of shear-thickening nanofluids can provide a controllable means of modifying reservoir flow pathways. For instance, Wagner and Brady [11] demonstrated that nanoparticles suspended in a carrier fluid could form hydroclusters under high shear conditions, significantly increasing the fluid's viscosity and thus providing the necessary rheological properties to manage flow patterns. This property of STNFs is essential for the sustained performance of EGS, as it enables operators to maintain a balanced flow distribution, preventing the premature cooling of the geothermal reservoir and extending its operational life.
Shear-thickening nanofluids hold significant promise for enhancing the performance and extending the operational life of EGS reservoirs by mitigating thermal short-circuiting. However, despite their vast potential, research on the effectiveness and practical application of these nanofluids remains limited. Further investigation is needed to better understand their behavior under subsurface conditions and to optimize their use in real-world geothermal operations.
3.1.2 Altering Enhanced Geothermal Systems Reservoir Permeability.
EGS requires permeable pathways to ensure fluids can circulate through the reservoir, allowing the efficient extraction of heat. The permeability of these fractures is key in determining how efficiently heat can be extracted as part of an EGS operation, as it directly influences the flow pathways of fluids and determines the ability to transfer heat from the deep rock formations to the surface. Excessive fluid loss to regions of highly conductive fracture or regions where fractures are forcefully closed due to confining pressures can significantly compromise fluid circulation, reducing the overall efficiency of thermal energy extraction. In traditional EGS operations, fluid injection into the reservoir creates or expands fractures, establishing a network through which the working fluid can circulate and extract heat. The permeability of these fractures needs to be carefully managed to maximize fluid retention in targeted zones and prevent undesired fluid migration. When the permeability is too high, excessive fluid loss to the formation occurs, reducing the fluid's residence time in the heat exchange zone and leading to lower thermal recovery. Conversely, fracture closure under confining pressures can restrict fluid flow, further limiting the system's ability to extract heat efficiently. STNFs have recently emerged as potential agents for dynamic permeability control in EGS. These nanofluids exhibit a unique non-Newtonian behavior where their viscosity increases significantly under an applied shear rate [25]. This property can be leveraged to dynamically alter fracture permeability within EGS reservoirs, optimizing fluid flow in response to changing operational conditions. In contrast to conventional fluids used in EGS, which often lead to fracture closure under the confining pressure of deep reservoirs, STNFs offer a dynamic response to varying shear conditions. This adaptability can enhance fluid retention within fractures, prevent excessive fluid loss to regions of high permeability, and ultimately improve the thermal efficiency of the system. During fluid injection in an EGS reservoir, existing fractures experience high shear rates due to the pressure and velocity of the working fluid [38]. These high shear rates act as a catalyst for promoting the shear-thickening behavior of nanofluids. As the shear rate increases, hydrodynamic forces drive the formation of transient particle clusters, known as hydroclusters, within the nanofluid. This aggregation of nanoparticles results in a significant increase in the fluid's viscosity, creating a plugging effect within the fractures [18,20,24]. The rise in viscosity under high shear rates reduces fluid mobility, thereby temporarily lowering the permeability of the fractures. This “plugging” mechanism prevents excessive fluid loss into regions of the reservoir with high conductivity, allowing more fluid to be retained in the heat exchange zone. By reducing fluid loss, the working fluid remains in contact with the hot rock formations for a longer duration, enhancing heat transfer and increasing the efficiency of the geothermal system. The ability of STNFs to alter viscosity in response to shear rates enables dynamic regulation of flow resistance within the fractures. When the shear rate decreases, such as when fluid injection slows or fluid moves to less conductive regions the viscosity of the nanofluid also decreases, restoring fracture permeability As indicated by Prabhu and Singh [28] where the shear-thickening nanofluids show the ability of reversing to shear-thinning behavior. This reversible alteration of fracture permeability allows for greater control over fluid flow paths and can be used to optimize fluid distribution in the geothermal reservoir. The shear-thickening fluids, through their ability to transition from a liquid-like to a solid-like state under applied stress, can significantly alter the permeability with minimum damage to the reservoir [11]. In addition to their improved rheological properties, shear-thickening nanofluids have also been assessed as potential plugging agents through the gelation mechanism. Hunt et al. [39] investigated the potential of silica-based nanofluid suspension to act as a plugging agent in geothermal reservoirs. Through numerical and experimental investigation, their study suggested that the silica-based nanofluid is a good candidate for blocking, diverting, and modifying fracture flow networks in EGS systems. While shear-thickening nanofluids exhibit significant potential for dynamically altering permeability in EGS reservoirs due to their specialized rheological properties, the understanding of their full impact on EGS reservoirs remains limited. Experimental and numerical studies exploring the interactions between shear-thickening nanofluids and the complex geological formations of EGS are currently scarce. The unique behavior of shear-thickening nanofluids suggests they could play a crucial role in controlling fluid loss, enhancing fluid retention, and optimizing thermal energy extraction. However, the specific mechanisms by which they influence fracture networks and permeability in the extreme conditions of EGS (high temperature, pressure, and complex rock structures) are not yet fully understood. Most existing research focuses on the general rheological behavior of shear-thickening nanofluids in confined systems and porous media, but few studies directly address their application in geothermal environments. Further research is necessary, including both laboratory experiments that mimic the high-temperature and high-pressure conditions of geothermal reservoirs and numerical simulations to model their behavior under different reservoir conditions.
3.2 Enhancing Thermal Energy Extraction Efficiency.
EGS often face several challenges that significantly hinder thermal energy extraction efficiency. Problems like thermal short-circuiting, reservoir drawdown, and fluid loss can dramatically reduce the effectiveness of heat transfer within the system. STNFs, for example, have the potential to address these problems by increasing both the thermal conductivity of the fluid and its overall heat transfer capacity, thus enhancing the efficiency of thermal energy extraction from EGS reservoirs.
3.2.1 Effective Thermal Conductivity.
The effective thermal conductivity is the parameter that highlights the shear-thickening effect of the working fluid on the energy extraction efficiency of EGS. Nanofluids tend to possess higher thermal conductivity than conventional heat transfer fluids hence they work as a suitable medium for enhancing the heat transfer in EGS systems. Thermal conductivity is the first-priority property of a solid or liquid substance, which decides how efficiently it can conduct heat. It highlights how easily heat flows through a substance. This property directly affects the overall efficiency of extracting and transferring heat from the geothermal reservoir. Several mechanisms explain the enhancement of thermal conductivity in shear-thickening nanofluids. In their 2004 study, Eastman et al. [40] reported four key mechanisms responsible for the thermal conductivity enhancement observed in nanofluids. These mechanisms provide insight into how nanoparticles improve the heat transfer performance of base fluids. Following is an explanation of each mechanism:
Brownian motion of nanoparticles: Brownian motion of nanoparticles refers to the random, irregular motion of the particles in the fluids. In nanofluids, this motion tends to create small convection currents that enhance heat transfer within the fluid [40]. The nanoparticles continuously move and interact with the surrounding base fluid, creating localized mixing that facilitates better thermal energy distribution. The random movement of nanoparticles within the fluid increases the overall mobility of the fluid's molecules, improving thermal diffusion. This increased movement helps transfer heat more efficiently throughout the fluid. The effectiveness of the Brownian motion is impacted by both the nanoparticle size and the temperature of the reservoir.
Formation of layers at the interface between the nanoparticle and the base fluid: At the interface between nanoparticles and the surrounding base fluid, interfacial layers form due to interactions between the solid nanoparticle surface and the fluid molecules [40]. These layers are structured differently from the bulk fluid and can act as pathways that improve the thermal transport properties of the nanofluid. The formation of an ordered layer of fluid molecules around the nanoparticles provides an additional mechanism for heat transfer, as these layers facilitate better energy exchange between the nanoparticles and the base fluid. This enhanced heat transfer at the particle–fluid interface can lead to a significant increase in thermal conductivity.
Particle clustering effect: The particle clustering effect occurs when nanoparticles aggregate into clusters or chains within the fluid, providing an efficient path for thermal transport. These clusters create a network of thermally conductive pathways that span the fluid, allowing for faster heat transfer across the fluid medium. Clustering reduces the distance that heat needs to travel through the base fluid, allowing it to move more rapidly through the system. The formation of conductive nanoparticle chains effectively bridges gaps between different regions of the fluid, significantly enhancing thermal conductivity. This mechanism is particularly relevant in high-concentration nanofluids. Keblinski et al. [41] emphasized that the enhancement in thermal conductivity due to particle clustering is a result of the formation of localized particle-rich zones. These zones, created by particle agglomeration and settling, exhibit lower thermal resistance, thereby contributing to improved heat transfer.
The ballistic nature of the thermal transport of the nanoparticles: The ballistic nature of thermal transport refers to the rapid transmission of heat through nanoparticles without significant scattering, akin to how heat propagates in a solid. Nanoparticles, especially metals, have high thermal conductivities and can transport heat more efficiently than the surrounding fluid. When heat is transferred to nanoparticles, it moves quickly across their surface due to the inherent conductive properties of the material. Because nanoparticles are smaller than the mean free path of phonons (heat-carrying particles), heat can travel through them without being scattered as it would be in larger particles or bulk materials. This leads to faster and more efficient heat transfer compared to the base fluid alone.
In addition to these mechanisms, the effective thermal conductivity of nanofluids is influenced by many factors. These parameters were highlighted in a study conducted by Pinto and Fiorelli [42]. Figure 8 shows some of the parameters impacting the effective thermal conductivity of shear-thickening fluids.
![Parameters dictating the nanofluids' effective thermal conductivity (adapted from Pinto and Fiorelli [42])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f008.png?Expires=1740397584&Signature=ckYH3O3xqb8G4SsjmZFw-DY0g0ImLNuSrjJFhVoYN0GoB5QOJzSz7yp37FRiT0r5LaTkYPn0WrHtC4Jyc6K9qCvTXa7ulZDmaysJ~LemEgbL2oz0vjBw~4o2P015gac31Xml69Ee3VerpzoaaudCMPvwxqskg4oRTt5lVNR2054oLVwof~6KK~ALTS5WS9kA3iy3Ip1K3WU6GuHWevNbyqogozwN87HhWLVYtN4-KbLXZgh3JQjWS7lFvG4-PIbpGF8bxGVfpQG9LXMO5Ibvdp2R1Xyb44sXWK6UXTWCjKaNTBWIEYmpy9plq0rCA8T3Cn6X0JOv8aLizTBDleM6ZQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Parameters dictating the nanofluids' effective thermal conductivity (adapted from Pinto and Fiorelli [42])
![Parameters dictating the nanofluids' effective thermal conductivity (adapted from Pinto and Fiorelli [42])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f008.png?Expires=1740397584&Signature=ckYH3O3xqb8G4SsjmZFw-DY0g0ImLNuSrjJFhVoYN0GoB5QOJzSz7yp37FRiT0r5LaTkYPn0WrHtC4Jyc6K9qCvTXa7ulZDmaysJ~LemEgbL2oz0vjBw~4o2P015gac31Xml69Ee3VerpzoaaudCMPvwxqskg4oRTt5lVNR2054oLVwof~6KK~ALTS5WS9kA3iy3Ip1K3WU6GuHWevNbyqogozwN87HhWLVYtN4-KbLXZgh3JQjWS7lFvG4-PIbpGF8bxGVfpQG9LXMO5Ibvdp2R1Xyb44sXWK6UXTWCjKaNTBWIEYmpy9plq0rCA8T3Cn6X0JOv8aLizTBDleM6ZQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Parameters dictating the nanofluids' effective thermal conductivity (adapted from Pinto and Fiorelli [42])
A comparative study by Wen et al. [43] analyzed the thermal conductivity of various materials, including polymers, solids, and liquids, showing that commonly used nanoparticles such as Al, Cu, Ag, Si, and Zn have thermal conductivities that are vastly higher than standard heat transfer fluids like water, ethylene glycol, and mineral oil as illustrated in Fig. 9. These findings demonstrate that integrating nanoparticles into working fluids significantly enhances their thermal conductivity, which, in turn, improves the thermal energy extraction capacity of nanofluids in EGS applications.
![Thermal conductivity comparison of common polymers, liquids, and solids (adapted from Wen et al. [43])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f009.png?Expires=1740397584&Signature=DZqxLDeqQAtJQAnN1XnoBaEooVEkVfuSn~HrMq0kXtZ6mLc6COoUtuEjyJT2dF0RbPX2tqab-RioelbfcHxWQp8ESRDxjcnR05TgGp4Vs9QGAXikyynD-2MuhA-k-v9F7yMdMahPIIJbSlLZCD5fWO~f0iQRB7QI4SJXUOLHKMGKYSvKzBbf69tJAmQpekdp3-EoQO~qXoQrp0BWLc76RPbCqDNRf8~R4MKX~QQ8RExBrIfHCiwh0LM2mxxxspODhxmRWd-SNxpEAaTSwdciCSHHZ3FTZ7NB0KWoz1deKeq1wJFbpsJi1eUFSC4qgYM2Zkn26QRcVVBOu9qIs1Hn3g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Thermal conductivity comparison of common polymers, liquids, and solids (adapted from Wen et al. [43])
![Thermal conductivity comparison of common polymers, liquids, and solids (adapted from Wen et al. [43])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f009.png?Expires=1740397584&Signature=DZqxLDeqQAtJQAnN1XnoBaEooVEkVfuSn~HrMq0kXtZ6mLc6COoUtuEjyJT2dF0RbPX2tqab-RioelbfcHxWQp8ESRDxjcnR05TgGp4Vs9QGAXikyynD-2MuhA-k-v9F7yMdMahPIIJbSlLZCD5fWO~f0iQRB7QI4SJXUOLHKMGKYSvKzBbf69tJAmQpekdp3-EoQO~qXoQrp0BWLc76RPbCqDNRf8~R4MKX~QQ8RExBrIfHCiwh0LM2mxxxspODhxmRWd-SNxpEAaTSwdciCSHHZ3FTZ7NB0KWoz1deKeq1wJFbpsJi1eUFSC4qgYM2Zkn26QRcVVBOu9qIs1Hn3g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Thermal conductivity comparison of common polymers, liquids, and solids (adapted from Wen et al. [43])
The application of shear-thickening nanofluids in EGS, is largely influenced by the formation of hydroclusters under shear conditions. These hydroclusters are formed from the aggregation of clustering of nanoparticles in the fluid. The particle clustering effect in shear-thickening nanofluids is critical for optimizing their heat transfer properties, as these clusters form localized regions that can reduce thermal resistance and enhance thermal conductivity. A study by Kakac and Pramuan-Jaroenkij [44] delved into the complex interplay between particle clustering and thermal conductivity enhancement in nanofluids. Their research indicated that while moderate clustering promotes higher thermal conductivity, excessive clustering can lead to diminished heat transfer performance. This is because overly compact particle clusters create bottlenecks for the fluid flow, increasing viscosity and inhibiting the efficient transfer of heat between the particles and the carrier fluid. To achieve optimal thermal performance, it is necessary to maintain an intermediate level of clustering where the particles are closely packed but not overly compact. Keblinski et al. [41] also emphasized that the structure of these clusters is critical; less compact, more porous clusters tend to offer a greater enhancement in heat transfer, as they allow more interaction between the nanoparticle surfaces and the surrounding fluid. The study highlighted the need to balance clustering to avoid excessive aggregation that may reduce the overall heat transfer capability. Figure 10 shows the impact of clustering of particles on the enhancement of thermal conductivity in a study conducted by Wen et al. [43]. Their study revealed that as particle clustering initially increases, thermal conductivity improves sharply due to the creation of heat-conducting pathways formed by the particle-rich zones. However, after reaching an optimal clustering level, further increases in clustering lead to a drop in thermal conductivity, as densely packed clusters create more thermal resistance and hinder effective heat transfer. In the initial region, as particle clusters form, thermal conductivity increases significantly. This can be attributed to the improved connectivity between particles, which allows heat to transfer more easily through the nanofluid. Beyond the optimal point, the clustering becomes excessive, reducing the surface area available for heat transfer between the fluid and the nanoparticles, thus causing a decline in thermal conductivity.
![Effect of particle clustering on thermal conductivity (adapted from Wen et al. [42])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f010.png?Expires=1740397584&Signature=kW~Q70UDy0VsK04rIJ~lVofDpVAKhfpnVruISBETU~Qs~7WCYGX3PauAnK85tiHXrfLSrApxleTpsUhmgQvBum740IgxeB-woLBJco3vEXFc11bdHYf6RTX4qSSPfaaeiW6NmaG2FoH9ycNnqKFlCf2BuuRSFrcx0bctgrQYILWcZe3-xshiOdz6L9utUEji4SjetEi50Dj~k9dcZAprYUglPy7MWoSJbagtCUMgZWAfQyjYfKAh5PRt0wxXsHKvOclE93s7KwmBWnwsi30yJh9CtEtPLT3MsMcVy6bbp4jl0wjjCqjuvulTOC~fuOkRzhNtilku01aO11x2BE-1-Q__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Effect of particle clustering on thermal conductivity (adapted from Wen et al. [42])
![Effect of particle clustering on thermal conductivity (adapted from Wen et al. [42])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f010.png?Expires=1740397584&Signature=kW~Q70UDy0VsK04rIJ~lVofDpVAKhfpnVruISBETU~Qs~7WCYGX3PauAnK85tiHXrfLSrApxleTpsUhmgQvBum740IgxeB-woLBJco3vEXFc11bdHYf6RTX4qSSPfaaeiW6NmaG2FoH9ycNnqKFlCf2BuuRSFrcx0bctgrQYILWcZe3-xshiOdz6L9utUEji4SjetEi50Dj~k9dcZAprYUglPy7MWoSJbagtCUMgZWAfQyjYfKAh5PRt0wxXsHKvOclE93s7KwmBWnwsi30yJh9CtEtPLT3MsMcVy6bbp4jl0wjjCqjuvulTOC~fuOkRzhNtilku01aO11x2BE-1-Q__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Effect of particle clustering on thermal conductivity (adapted from Wen et al. [42])
The temperature is another very important factor that affects the thermal conductivity of nanofluids, especially in the EGS where the operating temperature can usually exceed 150 °C. Nanoparticles are very susceptible to temperature modification, and as temperature increases, the fluid viscosity will decrease, which could promote the mobility of particles and in turn enhance the rate of heat transfer, by increasing the mobility of particles in the suspension. Also, the ability of nanoparticles to move becomes more pronounced at higher temperatures due to the Brownian motion, thus, enhancing the thermal conductivity of the nanofluid [45]. Bobbo et al. [45] in their experimental study on the impact of temperature on the thermal conductivity of nanofluids, investigated the thermal conductivity of various nanoparticle volume fractions at different temperatures. Their experimental investigation demonstrated that as temperature increases, the effective thermal conductivity of nanofluids increases for all the concentrations of nanoparticles investigated. The positive correlation between the temperature and effective thermal conductivity of nanofluids can be advantageous in geothermal applications, where fluids operate under high-temperature conditions, as it can significantly improve thermal energy extraction efficiency. Figure 11 illustrates how temperature affects the thermal conductivity of nanofluids of various concentrations of nanoparticles. Their study highlighted that thermal conductivity increases with temperature for all nanofluid concentrations. The low thermal conductivity of nanofluids at low temperatures can be explained by the reduced mobility of nanoparticles and lower Brownian motion. However, as the temperature rises, thermal conductivity improves significantly, particularly for nanofluids with higher nanoparticle volume fractions. This is because, at elevated temperatures, the enhanced kinetic energy of nanoparticles leads to more effective heat transfer. Moreover, higher volume nanoparticle fraction provides more thermal pathways, amplifying thermal conductivity.
![Effect of temperature on the thermal conductivity of various nanofluids (adapted from Bobbo et al. [45])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f011.png?Expires=1740397584&Signature=aYghzUOoiUS9yqoAKmWo9zdy9mw-DY468mCjNCuaG72brXc6Y~dJrW2UiFaWzT~hT34WQG4eo~1XKA8VdGJu8~Hq-AiCqQzkZQJ0oMj4I86vgnHAdXwNigBrafBYJNavg0kiamLSK9eLEZmglvYuEgq~ZJz0-EuQR~HK7KTf~3UNlrMuvjEUcXPxTxrMm8catEHkNNGQV0FcpAR4IXrj2jDRsIU~9ZP4hLgNf9ZYBo08wMIXO54~u0eEzDnx7GvPIhMvjl-WGbu6GmTgslPp2aXhD6O0xO~0uBTQqnt8KqHD4L1KgN5Cam~vSq~tLZjtDrEc8oEDliKsY0C~lFtC6g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Effect of temperature on the thermal conductivity of various nanofluids (adapted from Bobbo et al. [45])
![Effect of temperature on the thermal conductivity of various nanofluids (adapted from Bobbo et al. [45])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f011.png?Expires=1740397584&Signature=aYghzUOoiUS9yqoAKmWo9zdy9mw-DY468mCjNCuaG72brXc6Y~dJrW2UiFaWzT~hT34WQG4eo~1XKA8VdGJu8~Hq-AiCqQzkZQJ0oMj4I86vgnHAdXwNigBrafBYJNavg0kiamLSK9eLEZmglvYuEgq~ZJz0-EuQR~HK7KTf~3UNlrMuvjEUcXPxTxrMm8catEHkNNGQV0FcpAR4IXrj2jDRsIU~9ZP4hLgNf9ZYBo08wMIXO54~u0eEzDnx7GvPIhMvjl-WGbu6GmTgslPp2aXhD6O0xO~0uBTQqnt8KqHD4L1KgN5Cam~vSq~tLZjtDrEc8oEDliKsY0C~lFtC6g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Effect of temperature on the thermal conductivity of various nanofluids (adapted from Bobbo et al. [45])
Beyond temperature and particle clustering effects, other critical factors include the volume fraction and size of nanoparticles. These parameters can have a significant impact on the overall behavior and performance of nanofluids, particularly in high-temperature geothermal settings. The volume fraction has a significant impact on the effective thermal conductivity of nanofluids. Baheta and Woldeyohannes [46] highlighted the impact of volume fraction by demonstrating that the effective thermal conductivity of Al2O3–water nanofluids increased with an increasing volume fraction of nanoparticles. This is due to the increased number of thermal pathways that nanoparticles provide for heat transfer through the fluid. When more nanoparticles are present, the distance between them decreases, thereby leading to more efficient heat transfer by conduction. Moreover, as the volume fraction increases, the probability of particle–particle interactions rises, leading to better thermal conductivity enhancement. However, there is a limit beyond which further increases in volume fraction can result in agglomeration or viscosity changes, which may counteract the benefits of enhanced thermal conductivity. This highlights the importance of determining an optimal volume fraction for each specific nanofluid application to prevent issues related to high viscosity or particle settling, which could reduce the overall efficiency of the geothermal system. As indicated in their study, as the volume fraction increases, there is a sharp rise in thermal conductivity due to the creation of more heat-conducting pathways within the nanofluid. Figure 12 highlights the relationship between thermal conductivity and the volume fraction and size of nanoparticles. The impact of the volume fraction of nanoparticles on the effective thermal conductivity was further highlighted by Timofeeva et al. [47]. Their study indicated that nanoparticle volume fraction is generally the most significant factor as it has a strong positive effect on thermal conductivity and heat transfer efficiency.
![The impact of nanoparticles on the effective thermal conductivity of Al2O3–water nanofluids (adapted from Baheta and Woldeyohannes [46])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f012.png?Expires=1740397584&Signature=eaPBQRJlRg8h-0O-3jAZNmfBW-Nqq~MAjfuFaI-5BdfXPgYwQ4x9ErZy~gbZIwVGTJnsbcVbsU2o58H3v7atsLkZ8C4g5DKfgrjnS4t0toIfS6med7D5pDx~BM9UKN7b2yynH8hULlxIZe~yd4BG37KnriqASgExRbJo0GeiZYnBsRCubbSwhHOuvELdLj-zS6cBUG3JVqaPUaBLPWiqSxUrBl8OYLm5Fnqpr7p-EMaguQRc-uXQxTOD6O6ixf~TOOM7erqDf0N9ub3IGlaKfFWiTH-WYMDqBIM2~8BdPpjOnHFhA-Y2DEy~46zrRZB1D2orzDXqnGts2hj32zm71A__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
The impact of nanoparticles on the effective thermal conductivity of Al2O3–water nanofluids (adapted from Baheta and Woldeyohannes [46])
![The impact of nanoparticles on the effective thermal conductivity of Al2O3–water nanofluids (adapted from Baheta and Woldeyohannes [46])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f012.png?Expires=1740397584&Signature=eaPBQRJlRg8h-0O-3jAZNmfBW-Nqq~MAjfuFaI-5BdfXPgYwQ4x9ErZy~gbZIwVGTJnsbcVbsU2o58H3v7atsLkZ8C4g5DKfgrjnS4t0toIfS6med7D5pDx~BM9UKN7b2yynH8hULlxIZe~yd4BG37KnriqASgExRbJo0GeiZYnBsRCubbSwhHOuvELdLj-zS6cBUG3JVqaPUaBLPWiqSxUrBl8OYLm5Fnqpr7p-EMaguQRc-uXQxTOD6O6ixf~TOOM7erqDf0N9ub3IGlaKfFWiTH-WYMDqBIM2~8BdPpjOnHFhA-Y2DEy~46zrRZB1D2orzDXqnGts2hj32zm71A__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
The impact of nanoparticles on the effective thermal conductivity of Al2O3–water nanofluids (adapted from Baheta and Woldeyohannes [46])
Another important factor affecting the thermal conductivity of nanofluids is particle size. Smaller nanoparticles, with a greater surface area-to-volume ratio, tend to have better heat transfer compared with bigger particles. Baheta and Woldeyohannes [46] reported that a decrease in the size of nanoparticles causes a significant increase in the effective thermal conductivity of Al2O3–water nanofluids. Smaller nanoparticles can interact more with the molecules of the surrounding fluid and thus impact the frequency of energy exchange, and this is ultimately reflected by an increase in thermal conductivity. The challenge of smaller particles is their susceptibility to a higher chance of agglomeration, especially with high-volume fractions, because of stronger van der Waals forces. Agglomeration is a drawback due to it creating localized regions of poor heat transfer performance, thus reducing the overall stability of the fluid. Thus, the stability of the nanofluid must be taken into crucial consideration when selecting the best particle size for a geothermal application.
The thermal conductivity of shear-thickening nanofluids is highly dependent on nanoparticle clustering, temperature, particle size, and volume fraction. Appropriate clustering of nanoparticles can increase heat transfer by forming localized high thermal conductivity regions, and an increase in temperature can increase nanoparticle mobility and hence facilitate heat transfer. However, clustering beyond a threshold results in adverse effects on the effective thermal conductivity. Hence, particle dispersion is crucial in formulating proper nanofluids. Nanoparticle size and volume fraction play an equally important role in determining the thermal conductivity of nanofluids. Increasing volume fraction increases thermal conductivity by providing more conductive pathways. Similarly, nanoparticles of smaller size increase thermal conductivity due to their large surface area, but they also increase the chance of agglomeration and hence fluid stability. In EGS, nanofluids can be injected downhole, accelerating natural convection and increasing thermal energy extraction. In general, optimal nanoparticle volume fraction and size can increase thermal conductivity and heat transfer efficiency in EGS. Numerous studies have demonstrated the effectiveness of nanofluids to improve the performance of heat exchangers in various geothermal systems such as surface and aquifer-based systems. However, only a few studies have looked into nanofluids in EGS, where the focus needs to be on improving well-to-well heat transfer along the reservoir. Hence, there is a need for future research focusing on these interactions to better understand how shear-thickening nanofluids can improve efficiency and how they can operate under real-world conditions in EGS.
3.2.2 Specific Heat Capacity.
The heat capacity of the material is considered as its capability for thermal energy storage. The energy-carrying capacity of the nanofluid is directly influenced by the specific heat capacity. Specific heat capacity is one of the most important properties that may affect the rate of heat transfer of a nanofluid. Higher specific heat capacity allows more efficient heat absorption and transfer in geothermal reservoirs; therefore, this is one of the key factors in optimizing the thermal performance of nanofluids for EGS applications. The overall specific heat capacity of the resulting nanofluid could be increased or decreased, depending on the type, size, and volume fraction of the nanoparticles used. Generally, the base fluids, such as water, have comparatively high specific heat capacities. However, the addition of nanoparticles such as Al2O3, SiO2, or Cu can reduce the specific heat capacity since these nanoparticles have lower heat storage capacity compared to the base fluid in general. According to Sekhar and Sharma [48], similar to effective thermal conductivity, the specific heat capacity has been considered to be heavily dependent upon nanoparticle size and concentration, nanofluid temperature, and base fluid type. Generally, the base fluids are of a fairly high specific heat capacity. However, with the addition of some types of nanoparticles, such as silica and alumina, into it, the overall specific heat capacity for the nanofluids would likely fall because these nanoparticles themselves have typically lower heat storage capacity compared to the base fluid. It has been noted by Zhou and Ni [49] that the specific heat capacity of the nanofluid decreases with increasing nanoparticle concentration as described in Fig. 13. Even with such a reduction in the specific heat capacity, the overall heat transfer efficiency could still be increased owing to thermal conductivity and convective heat transfer enhancement promoted by the nanoparticles as shown by Wen et al. [43]. While nanoparticle materials differ in specific heat capacity, the actual size and surface area of the nanoparticles also have an effect. Smaller nanoparticles, being higher in surface area-to-volume ratio, can interact more effectively with the base fluid molecules to efficiently enhance the energy transfer mechanism and thus offset the lower specific heats of the particles.
![Specific heat capacity of nanofluids as a function of the volume fraction of alumina nanoparticles (adapted from Zhou and Ni [49])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f013.png?Expires=1740397584&Signature=iKR4vPmSFx~YHLuH9tHev4Dgd8ZlBrRceGcLahjKvNiKyES0BIXabjBpkvxiuAEqS~2jolsJrKIvwb0ay~3juUaiJ0NZl6P1QUDbQTJwOJe1uI7zKyKd56sKX1mWrE2o~QPULEH23Rt7eTMhibj0fnJ9PvQv3nAIuV539cbORbA6pqh9KGYuHyZlhf6HuDFSeUkZL0DNo7b8JDcRtOIFF~YALUHvmNPvq7Xf1oL3h2REthn5-LM3OWEhQS1xWe7LIG6MaJEH0goWdGLF8wkjyGvbxw4HdyvKtSTBdPmbswkdNKKNQvfgT~I3-J80ZNFlAJ636iVtXk6bl6IpkGUc8Q__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Specific heat capacity of nanofluids as a function of the volume fraction of alumina nanoparticles (adapted from Zhou and Ni [49])
![Specific heat capacity of nanofluids as a function of the volume fraction of alumina nanoparticles (adapted from Zhou and Ni [49])](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/openengineering/4/10.1115_1.4067561/1/m_aoje_4_040801_f013.png?Expires=1740397584&Signature=iKR4vPmSFx~YHLuH9tHev4Dgd8ZlBrRceGcLahjKvNiKyES0BIXabjBpkvxiuAEqS~2jolsJrKIvwb0ay~3juUaiJ0NZl6P1QUDbQTJwOJe1uI7zKyKd56sKX1mWrE2o~QPULEH23Rt7eTMhibj0fnJ9PvQv3nAIuV539cbORbA6pqh9KGYuHyZlhf6HuDFSeUkZL0DNo7b8JDcRtOIFF~YALUHvmNPvq7Xf1oL3h2REthn5-LM3OWEhQS1xWe7LIG6MaJEH0goWdGLF8wkjyGvbxw4HdyvKtSTBdPmbswkdNKKNQvfgT~I3-J80ZNFlAJ636iVtXk6bl6IpkGUc8Q__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Specific heat capacity of nanofluids as a function of the volume fraction of alumina nanoparticles (adapted from Zhou and Ni [49])
In EGS reservoirs, where temperatures can exceed 200 °C, the specific heat capacity of the nanofluid becomes even more critical. High-temperature conditions can lead to increased energy demands, and a nanofluid with an optimized balance between specific heat capacity and thermal conductivity will have a higher potential for extracting and transporting geothermal heat. Additionally, it's important to consider the effect of temperature on the specific heat capacity itself, as this property tends to vary with changing temperatures [45]. Given the complexities involved, future studies should focus on exploring how specific heat capacity interacts with other thermal properties, such as thermal conductivity, viscosity, and density under the high-pressure, high-temperature conditions typical of EGS. Further research could help optimize the design of nanofluids that maximize both heat storage and heat transfer, leading to significant improvements in the efficiency and sustainability of geothermal energy extraction.
4 Challenges of Shear-Thickening Nanofluid Applications in Enhanced Geothermal Systems
The unique ability of shear-thickening nanofluids to locally increase the viscosity and consequently control the flow of working fluid makes them increasingly attractive for applications in EGS. The employment of such more advanced fluids in EGS is, however, confronted by additional stumbling blocks that still need to be sufficiently solved for effective application in EGS reservoirs. The fractures undergo significant pressure, temperature, and shear force fluctuations, all of which lead to challenges associated with the stability, temperature sensitivity, and environmental impact of the use of the shear-thickening nanofluids.
4.1 Agglomeration and Stability of Shear-Thickening Nanofluids.
One of the primary challenges in using shear-thickening nanofluids in EGS is the agglomeration and stability of nanoparticles under high-pressure and high-temperature conditions. Nanoparticles tend to agglomerate due to van der Waals forces, especially under shear forces, leading to the formation of larger clusters or aggregates. While clustering can enhance the fluid's thermal conductivity through hydrocluster formation, excessive clustering can hinder effective heat transfer. As Wen et al. [43] highlighted, the beneficial effects of clustering reach a threshold, beyond which the fluid's thermal performance declines due to increased viscosity and reduced particle mobility. Achieving optimal clustering of nanoparticles remains a significant technical challenge. As discussed by Keblinski et al. [41], particle clusters that are too compact can hinder thermal conductivity, while loose clusters promote better heat transfer. However, the dynamic nature of geothermal reservoirs makes it difficult to control clustering in real-time. Factors such as changes in temperature, pressure, and shear rate all influence nanofluids' behavior, making it challenging to maintain the ideal clustering conditions throughout the fluid's lifetime in the reservoir. There is still a limited amount of research on how to effectively control the rate of nanoparticle clustering and agglomeration under the extreme conditions typical of EGS reservoirs. The complex interactions between temperature, pressure, and shear forces in these environments make it difficult to maintain the stability of nanoparticles, leading to challenges in ensuring consistent heat transfer and fluid flow behavior. Developing strategies to manage these interactions and prevent excessive clustering or agglomeration is crucial for optimizing the performance of shear-thickening nanofluids in geothermal applications. Further experimental and theoretical studies are needed to address this gap and to tailor nanofluid formulations to withstand harsh geothermal conditions.
Moreover, nanoparticle agglomeration exacerbates the instability of the fluid, leading to sedimentation, especially at elevated temperatures common in EGS reservoirs. High-temperature conditions in geothermal systems tend to accelerate particle agglomeration and lead to rapid degradation of the nanofluid's properties. This is a significant challenge, as nanofluids must maintain stability over long periods in the subsurface for efficient heat transfer. Additionally, it can be challenging to maintain the long stability of the nanoparticles in the nanofluid over prolonged operational periods. It is important to ensure that the nanoparticles remain dispersed within the carrier fluid without settling or aggregation to ensure consistent heat transfer efficiency in EGS. The extreme temperature and pressure conditions of EGS tend to promote the degradation and instability of the nanoparticles in the EGS reservoir. The overtime degradation of nanofluids can result in a loss of the nanofluid's ability to enhance heat transfer or provide shear-thickening properties to control fluid flow and mitigate short-circuiting.
4.2 Environmental Impact.
STNFs offer significant advantages in enhancing geothermal energy extraction due to their improved thermal properties and potential to generate sufficient viscosity for flow control, however, their application poses notable environmental challenges. The use of nanoparticles such as silica and alumina in formulating STNFs raises toxicity concerns, especially if these fluids escape into surrounding groundwater systems. As Kumar et al. [50] highlighted, factors like base fluid, nanoparticle morphology, crystallinity, and volume fraction play a pivotal role in determining the toxicity levels of nanofluids. This becomes particularly concerning in EGS, where natural and induced fractures could facilitate the leakage of these nanofluids into the environment. A study by Elsaid et al. [51] using LCA revealed that the environmental impact of alumina-based nanofluids is strongly linked to their preparation method. For example, the negative environmental effects of the production of alumina nanoparticles, produced through the one-step synthesis method, were three times higher than those of the alumina nanoparticles produced with the two-step synthesis method, illustrating the importance of choosing proper production techniques. Previous works found nanofluids can enhance heat transfer, and hence improve the efficiency of heat recovery from EGS. However, the environmental impact of some nanoparticles used in the synthesis of the shear-thickening nanofluids has not been evaluated for a long-term duration. The toxicity level of some nanoparticles might be high enough to cause pollution of the subsurface environment when applied in a geothermal reservoir. It is therefore highly recommended to investigate the environmental effects before their applications in geothermal use.
5 Conclusions
Geothermal energy is rapidly emerging as a leading source of sustainable energy due to its high energy output potential and minimal environmental footprint. However, despite its promising prospects, technologies like EGS remain underdeveloped. This comprehensive review has examined the potential of shear-thickening nanofluids in advancing EGS applications. Shear-thickening nanofluids through their improved thermal properties and unique rheological properties offer innovative solutions to key challenges in EGS, such as mitigating thermal short-circuiting, improving fluid flow control, and enhancing thermal energy extraction efficiency. The review highlights the ability of these nanofluids, through mechanisms like hydroclustering, to dynamically adjust their viscosity, making them highly effective in optimizing fluid behavior within fractured geothermal reservoirs.
While shear-thickening nanofluids present significant advantages, several challenges must be addressed to fully leverage their potential. These include maintaining stability under extreme temperature and pressure conditions, preventing nanoparticle agglomeration, and addressing environmental concerns related to their use. This review underscores the need for further research to understand the complex interactions between nanoparticles, base fluids, and geological environments, particularly within the harsh conditions of EGS reservoirs.
Improving the long-term stability of shear-thickening fluids, controlling nanoparticle clustering, and minimizing environmental impact should be the focus of future studies. Finally, additional experimental and computational studies are still required to optimize the formulation and application of shear-thickening nanofluids to attain the best thermal and flow control properties in real-world geothermal systems. As more work is done, shear-thickening nanofluids have the potential to greatly increase the efficiency and sustainability of geothermal energy systems and contribute to increased widespread use of renewable energy technologies in the future.
Acknowledgment
Financial support was provided by the University of Oklahoma Libraries' Open Access Fund.
Conflict of Interest
The authors of this work declare that there are no conflicts of interest regarding the publication of this paper.
Data Availability Statement
The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.
Nomenclature
- Ag =
silver
- Al =
aluminum
- Al2O3 =
alumina
- C =
Celsius
- Cu =
copper
- DPD =
dissipative particle dynamics
- DST =
discontinuous shear thickening
- EGS =
enhanced geothermal system
- LCA =
life cycle assessment
- ODT =
order–disorder transition
- PEG =
polyethylene glycol
- Si =
silicon
- SiO2 =
silica
- STF =
shear-thickening fluid
- STNF =
shear-thickening nanofluid
- Zn =
zinc