In recent years, the demand for more efficient cooling circuits has resulted in active studies of nanofluids, two-component liquids consisting of a base fluid, and dispersed nanoparticles with high thermal conductivity. From the viewpoint of both physics and chemistry, nanofluids are systems that require the characterization of many interconnected thermal and chemical properties. This perspective article sums up the state of the art and recent trends in the development and applications of nanofluids and especially carbon nanofluids. A focus of the paper is the possibilities of photothermal and photoacoustic methods—as techniques combining molecular spectroscopy and thermal characterization—for the assessment of thermal conductivity and thermal diffusivity of nanofluids. The possibilities of photothermal spectroscopy for wider characterization of nanofluids and related materials are discussed and compared with other techniques. As nanofluids are one of the examples of complex objects dedicated to photothermal spectroscopy, more general outlooks of phototermics are also discussed.

Many state-of-the-art industries as well as critical technologies such as nuclear and solar energetics, microelectronics, and computer technologies require efficient cooling systems, which mainly rely on liquid circuits.1–5 Most often, the coolant fluids in such circuits are water, ethylene glycol, and various oils.6–8 However, their thermal conductivity is not always sufficient, which gives an incentive to search for ways to enhance the heat transport. Over the past 15 years, two-component liquid coolants consisting of a base fluid and dispersed nanoparticles (NPs) with a size range of 1–100 nm, nanofluids (NFs) have been actively studied and implemented.4,5 Such coolants increase the heat-transfer efficiency due to high thermal conductivity of the disperse phase. Of special interest are carbon nanofluids (CNFs), which are very advantageous due to their high thermal conductivity and chemical inertness.

In the past three to four years, the number of papers in this field has increased significantly, both in the field of new materials to create NFs and in approaches to use NFs for solving topical problems. According to Web of Science®, there has been an exponential increase in the number of publications on this topic, and over the past five years, more than 12 000 publications have been issued. The research on NFs has resulted in numerous reviews9–18 summing up nanofluid composition and properties2,3,7–12,14–17,19–26 as well as their applications2,3,18 or dedicated to specific types of NFs such as CNFs.14,23,27–29

From the viewpoint of both physics and chemistry, nanofluids have many interconnected properties. For both technological and medical applications, the key NF parameters are thermal conductivity, viscosity, and heat capacity of dispersions. It is thus important to have methods that can adequately determine these parameters. Moreover, the application of NFs in industry and at some facilities require the chemical composition, size, and concentration of nanoparticles along with thermal parameters. Finally, an important practical task is the constant control or monitoring of thermal parameters, concentrations, and the composition of the dispersed phase during their prolonged operation as the chemical transformation, aggregation, or other processes may seriously change the properties of the nanofluid.

A single method is incapable of solving all these tasks; thus, the development of methods that provide a comprehensive diagnosis of NF is required. Photothermal methods combine the possibilities of both optical/IR techniques of molecular spectroscopy and thermal characterization. Photothermal spectroscopy (PTS) has a high sensitivity for the determination of small amounts of substances, provides a high accuracy of thermal parameters, and is not destructive.30–37 Photothermal spectroscopy is promising for the characterization of disperse systems of various nature, from natural to engineered nano-size objects.30,38–43 Thus, the development of the methodology of photothermal spectroscopy for nanofluids and their use in nanofluid applications is relevant.

The aim of this perspective paper is to review the recent trends in development and applications of nanofluids, especially carbon nanofluids, and discuss the outlooks of photothermal methods in the characterization of thermal parameters of nanofluids as well as in a more comprehensive characterization of these materials.

The term “nanofluids” is somewhat ambiguous as it may refer to heat-transfer nanofluids as well as “nanofluidics” as the miniaturized flow techniques in nanometer-size channels (We avoid the term “nanofluidic” in this paper due to this ambiguity.). Moreover, nanofluids used for heat transfer are divided into two types: heat-conducting and heat-accumulating (thermal storage) nanofluids. Heat-conducting nanofluids provide an explicit gain in the thermal conductivity in comparison with the base fluid, thus improving the critical heat flux. Thermal-storage nanofluids are used for heat accumulation by the fluid followed by their release after a certain time or in a specific place of the circuit by forced heat transfer.44,45

An increase in the thermal conductivity of the medium as a whole in a NF may be explained by the contribution of the disperse phase through an effective medium theory, with the most conventional static model based on Maxwell's equations,46,
(1)
Here, the increase in the thermal conductivity of NF k n f over the base fluid k b f is determined by the volume fraction of nanoparticles φ n p and the constant x = k n p / k b f, where k n p is the thermal conductivity of nanoparticles. The developed model considers stationary spherical nanoparticles in the base fluid and take into account only the volume fraction of nanoparticles.47,48 However, in many cases, the effect of nanoparticle concentrations cannot be described by this simple equation as the heat transfer in nanofluids may be the result of nanostructures formed (Fig. 1) involving multiple heat-transfer mechanisms: Brownian motion (still controversial since it is too slow in comparison with heat diffusion; however, it could have an important indirect role in particle clustering), liquid layering at a liquid–particle interface, heat transport in nanoparticles (ballistic conduction), or nanoparticle clustering.49–51 
FIG. 1.

Nanofluid types: TEM images of the microstructures of (a) ordinary and (b) functionalized nanofluids of silica nanoparticles and (c) an Al2O3–water nanofluid. Reproduced with permission from X.-F. Yang and Z.-H. Liu, Nanoscale Res. Lett. 6, 494 (2011). Copyright 2011 Author(s). Reproduced with permission from Khaleduzzaman et al., Procedia Eng. 105, 406 (2015). Copyright 2015 Author(s).

FIG. 1.

Nanofluid types: TEM images of the microstructures of (a) ordinary and (b) functionalized nanofluids of silica nanoparticles and (c) an Al2O3–water nanofluid. Reproduced with permission from X.-F. Yang and Z.-H. Liu, Nanoscale Res. Lett. 6, 494 (2011). Copyright 2011 Author(s). Reproduced with permission from Khaleduzzaman et al., Procedia Eng. 105, 406 (2015). Copyright 2015 Author(s).

Close modal

Sometimes the dispersed nanoparticles act as thermal insulators; for example, even metallic powders can be as insulating as ceramic powders.52 Also, aerogels are considered one of the most promising insulation materials.9 For nanoscale objects, interfacial contact resistance plays an important role in heat transfer. Basically, certain attempts are made to reduce the resistance and enhance thermal conductivity. Molecular-dynamics simulations reveal that ordered water layers around nanoparticles53 and polar functional groups54 lead to a low Kapitza resistance and enhance local thermal conductivity of the water shell adjacent to the nanoparticle.55 However, some scientific groups are interested in systems, in which thermal diffusivity decreases with nanoparticle concentrations. Studies reveal carbon56 and CdTe57 quantum dots to be promising candidates as thermal insulating materials.

Thus, to be considered a practical heat-conducting nanofluid, a disperse system must have not only a high thermal conductivity but also a low viscosity, ideally equal to the viscosity of the base fluid. The latest advances in nanoscale fabrication make it possible to produce metallic and nonmetallic particles with a wide range of mechanical, optical, electrical, and thermal properties, which can be used as a disperse phase of nanofluids.2 The main types of nanoparticles and NFs and their applications are presented in Fig. 2.

FIG. 2.

Types of nanofluids, their disperse phases, and their common applications and limitations.

FIG. 2.

Types of nanofluids, their disperse phases, and their common applications and limitations.

Close modal

Metal nanoparticles usually include but not limited to aluminum, copper, silver, and gold since they were quite widespread and well-known colloidal systems.4,5,58,59 However, they are chemically active, which leads to the impossibility of using them in a number of areas, as well to their rapid deterioration.1,2,23,60 Their use is most widespread in nuclear energetics and closed circuits.1,61 For noble-metal particles, the disadvantage of NFs is the price of large volumes of nanoparticles. The second type of NFs is nanoparticles of metal oxides, such as Al2O3, Fe3O4, CuO, TiO2, etc.4,58,59 They are less expensive than metal particles but also have lower thermal conductivities.

In the past decade, the number of publications devoted to the study of thermally conductive CNFs increased dramatically.4,9,23,62–73 Here, main carbon nanomaterials—single-wall (SW) and multiwall (MW) carbon nanotubes (CNTs), nanodiamonds, graphene oxide, carbon dots, etc.—serve as the disperse phase. They are less reactive in comparison with metals and oxides69,74–81 and are stable and environmentally friendly;82,83 thus, they cause less corrosion, are less prone to sedimentation, do not clog communication lines, etc. They are discussed in more detail in Subsection II D.

The above-mentioned nanofluids belong to the single-phase class. In recent years, a novel NF class consisting of two solid materials dispersed in a fluid has appeared, hybrid nanofluids.12,16 These NFs lead to a further increase in thermal conductivity. Among hybrid NFs are all mixtures, of the same or different types of nanoparticles: from metals and oxides to CNTs, carbon dots, and microencapsulated phase-change materials (MEPCMs).12,16 For example, the authors of the paper73 succeeded in producing nanofluids based on hybrid nanoparticles from functionalized MWCNTs and graphene in de-ionized water and ethylene glycol without stabilizers. For a system on de-ionized water, an increase in thermal conductivity of 20% relative to the base fluid was observed at a volume fraction of hybrid nanoparticles of 0.05%.73 However, hybrid nanofluids, even more than single-phase ones, require the research of combinations of nanoparticles, their mixing ratio, the stability of hybrid nanofluids, etc., as well as understanding the mechanisms that contribute to the total heat-transfer enhancement.12,84

As a whole, three major research directions of NF are (1) the search for systems of new potential nanofluids; (2) applying the well-studied nanofluids in various industries, e.g., in the field of energetics; and (3) describing and predicting the thermophysical properties of nanoparticle-based fluid systems using models such as the Maxwell or Hamilton–Crosser models.25,58,69

Regardless of type, two-stage or one-stage approaches are used to produce nanofluids. Naturally, depending on the nature of nanoparticles and the base fluid, the conditions, e.g., the treatment protocol, time, or concentrations, may change, but the principle does not. Most often, a two-stage production approach is used. Here, nanoparticles are first synthesized in a dry form by a chemical or physical technology. At the second stage, the resulting nanoparticles are dispersed into a liquid by stirring, solvent replacement, or sonication.5,7,58,59,85 To increase the system stability, cationic or anionic surfactants are often used as additional components.

If producing nanofluids by a two-stage method is difficult, e.g., due to the impossibility of direct “dissolution” of nanoparticles in the base liquid, a one-stage method is used, which omits the stage of nanoparticle isolation after their synthesis. This involves several approaches to producing nanofluids.

  • The method of direct evaporation consists of the evaporation of the material and the subsequent condensation of nanoparticles right in the base liquid, which produces more stable dispersions due to a decrease in aggregation.5,7,25,58,59,85

  • Chemical reduction is mainly used for nanofluids based on metals and metal oxides. For this, a solution of a metal salt in the base fluid is obtained, and then a reduction reaction is carried out, leading to the formation of the solvate into the nanoparticle phase.25 

  • Nanofluids based on noble metals, silver, and gold are produced by laser ablation. A metal plate is placed in a base liquid and a laser beam is focused on its surface, as a result of which the metal evaporates and condenses in the base fluid.25 

  • Interfacial transfer is also used, which consists of dissolving the precursor and its further transfer by carrier reagents (usually amines) into the base fluid, where the chemical reaction of nanoparticle synthesis occurs.25,59

The main disadvantage of a one-stage method is the difficulty of removing impurities of unreacted substances from the resulting nanofluid, which can affect the stability, thermal parameters, and chemical and environmental properties.25 

The main areas of application of nanofluids are presented in Fig. 3.9 In recent years, there has been a tendency toward the miniaturization of already existing devices and machinery, which also leads to a decrease in cooling circuits, in which a small amount of refrigerant can no longer cope with the task of removing heat. The development of methods for obtaining energy from alternative sources, in particular, the use of solar energy, is also a prerequisite for the study of nanofluids and their application in this field.

FIG. 3.

Widespread application fields for nanofluids. Reproduced with permission from Qiu et al., Phys. Rep. 843, 1 (2020). Copyright 2020 Author(s).

FIG. 3.

Widespread application fields for nanofluids. Reproduced with permission from Qiu et al., Phys. Rep. 843, 1 (2020). Copyright 2020 Author(s).

Close modal

One of the industries in need of better cooling systems is nuclear energetics, as the low thermal conductivity of water and mineral oil, which are often used as base fluids, is a major limiting factor toward greater compactness and efficiency of reactors. Now, NFs with nanoparticles of metal oxides, copper, or aluminum are often used.1,61

The next topical task in the development of NFs is solar energetics. In this area, such NFs as Cu–water, Al2O3–water, CuO–ethylene glycol, carbon nanotubes–oil, and Fe3O4–water are being developed.2,86 Here, commercial solutions such as JJ Bioenergy Ltd (UK) have appeared in the market.

Third, the power of computers constantly increases and the advances in instrument making results in more and more miniature electronic devices. However, during the operation of these devices, a large amount of heat is produced, and the existing systems of air and water cooling are not efficient, which leads to reduced stability and a shortened service life of expensive computing systems. The replacement of water with nanofluids results in a 10 ° lower temperature of the processor (Fig. 4).4,5 NFs used in computer cooling circuits include some commercially available solutions such as Ice Dragon Cooling (http://www.icedragoncooling.com).

FIG. 4.

Maximum temperature of the CPU surface in terms of the Reynolds number in different liquid blocks for the water and a hybrid nanofluid containing graphene nanoplatelets decorated with silver nanoparticles. Reproduced with permission from M. Bahiraei and S. Heshmatian, Appl. Therm. Eng. 127, 1233 (2017). Copyright 2017 Elsevier Ltd.

FIG. 4.

Maximum temperature of the CPU surface in terms of the Reynolds number in different liquid blocks for the water and a hybrid nanofluid containing graphene nanoplatelets decorated with silver nanoparticles. Reproduced with permission from M. Bahiraei and S. Heshmatian, Appl. Therm. Eng. 127, 1233 (2017). Copyright 2017 Elsevier Ltd.

Close modal

NFs are considered promising for various industrial apparatuses (evaporators, concentrating installations, etc.) and in many chemical-industry processes to increase the efficiency and reduce operating costs.87 To improve the cooling system, nanoparticles such as Al2O3, Cu, and CuO can be used.60 As well, commercial solutions such as HTF Compact Nano Thermo Fluid (HTF Compact, TCT Nanotech, Italy) and Advanced Thermal Solutions, Inc. (USA) have entered the market recently.

Nanofluids can be used as thermally conductive lubricants for electric motors and other mechanisms as contributing to the reduction of friction than traditional lubricants, which leads to the increased lifetime of mechanisms.23,60 Also, they start to find applications in deep-hole drilling as heat sink and lubricant solutions.88 

In the regions where the average daily temperature is quite low, heating systems for houses are used. They work due to the circulation of, most often, a mixture of water and ethylene glycol. The use of nanofluids in such systems makes them more compact without a loss of efficiency of heat transfer; also, due to the lubricating properties of nanofluids, the service life of pumps for the circulation of the liquid increases.59 This direction is interconnected with the next stage of development of Internet of Things, in which smart cooling circuits at the appliance and house levels are required.89 

Finally, tests of NFs in two-phase thermosyphons as advanced heat-transfer technologies in applications from energy conversion systems to electronics cooling have started.90 A closed two-phase thermosyphon utilizes the countercurrent flow of a liquid and a vapor for heat transfer and consists of a liquid pool contained in the heated section or evaporator, an adiabatic section, and a cooled or condenser section.91 NFs may play a crucial role in thermosyphon efficiency.

The use of heat-conducting nanofluids is not limited only to the tasks of efficient heat removal. Many nanofluids, especially CNFs based on carbon nanoparticles, are considered potential biocompatible thermal or photothermal materials for thermal-transport drug delivery, therapeutic purposes,92–94 or as theranostic agents—bio-nanofluids.95–98 Bio-nanofluids based on nanodiamonds and carbon dots are advantageous due to their low cytotoxicity, high water solubility, favorable biocompatibility, and good photostability;99 in several cases, they provide other important properties such as light absorption, IR emission, or fluorescence.100,101 Due to these features as well as easy bioconjugation and a high specific surface area, they are perspective materials in biomedical imaging and sensing. This requires reliable and much more detailed information about the physicochemical and thermophysical properties of bio-nanofluids. In particular, precise values of thermal diffusivity and thermal conductivity are required for understanding the mechanism of laser therapy and theranostics, e.g., for switching between photochemical and photothermal modes,102–104 calculating the dose and irradiation parameters, predicting the risk factors, etc.105 

The main characteristics of both technological and biomedical purposes of thermally conductive NFs are thermal conductivity and thermal diffusivity.9,11,19,85,106,107 The latter characterizes the rate of heat transfer throughout the material; thus, it is usually obtained from the measurements (transient methods), and it is directly related to thermal conductivity. Thermal conductivity k and thermal effusivity e T can be calculated from the experimental thermal diffusivity D T and from the specific heat and density (or volume heat capacity C V = ρ C P) of the test sample,
(2)
(3)
Thermal effusivity is somewhat undervalued in NF research, but it is very important as a measure of ability of the sample to exchange heat with the materials in contact and determines the contact temperature T c of two objects that touch each other as
(4)
where T 1 and T 2 are temperatures and e 1 and e 2 are thermal effusivities of objects. It is important that this property can be directly measured by photothermal techniques such as photopyroelectric (PPE) and thermal-wave resonator cavity (TWRC) techniques as well as photoacoustic (PA) modalities (Sec. IV A).

The volume fraction of the dispersed phase is one of the parameters that can be varied to obtain disperse systems with the required thermophysical properties. This parameter affects the thermal conductivity of the colloidal system, which begins to increase starting from a certain concentration of nanoparticles, while below which the thermal conductivity remains indistinguishable from the base fluid.5,29,47,106 With a large volume fraction of the dispersed phase, sedimentation processes begin to occur, which result in a decrease in the stability and efficiency of NFs. The concentration of nanoparticles as well as the conditions for preparing dispersions affect the size of nanoparticles,108 which alters the thermophysical properties of NFs. Typically, thermal conductivity increases with a decrease in the nanoparticle size.5,47,106 Thus, it is necessary to determine the volume fraction of the dispersed phase and monitor its change during NF operation (Fig. 5).

FIG. 5.

The intrinsic mechanisms for the influence of various factors on the thermal conductivity of nanofluids. Reproduced with permission from Qiu et al., Phys. Rep. 843, 1 (2020). Copyright 2020 Author(s).

FIG. 5.

The intrinsic mechanisms for the influence of various factors on the thermal conductivity of nanofluids. Reproduced with permission from Qiu et al., Phys. Rep. 843, 1 (2020). Copyright 2020 Author(s).

Close modal

The introduction of the dispersed phase into the base fluid makes it possible to aim other properties of the fluid.5–8,24 An important parameter of nanofluids that has received less attention compared to thermal conductivity is the volume heat capacity. Different nanoparticles may decrease or increase the specific heat compared to the base fluid.21,85 Also, the nature of nanoparticles affects the temperature dependence of Cp; it can either increase or decrease with temperature. The Cp value is also affected by the volume fraction of dispersed particles in the nanofluid. To date, there is no fully reliable model for the heat capacity of nanofluids.

Nanoparticles increase the dynamic viscosity of the fluid, which is a negative effect for any heat-sink and heat-transfer applications. Thus, the dynamic viscosity is the second most important parameter that determines the applicability of nanofluids.109,110 As a rule, the dynamic viscosity increases with a decrease in the size of nanoparticles.

Even if a disperse system has thermophysical parameters that ensure an efficient heat transfer, it cannot be called a nanofluid if it has a low sedimentation stability.10,70 The aggregation leads to sedimentation and may reduce the thermal conductivity due to a lower mobility of nanoparticles. The presence of a stabilizer (dispersant) increases the stability of the colloidal system and makes it possible to obtain dispersions with a larger volume fraction of the dispersed phase.5,29 However, the amount of dispersant also affects the thermal conductivity; as the dispersant concentration increases, the thermal conductivity may decrease.5,29 For this, the methods of light scattering, sedimentation, or spectrophotometry are used, and the electrokinetic potential is also measured.10,15,22,25 This parameter provides a value characterizing the stability of nanofluids and also shows the surface charge of nanoparticles in the system.25,85

Thus, an important task is to find the optimum content of nanoparticles and extra reagents and the conditions for obtaining the most efficient system with the highest possible stability. Most studies are directed toward devising new nanofluids rather than finding the optimal parameters for the efficient use of already designed dispersed systems.

The special interest of CNFs results from high thermal conductivities of carbon nanomaterials and chemical properties (Fig. 6).64 This also makes CNFs more stable in time and environmentally friendly. Nanodiamonds and fullerenes and their aqueous dispersions raise even a more serious interest as promising biocompatible materials.95–98 

FIG. 6.

Thermal properties of carbon allotropes and their derivatives (the diagram based on average values reported in the literature). Reproduced with permission from A. A. Balandin, Nat. Mater. 10, 569 (2011). Copyright 2011 Nature Publishing Group.

FIG. 6.

Thermal properties of carbon allotropes and their derivatives (the diagram based on average values reported in the literature). Reproduced with permission from A. A. Balandin, Nat. Mater. 10, 569 (2011). Copyright 2011 Nature Publishing Group.

Close modal

Clinical studies impose other requirements on CNFs. Of special control is the chemical composition and purity, toxicity, etc.; thus, CNFs with the optimum thermophysical properties cannot be directly proposed as bio-nanofluids.99,111–114 However, many target properties of carbon nanofluids for heat sink and medical problems match (stability in time, concentration of nanoparticles, low aggregation, etc.). Today, the research of CNFs is progressing in the following directions:

  • Techniques for preparing CNFs with different concentrations of nanoparticles are developed; the attempts to increase the concentration in different ways (surfactant admixtures, ultrasound treatment, etc.) are made; and the stability of CNFs reveals itself as an important and not fully investigated problem. It is noteworthy that stable aqueous CNFs find wide applications in biomedical research. Carbon nanoparticles that are stable in water are used for drug delivery, as contrast agents, in photodynamic therapy, etc.115,116

  • The studies of the effect of concentration, size, shape, surface condition, type of nanoparticles, solvent, temperature on thermal conductivity, heat capacity, and viscosity of CNFs are performed;14,80,81,117,118 however, the systematic research in this direction is almost not carried out.

  • Methods of physicochemical characterization of CNFs are developed, in particular, reliable measurements of thermal conductivity in a wide range of concentrations.11,48,119,120 A challenging task is the measurement of particle size in colloidal solutions and monitoring the inevitable aggregation of nanoparticles in CNFs. The existing methods (e.g., dynamic light scattering) sometimes do not provide reproducible results.121 

  • Physical models that seek to describe the observed patterns, especially the dependence of thermal conductivity of CNFs on the type, concentration, shape, and size of nanoparticles, and the properties of the base fluid are in development.9,20,107 Noteworthy is the proposed models that do not give an adequate description of the thermal properties of CNFs and, in most cases, are adapted for the description of systems containing metal rather than carbon nanoparticles.122,123

Carbon nanotubes are the most widespread materials for producing CNFs. The disperse phase in this case, most often, is a mixture of multi-walled carbon nanotubes as most accessible and cheap.124 However, single-walled CNTs are characterized by the highest (up to 6000 W/m/K)64 thermal conductivity coefficient. As CNTs are hydrophobic, stable dispersions (up to 1% v/v) require ultrasonic treatment and a stabilizer surfactant.9 In this case, to correctly assess the increase in the thermal conductivity coefficient, it is necessary to measure the base fluid with the same amount of the surfactant. In general, the addition of a surfactant does not affect thermophysical properties; however, up to 6 wt. % cetyltrimethylammonium bromide may lead to a decrease down to 5% in the thermal conductivity coefficient.65 An important parameter of carbon nanotubes is the length-to-diameter ratio; prolonged ultrasonic treatment can decrease it and, as a consequence, degrade the thermal conductivity coefficient. As a rule, an increase in the number of walls also negatively affects thermal conductivity.118,125 However, this regularity is not observed in all the experimental studies.65 Since carbon nanotubes are two-dimensional flat structures rolled into a tube, the models for the thermal conductivity of nanofluids need to be seriously modified compared to other nanoparticles.9 Finally, CNTs are toxic, which significantly limits their use.

For dispersions of hydrophilic nanoparticles, nanodiamonds are widely used among CNFs capable of forming stable aqueous solutions. Diamond has many unique properties,99 including a high thermal conductivity coefficient (up to 2000 W/m/K).64 However, nanodiamonds are sp3 diamond cores covered with sp2 graphite-like phase shells, which are responsible for lowering thermal conductivity.126,127 Therefore, the thermal conductivity of nanodiamond-based CNFs directly depends on the purity and the method of production of both nanodiamonds and the nanofluid. Also, it is not entirely correct to translate the thermal properties of bulk materials to nanostructures since the contact resistance is of paramount importance, and the thermal conductivity regime can change from a diffuse to a quasi-ballistic (collisionless heat transfer). In addition, nanodiamond is a powder, and the heat-conducting properties of the powder are formed by surface contacts of spherical particles and the thermal conductivity of the gas gaps in the vicinity of thermal contacts. The thermal conductivity of powders is much lower (by a factor of 10–100) than the bulk material. Not many studies deal with the thermal conductivity of nanodiamonds. Composites obtained from detonation nanodiamonds sintered at pressures of 5–7 GPa and temperatures of 1100–1900 °C were studied; rather low (of the order of 10–50 W/m/K) values of the thermal conductivity of detonation nanodiamonds were found.126 They used a home-made setup for measuring thermal conductivity by a stationary heat flux. Another research group used a commercial analyzer based on a modified transient plane source (TPS) method and equipped with a special kit for testing powders and liquids.127 Even lower (tenths of W/m/K for a porosity of 88% or a relative density of 12%) values of thermal conductivity for nanodiamond powders were obtained. The authors theoretically calculated the thermal conductivity according to the modified Maxwell model. The calculations are in good agreement with the experimental data, and the extrapolation of the model to low (0.1%) porosity indices showed that the thermal conductivity strongly increases when the nanodiamond powder becomes a solid material. The values are in good agreement with the previous data.126 The thermal conductivity of nanodiamonds was also calculated by molecular dynamics.127 The thermal conductivity of nanodiamonds decreased from 28 to 10 W/m/K with a decrease in the sp3 carbon fraction until the number of sp2 bonds exceeded the number of sp3 bonds. Furthermore, the thermal conductivity is less sensitive to a further increase in the sp2 fraction of carbon.

Due to a developed surface of nanodiamond particles, it is possible to control their physicochemical properties. The thermophysical properties of ND nanofluids based on water,69,75–80,128,129 water–glycol,81,130–137 and other organic solvents were studied.68,80,81,138–140 However, the heat-conducting properties of two-phase systems containing nanodiamonds have not been studied systematically, and one of the recent reviews on nanodiamond nanofluids14 shows a clear tendency of a relative increase in thermal conductivity with concentration and temperature; however, the values are quite scattered showing a rather contradictory 5%–20% increase;69,74–78,80,141 therefore, it is almost impossible to determine a priori how effective would be the addition of nanodiamonds to a base fluid. The same situation is with other carbon nanofluids. Of importance is the fact that the majority of studies relied on a rather unprecise implementation of the non-stationary hot-wire method (a KD-2 pro instrument proposed for technical solutions), which requires a large volume of the solution, is convection-dependent in low-viscosity solutions, and provides the accuracy of ±5% at best.

Over the past decade, an increasing number of studies on CNFs have been associated with colloidal solutions of graphene,142,143 graphene oxide,117,137,144,145 and their hybrid nanofluids.27,28 A rather high (5000 W/m/K)146 coefficient of thermal conductivity was experimentally determined for this material. Ultrasonic treatment is required to produce graphene-based nanofluids; less often the stabilizers are used. Still, there is an acute problem of producing stable dispersions147 containing sufficient quantities to change the thermophysical properties of the base fluid. As in the case of nanodiamonds, the maximum achievable concentrations and the corresponding increases in thermal conductivity differ greatly between the reports, which may be a consequence of the use of different methods for producing nanoparticles. Also, the actual values of the thermal conductivity of the dispersed phase are much lower than assumed.143 This is due to the fact that the size of small sheets of graphene in solution can be less than the mean free path of quasi-particles, phonons responsible for heat transfer. In addition, the contact resistance is high, and the oxidation leads to the appearance of defects at which, as well as at the boundaries of the nanostructure, phonons are scattered, which prevents heat transfer. Estimation of the thermal conductivity of in-plane graphene and graphene oxide resulted in rather small (4.9 ± 0.6 and 6.8 ± 0.8 W/m/K, respectively) values.143 

The addition of fullerenes to water does not lead to an increase in thermal conductivity as the thermal conductivity coefficient of fullerene is lower (0.4 W/m/K) than the values typical for water. An increase in the thermal conductivity of toluene upon the addition of fullerenes (a mixture of C60 and C70, less than 0.4% v/v) was less than 1%,148 and the addition of 5% v/v C60 to a mineral oil (0.1 W/m/K) led to an increase in the thermal conductivity by 6%.70 A fullerene–mineral oil system turned out to be promising for use in compressors of freezing systems since it has good lubricating properties, which increases the compressor life, and also has a higher thermal conductivity than the mineral oil, which is necessary for more efficient cooling.72 

Still, the potentialities of carbon-based dispersions are an open discussion. First, their application demands assessing the concentration of the nanophase and total composition of the dispersion as well as the knowledge of the characteristic size and the aggregation state. Their thermal parameters, first of all thermal conductivity, are sometimes rather contradictory and doubtful.1,60 The accuracy and precision of the existing data often suffer from the errors in calculation, changes in the sample by an immersible measurement system,11,119 and convective effects at long measurement times or for large volumes. Understanding heat transfer in carbon-based dispersions still lacks experimental techniques providing the accurate data in situ.

Measuring the thermal conductivity and thermal diffusivity of nanofluids is carried out with various methods. Experimental techniques are divided usually into two principal groups: (i) the steady-state techniques performing a measurement when the sample reaches the thermal equilibrium and (ii) transient methods.26 Among the latter, photothermal techniques will be considered separately (see Sec. IV). In this section, the most common techniques are briefly listed. They are the transient hot-wire (THW) method, the 3ω method, the transient plane source (TPS), the temperature oscillation, and laser flash (LF) methods.11 The relevance of these methods depends on the availability of commercial equipment, price, versatility, and practical simplicity.

The most common is THW (both commercially available and homemade apparatuses);9,11,19,20,26 however, this method should be considered more critically. Even for a homogeneous medium, certain conditions must be fulfilled to eliminate forced convection; e.g., the fluid sample and the thermal sensor must be kept completely still during the measurement. Thus, it may be necessary to place the sample on a vibration-isolation table and shut down heating, ventilating, and air conditioning systems in the measurement room. Thus, the water bath should be turned off before the data acquisition and the temperature must not exceed 50 °С for aqueous solutions. The method suffers from practical drawbacks due to the need for a large volume of liquid; also, the accuracy may be affected by the presence of ions of the conducting fluids around the hot wire so often that the wire should be electrically insulated (usually implemented in a transient short hot wire, an improved design of the method).149 

In the case of nanofluids, additional problems appear. Gravity effects can cause inhomogeneous nanoparticle dispersity over the fluid producing a temperature gradient along the hot wire, which increases the measurement error. Such complications may lead to a serious measurement bias: an anomalous enhancement of the effective nanofluid thermal conductivity and as a result to large discrepancies.119 To avoid these problems, a standardized methodology for nanofluid measurement is on demand. The information on sample preparation, sample size, all measuring conditions, as well as the number of replicate measurements, the data on the basic fluid, and uncertainty must be pointed out.

Other transient techniques find applications on nanofluid characterization, but they are not so widespread. Just as THW, the 3ω method uses a radial flow of heat but applies a temperature oscillation instead of a time-dependent response. Basically, a short wire immersed in the test fluid or liquid is placed on a quartz substrate on which a thin metal heater is attached, thereby allowing the use of small (droplet) liquid volumes.150 Another advantage is the possibility of studying the gravitational effect on the thermal conductivity of disperse media by changing the orientation of the test system. Low heating (0.5 K) and fast temperature-dependent measurements help suppress convection interference for which the effect decreases with frequency.151 All nanofluid measurements are done by home-made instruments.150–156 Examples are Al2O3–H2O,150 TiO2–H2O,151,152 SiO2–H2O, ethanol, EG,151 CuO–H2O,153 hybrid nanofluids (numerous CNTs attached to an alumina/iron oxide sphere in poly-alpha-olefin oil),154 Bi3Te2 nanorods–oil,155 and single-wall CNTs–H2O (the convective heat-transfer coefficient is also measured).156 Similar to the wire in THW, a hot ball sensor is applied to assess thermal diffusivity and conductivity of an aqueous Ag nanofluid.157 

The transient plane source method is attractive for NFs because test instruments are commercially available.11 TPS was applied for various nanofluids: Al2O3–H2O, Cu–H2O, and carbon nanotubes–R113 refrigerant.158–160 Manufacturers continue to upgrade the measurement system by offering a special cell (a modified transient plane source).161 It should be mentioned that without prior knowledge of density and isobaric heat capacity, thermal conductivity is calculated with the iterative method by the software. Fast response (0.8 s), small (1.25 ml) sample volume, low energy power, and horizontal presentation of the sample to the sensor help eliminate the effect of heat convection, but the better the parameters, the higher the instrument price.162 

The purely thermal technique—the temperature oscillation method—is not widespread, perhaps, due to its specific principle, instrumentation, and theory. The setup consists of a hollow insulating cylinder and the central hole is closed from both sides by two metal discs leaving a central cylindrical cavity for the test fluid. A sinusoidal temperature input is applied at the outer faces of the metal disks. To find the thermal conductivity of the test fluid, the amplitude attenuation and the phase shift in the temperature wave at the inner face of the disk and at the center of cavity are measured.

This technique was used to measure the thermal diffusivity of metal-oxide fluids in water,163 ethylene glycol, and transformer oil.164 The following advantages are claimed: (i) the use of a small oscillation amplitude (1.5 K) to retain constant fluid properties and to avoid natural convection and (ii) electrical components of the apparatus are away from the test sample; therefore, any liquid, irrespective of its electrical conductivity, can be measured.

The laser flash method is implemented as the most expensive commercially available technique and is commonly used for solid substances. Measurements of thermal diffusivity and specific heat allows the calculation of the thermal conductivity with an external measurement of the bulk density of the sample material only. A special sample holder and more complicated data processing with additional data on thermophysical parameters of the sample and container material are required to work with fluids.165 The main disadvantage of the method, especially for low-viscosity liquids, is convection due to a strong increase in the temperature in a short period of time. Also, LF lacks precision when measuring fluids with low thermal conductivities.48 

It was used for some nanofluids containing metal–oxide nanoparticles in water13,140,166 and water–alcohol mixtures,167 nanodiamonds in silicone oil,140 carbon nanotubes, exfoliated graphite, and heat treated nanofibers in a poly-alpha-olefin oil.168 LF was compared with TPS (a good agreement between the two methods)166 and THW (results by LF were significantly lower).13 The collision-mediated heat-transfer models were applied for explaining the difference in thermal conductivity values by various experimental methods. The authors169 showed that Brownian motion of the nanoparticles is limited because of the small liquid volume resulting in the reduction of the collision frequency of nanoparticles.

Steady-state techniques can be classified into a coaxial (concentric) cylinder method and a parallel plate method (including a cut-bar method). The latter has been implemented commercially in two types of equipment: guarded hot-plate instruments and heat-flow meters (measurements of the electrical power and heat flux, respectively). Only the second is adopted to measure liquids; however, to date, there are almost no experimental data on the use of this liquid cell. Some metal–oxide nanofluids were measured by home-made instruments.170,171 Home-made apparatuses of the concentric-cylinder method was commonly used for fluids172 but is rarely seen in the research on nanofluids.120,173 Steady-state methods have a simple theory based on Fourier's law providing the assessment of the thermal conductivity from the measurements, but they are time-consuming.

Fast, often portable, and relatively affordable equipment of transient methods is generally more widespread. Under the right conditions, they guarantee good characteristics (precision, 1% and accuracy, 5%). Still, the measurement of thermal conductivity of liquids, especially nanofluids, showing the complexity of the thermal transport mechanism, is a challenging task.174 

Methods referred to as photothermal spectroscopy (PTS) are based on the detection of thermally induced changes in the sample upon its interaction with electromagnetic radiation (photothermal effects). This is an established group of methods, which is used for the characterization of various materials.30,34,175–177 Thermal relaxation of spatially encoded electromagnetic radiation absorbed by an object under excitation leads to its nonuniform and dynamic heating.

PTS is suitable for assessing all the thermophysical parameters governing or associated with the heat distribution (thermal conductivity, thermal diffusivity, specific heat, refractive index, density, etc.).36,178–188 Also, PTS complements optical methods: transmission spectrophotometry, diffuse-reflection spectroscopy, and many IR modalities. While these methods measure transmission or reflection of the incident electromagnetic radiation (i.e., its non-absorbed part), PTS is based on non-radiative transitions of excited molecules, i.e., on the absorbed part of the radiation.30,37 Thus, PTS is used to assess extinction and absorption coefficients in liquid and solid samples down to the level of 10–9–10–6 absorbance units. Also, using Beer's law, PTS makes it possible to assess the concentrations down to 10–11 M and detect countable numbers of molecules.30 A small influence of the scattering matrix on the signal compared to purely optical techniques makes photothermal and especially photoacoustic spectroscopy invaluable tools for complex samples and in biomedical research.189–195 Moreover, the sensitivity of photothermal methods excels both purely optical as well as purely thermal-wave methods because PTS is based on the interdependence of changes in optical and thermal properties acting cooperatively to enhance the sensitivity196 and makes it possible to get the excitation spectra of photothermal properties.197–203 

Photothermal spectroscopy can be used to assess both thermal and optical sample properties with a locality governed by the characteristic rates of nonradiative heat transfer.30,34,175–177 Thus, PTS works with both volume- and surface-absorbing samples, as well as layered and discretely absorbing materials. As the excitation source is usually a laser, which can be focused to down to the wavelength-confined space (diffraction limit), all photothermal methods have a merit of being implemented as a microscopic, imaging, or microspectroscopic techniques.203–207 

These features of PTS are quite relevant for heterogeneous objects or dispersions, where the classical thermophysical or chemical methods result in averaged parameters of the whole sample only. A current trend is the application of photothermal and photoacoustic methods to the objects, for which other methods of optical and thermal characterization are difficult to use,—such as complex heterogeneous condensed systems in situ and in vivo.30,38–40 Photothermal studies of nanoparticle-containing materials show that the nature, the particle concentration, and their size make a critical effect on the development of the thermal profile in the sample and on the formation of the photothermal response of the material.41–43,208–212

PTS is an umbrella term for several techniques. They are commonly classified according to the result of the photothermally excited heating because of energy absorption and thermal relaxation. This leads to some processes in the whole sample or its (sub)surface layers: (1) the photothermal generation of thermal waves, (2) the formation of a non-uniform spatial field (profile) of temperature manifesting itself as a refractive-index or density fields, and (3) the emission of secondary radiation by a heated sample surface, photothermal radiometry (PTR).

Regardless of the detection approach used, photothermal techniques can be categorized as frequency-domain and time-domain (transient grating, forced Rayleigh scattering, laser flash, and thermal lensing).213 Also, the methods of PTS can be divided into two main categories: (1) contact techniques, in which the sample is in contact with the detection system, and (2) non-contact techniques, involving a remote detection system.214 The relevant feature of PTS is its non-destructive character, and both for optical and thermal parameters of materials, high precision of measurements is attained.

The format of this perspective paper does not allow the discussion of general possibilities of the methods; therefore, below are brief description of photothermal methods that have already found their use in the studies of NFs and related materials.

The best example of a contact technique is the photopyroelectric (PPE) technique based on the use of an opaque pyroelectric transducer in thermal contact with the test material to detect the temperature variations caused by light-induced periodic heating. The signal depends on the optical and thermal parameters of the test material and the PPE plate in a complex way, which is why usually some approximations and calibration are used. Usually thermal diffusivity and thermal effusivity of the sample are evaluated by making an excitation frequency scan and fitting the experimental curves for the dependence of the signal amplitude and phase on the frequency.

The back and front PPE techniques (BPPE and FPPE, respectively) allow the measurements of the thermal diffusivity and thermal effusivity of fluids, and the experimental uncertainty is as low as 2% and 1% for thermal diffusivity and effusivity, respectively.215,216 Other advantages of this method include its relatively low cost, and only a small (0.2–0.3 ml) volume of the sample is required with a short measurement time, where the concentration of the nanofluid remains constant in the measurement process, thus making this technique suitable for nanofluids.217 The limitation of these techniques is that not all the types of liquid samples can be used, as a reactive sample in direct contact with the transducer may damage it.

Thermal wave resonator cavity (TWRC or thermal-wave interferometry) is a simple, versatile, and accurate technique.218,219 TWRC is a kind of back-detection PPE when a thin metal foil front wall serves as a laser-induced oscillator source (a thermal-wave generator), while a pyroelectric PVDF back wall acts as a signal transducer and a cavity standing-wave-equivalent generator. In contrast with the frequency scans employed in conventional PPE techniques, TWRC uses a PPE detector with a variable sample-to-source distance, usually with a micro-linear stage, which provides the cavity length to vary with a micrometer step resolution (Fig. 7).220 The signal phase is a linear function of the sample thickness, and the thermal diffusivity of the sample can be determined from the slope. Because the cavity-length scan employs a selected thermal-wave frequency, it improves signal-to-noise ratios.221 

FIG. 7.

Cross section of the photopyroelectric experimental system. Reproduced with permission from López-Muñoz et al., Nanoscale Res. Lett. 7, 667 (2012). Copyright 2012 Springer.

FIG. 7.

Cross section of the photopyroelectric experimental system. Reproduced with permission from López-Muñoz et al., Nanoscale Res. Lett. 7, 667 (2012). Copyright 2012 Springer.

Close modal

A liquid-state compatible design of the TWRC was first applied for the measurement of the thermal diffusivity of one-phase liquids (15 ml); precision, 1% and accuracy, 1%–2%.222 Later, it has been employed for nanofluids: TiO2 nanoparticles dispersed in polyvinyl alcohol223 and water,224 Ag NPs in water,225 and urchin-like colloidal gold nanofluids in water, ethanol, and ethylene glycol.220 

Sometimes, these techniques are applied for nanofluid characterization in combination with other photothermal techniques: thermal diffusivity is assessed by thermal-lens spectroscopy (Sec. IV E) and thermal effusivity by PPE. The cases include Au NPs in water, ethylene glycol, and ethanol;226 TiO2 NPs in water;227 biodiesel containing Au NPs;212 and hybrid nanofluids (l-cysteine in combination with Au nanoparticles and protoporphyrin IX).228 NFs based on Fe3O4 and CoFe2O4 in water were investigated by both BPPE and FPPE photopyroelectric configurations with the TWRC technique as a complementary high-resolution scanning procedure.229,230

The photoacoustic (PA or optoacoustic) effect consists of a change in the pressure (acoustic pulse, PAS signal) caused by thermal expansion of the sample upon the absorption of electromagnetic radiation by its molecular structures and subsequent nonradiative relaxation. This change in pressure is detected with a microphone or piezotransducer. PA detection first used for thermal parameters for gases and solids214 can be applied to liquids231,232 as the physics underlying the photoacoustic effect has been developed.233 

In the assessment of parameters of liquids, usually, an open photoacoustic cell, OPC is used: a front configuration to measure the thermal effusivity234 and a thermal-wave transmission configuration for thermal diffusivity measurements.235 Conventional PA methodologies for thermal diffusivity measurement purposes in solids rely on the scanning of the PA signal as a function of the laser modulation frequency f. On the contrary, the PA methodology for liquids236 makes use of linear relations among the photoacoustic amplitude (on a semi-log scale) and phase as functions of the sample thickness. As in TWRC, the thermal diffusivity of the sample can be determined from the slope as B = π f / D T. The laser source is immersed in the sample, and the PA chamber (cell) consists of a cylindrical cavity in a stainless-steel body and communicated with a microphone (Fig. 8). The layer of a glass sealer of the PA chamber helps avoiding the limitation of PPE techniques to the kind of the liquid sample to be used because there is no contact with the transducer.235 PA techniques and the front PPE configuration confine the majority of photothermal methods for direct assessment of thermal effusivities.

FIG. 8.

Cross section of the photoacoustic experimental system. Reproduced with permission from López-Muñoz et al., Nanoscale Res. Lett. 7, 423 (2012). Copyright 2012 Author(s).

FIG. 8.

Cross section of the photoacoustic experimental system. Reproduced with permission from López-Muñoz et al., Nanoscale Res. Lett. 7, 423 (2012). Copyright 2012 Author(s).

Close modal

The method was applied for two-phase liquids; e.g., the thermal diffusivity of water-based Au236 and Al2O3237 nanofluids was determined. The instrument was improved by an accurate sample temperature control and verified the possibility to detect slight (around 1%) thermal-diffusivity variations.237 Due to the development of the theory, the method was used to evaluate the thermal effusivity of a Fe3O4–ethylene glycol nanofluid (a high-density suspension)238 and biodiesel filled with Au and Ag.239 Thermal effusivity and the refractive index of Al240 nanofluids in ethylene glycol were measured using PA spectroscopy and minimum deviation methods, respectively. A closed PA cell was applied for thermal diffusivity and effusivity measurement of fluids with low concentrations of TiO2 and Al2O3 NPs in water.241 A PA technique with piezoelectric detection was used as a non-destructive and noncontact tool to study thermal transport in nanofluids formed by carbon flurooxide mesoparticles;242 this technique was also adopted for the study of heat transport across the interface of a nanostructured solid (porous silicon) and a fluid.243 PA and thermal-lens techniques (Sec. IV E) sometimes were used together for thermal effusivity and diffusivity evaluation of a nanofluid (Ag NPs in ethylene glycol and ethanol); in this case, thermal conductivity can be calculated from this experiment alone, without external data.244 Similarly, the TWRC technique was used to assess the thermal diffusivity of samples and an OPC PA to the thermal effusivity of Ag nanowires in water.245 The thermal diffusivity and effusivity were found by fitting the theoretical expressions for each modality as a function of the sample thickness and frequency to the experimental data. The cell was calibrated with water to compare with the values reported in the literature.245 Likewise, the thermal characterization of a carbon-nanofiber–silicone based fluid was performed using these two photothermal techniques.219 

Photothermal radiometry is common in studies of solids due to the possibility of studying the surface structure, detecting a variety of defects, damage, heterogeneous areas in materials, etc. The incident modulated or pulsed radiation causes fluctuations of the temperature of the sample surface, which are dictated by the material underneath the cover layer and are recorded by an IR detector.204,213,246–248 By comparing the phase shift between the original signal and the temperature variation, the thermal properties can be extracted. This technique can be used in the front (photothermal emission) and rear configurations (photothermal radiometry), a setup similar to the laser flash technique.213 In this case, it is necessary to deposit a black layer on both surfaces of the sample to improve the laser absorption and increase the backside infrared emission.213 Apart from the features common to all the photothermal methods, the advantages of PTR are remote sensing, the relative simplicity of the experimental setup, and a high time resolution (10–8–10–7 s).248–250 The latter makes it possible to measure the spectra of intermediate products and to monitor fast processes.

Front-face modulated PTR was proposed for the estimation of thermal conductivity of liquids (water and sunflower oil) by fitting the experimental points of phase lag vs frequency measurement. The system consists of three layers. The first layer is constituted of steel (absorption of the heat flux), the second layer (thickness 500 μm) is the test liquid (opaque for thermal radiation), and the last one is made of glass, transparent in the visible range and opaque in the infrared. A small temperature oscillation (2 K) ensures that no natural convection occurs in the liquid layer.251 

Rear PTR was applied for thermal diffusivity measurements of Ag NPs in water by a calibrated scanning depth profile of the heat wave μs from the amplitude and phase signals.252 Thermal diffusivity is estimated using the dependence of the penetration depth on the excitation frequency f,

These remote techniques are well suited for investigation of thermo-optical properties including thermal diffusivity and nondestructive evaluation of solid samples: bulk materials, thick films as well as thin films or multilayers.213 The concept of this method is based on the deflection of a probe beam due to changes in the refractive index of the contact medium—a gas (more seldom, liquid) layer adjacent to the surface of the test sample—induced by a temperature change produced by an absorbed excitation laser radiation (Fig. 9). Depending on the relative position of these beams, two configurations can be distinguished: perpendicular (mirage effect) and collinear (photothermal mirror). The former can probe the contact medium at the front or rear surfaces, whereas the latter preferentially probes the material. Theoretical models are complicated; however, slopes of simple linear relations between two measurable parameters can be used to assess thermal diffusivity; for a more detailed information, see the paper.253 

FIG. 9.

Schematics of the probe-beam deflection near the sample surface. Reproduced with permission from Saadallah et al., Sens. Actuators A: Phys. 138, 335 (2007). Copyright 2007 Elsevier B.V.

FIG. 9.

Schematics of the probe-beam deflection near the sample surface. Reproduced with permission from Saadallah et al., Sens. Actuators A: Phys. 138, 335 (2007). Copyright 2007 Elsevier B.V.

Close modal

Despite the history and abilities of this method, only few investigations were associated with liquids, especially heterogeneous. A technique based on a mirage effect (Fig. 9) was demonstrated to determine the thermal diffusivity and, indirectly, the absorption spectrum of nonabsorbent liquids (paraffin oil) by fitting the experimental curve to the theoretical model of amplitude vs the square root modulation frequency.254 In a glass cell fulfilled with paraffin oil, a plexiglass plate covered with a thin black carbon layer (radiation absorbent) is introduced. Since the thermal diffusion length in liquids becomes lower than the probe-beam diameter for high frequencies, only one part of the beam is deflected. Therefore, a new mathematical expression of the deflection related to the probe-beam dimensions was established to calculate the “effective” deflection in liquids.254 The photothermal mirror technique was used for the thermal diffusivity measurement of ferrofluids. The samples were encapsulated in cuvettes of 0.5 cm thick on the side and 1.0 cm large. The authors applied a linear relation when plotting a phase collinear deflection as a function of the separation between the excitation and probe beams at a fixed frequency.255 The collinear configuration was used for detecting the Soret (thermodiffusion) effect in ferrofluid samples with two different surfactants. Thermodiffusion effects depend on the charge of the coating that covers the magnetic grains; however, refractive-index gradients for both ferrofluids presented the same trend for the same variation of particle concentration.256 

In the photothermal displacement technique, an intensity-modulated excitation laser beam impinges onto the sample along the normal direction like in other optical beam deflection techniques, whereas the probe laser is incident to the surface at an oblique angle. However, for liquids, the setup is more like in mirage-effect measurements. The cell is fixed on a three-dimension position mechanism stage. The temperature field is produced by heating a thin metal wire immersed in the fluid and oriented vertically and perpendicularly to the probe beam. It causes the probe beam to deflect from its original position (the distance between the probe laser beam and the wire is ∼300 μm, and it is measured with a high-precision gauge); the beam deflection is measured by a position-sensitive detector (Fig. 10).257 The detector and heater are separated from each other providing potentially more accurate data. Thermal conductivity and thermal diffusivity are obtained by fitting the experimental data to the numerical simulation data.

FIG. 10.

Optical path of a probe laser beam in a hot wire–laser beam displacement technique. Reproduced with permission from Ali et al., Rev. Sci. Instrum. 81, 074901 (2010). Copyright 2010 AIP Publishing LLC.

FIG. 10.

Optical path of a probe laser beam in a hot wire–laser beam displacement technique. Reproduced with permission from Ali et al., Rev. Sci. Instrum. 81, 074901 (2010). Copyright 2010 AIP Publishing LLC.

Close modal

This hot wire–laser beam displacement technique was applied for five homogeneous liquids: thermal conductivity, thermal diffusivity, and the temperature dependence of the liquid refractive index were measured.258 The same technique was used for measuring the thermophysical properties of Al NPs suspended in water, ethylene glycol, and ethanol.257 Thin-film metal lines/heaters and beam deflection applied for measurements of the thermal diffusivity of fluid mixtures (ethanol–water) and suspensions of nanoparticles (fullerenes C60 and C70 in toluene and Au NPs in toluene and ethanol) provided a precision of better than 1%.148 Thus, such a configuration can be considered a prototype for the nanofluid test measurements.

Techniques referred to as thermal-lens (photothermal-lens) spectrometry (TLS) are based on the formation of a lenslike element (refractive-index field) upon the absorption of excitation radiation. TLS belongs to slow photothermal techniques: the attainment of a stationary photothermal state or on mid- to long-scale (milliseconds to seconds) transient measurements. The signal is calculated as a relative change in the probe-beam intensity I p at a far-field detector plane at the moment t,30,
(5)
Here, P e is the excitation laser power, α is the linear light-absorption coefficient of the sample, d n / d T is the temperature gradient of the refractive index (thermo-optical constant), k is thermal conductivity, λ p is the probe laser wavelength, and B ( t ) is the spectrometer constant determined by the geometry of the optical scheme (the ratio of the waists of the laser beams and confocal distances). The geometrical parameters can be either strictly stable or controlled with the use of standard software tools; in any case, they are known. In optical and spectrochemical studies, TLS is used for measuring light absorption30 or assessing low concentrations,259,260 especially in small volumes (thermal-lens microscopy).261–265 Among all the photothermal methods, thermal-lens spectroscopy and microscopy have the largest pool of chemical applications, and in biomedical studies, it is second only to state-of-the-art photoacoustic tomography techniques.
In thermophysical studies, such slow photothermal techniques are used for (i) estimating macroscale thermal parameters of various liquids266,267 from steady-state signals and (ii) assessing heat-transfer parameters between the phases of a disperse system from transient signals. The thermal diffusivity is assessed from the characteristic time t c (usually, a micro- to millisecond scale) of the thermal-lens development, which is calculated from the time-resolved (transient) curve of thermal-lens measurements, Eq. (5), and the radius of the excitation beam ω e,
(6)

The absorption of the sample α is measured with high accuracy simultaneously with the time-resolved curve but represents a separate information channel. For the calculation, the radius of the probe laser in the sample should be known, the measurement of which introduces inaccuracy. Usually, thermal-lens characteristic time is defined as a target parameter when the experimental data are approximated by the theoretical equation of the time-resolved signal for a homogeneous solution. Therefore, a reference sample is sometimes used, water57,244,268–271 or toluene.272 For them, the characteristic time is determined, and to determine the thermal diffusivity of the sample, the ratio of the characteristic times and the known coefficient of thermal diffusivity are used. Occasionally, the thermal conductivity coefficient is obtained from a stationary thermal-lens signal; however, in this case, it is necessary to know the thermooptical constant d n / d T with respect to temperature for each sample.273 As mentioned above, TLS is combined with pyroelectric detection; therefore, the thermal diffusivity and thermal effusivity are determined from both methods, and then the coefficient of thermal conductivity is calculated from these parameters.212,226–228

Due to simplicity and rather easy interpretation, thermal-lens spectrometry is often used to determine the thermal diffusivity of colloidal solutions, especially two-phase systems containing nanoparticles of metals and their oxides (Table I).42,57,209,212,226,227,244,268–272,274–287 Not all the cases gathered in Table I are established NFs, but this collection shows the possibilities and problems of thermal lensing of disperse systems. In addition to the fact that for similar systems, the increments of thermal conductivity differ considerably, and the regularities of thermal properties on concentration and size differ. Unfortunately, this is typical for measurements of all the dispersed systems regardless of whether thermal or optical methods are used and may be associated with different physicochemical properties of two-phase liquids.

TABLE I.

Thermal diffusivity DT of nanofluids and related systems by thermal lensing.

Nanoparticle Base fluid Concentration, М Results Reference
Au + Rhodamine 6G  Water  5.5 × 10 −2  DT increases with the addition of NPs  274   
Ag + Rhodamine 6G  Water  1 × 10−3  The average DT is lower than that of water  275   
Ag/Au + neutral red  Ethanol  6.8 and 3.7 × 10−5  DT decreases with the addition of NPs  276   
Au  Water  6.6 × 10−4  DT increases when the particle sizes increase  277   
Au  Cellular culture medium  6.6 × 10−4  DT increases with the addition of NPs  278   
Au  Water, ethylene glycol, ethanol  6.6 × 10−4  DT enhanced by 9%, 1%, 8%  42 and 226  
Au  Biodiesel  1.0 × 10−2  DT increases with the addition of NPs  212   
Au  Water  1.0 × 10−4  DT decreases with the addition of NPs  268   
Au  Ethylene glycol : water, 50 : 50  1.5 × 10−9  DT increases with the addition of NPs  269   
Au  Polyvinyl alcohol–water  2.9 × 10−4  DT increases with the addition of NPs  279   
Au  Water  2.31 × 10−9  DT increases with the addition of NPs, depends on the shape  271   
Au, Ag  Water  2 × 10−4, 5 × 10−4  DT enhanced by 16%, 20%,  280   
Ag  Water  2.6 × 10−9  DT decreases with the addition of NPs  281   
Ag (rod-shaped)  Water  1.4 × 10−6  DT depends on the aspect ratio  270   
Ag (25–38.5 nm)  Polyvinylpyrrolidone–water  3.4 × 10−3  DT increases when the particle sizes increase  282   
Ag  Ethylene glycol–water  1.6 × 10−4  DT and effusivity (by PA) measured, conductivity calculated (5% and 3% enhancement)  244   
Ethanol–water 
Cu  Polyvinylpyrrolidone–water  5 × 10−2  DT increases with the addition of NPs  272   
TiO2  Water  4.7 × 10−2  DT and effusivity (by PPE) measured, conductivity calculated (12% enhancement)  227   
SiO2 (100–600 nm)  Water  6.2 × 10−3  DT increases when the particle sizes increase  209   
TiO2  4.7 × 10−2  DT increases with the addition of NPs 
TiO2  Water  No information  DT increases with the particle size and the calcination temperature  283   
Fe3O4 (6–63 nm)  Water  1.7 × 10−11  DT increases when the particle sizes increase  284   
Na2C2  Water  2.9 × 10−3  DT enhanced by 87%  285   
CdTe quantum dots  Water  2.1 × 10−4  DT is less than that of water and decreases when the particle sizes increase  57   
A mixture of carbon allotropes  Acetone  0.2 mg/ml  DT enhanced by 95% with soot annealed at 300 °C  286   
Silicone  Ethanol  4.5 mg/ml  DT is less than that of ethanol and decreases with the addition of NPs  287   
Nanoparticle Base fluid Concentration, М Results Reference
Au + Rhodamine 6G  Water  5.5 × 10 −2  DT increases with the addition of NPs  274   
Ag + Rhodamine 6G  Water  1 × 10−3  The average DT is lower than that of water  275   
Ag/Au + neutral red  Ethanol  6.8 and 3.7 × 10−5  DT decreases with the addition of NPs  276   
Au  Water  6.6 × 10−4  DT increases when the particle sizes increase  277   
Au  Cellular culture medium  6.6 × 10−4  DT increases with the addition of NPs  278   
Au  Water, ethylene glycol, ethanol  6.6 × 10−4  DT enhanced by 9%, 1%, 8%  42 and 226  
Au  Biodiesel  1.0 × 10−2  DT increases with the addition of NPs  212   
Au  Water  1.0 × 10−4  DT decreases with the addition of NPs  268   
Au  Ethylene glycol : water, 50 : 50  1.5 × 10−9  DT increases with the addition of NPs  269   
Au  Polyvinyl alcohol–water  2.9 × 10−4  DT increases with the addition of NPs  279   
Au  Water  2.31 × 10−9  DT increases with the addition of NPs, depends on the shape  271   
Au, Ag  Water  2 × 10−4, 5 × 10−4  DT enhanced by 16%, 20%,  280   
Ag  Water  2.6 × 10−9  DT decreases with the addition of NPs  281   
Ag (rod-shaped)  Water  1.4 × 10−6  DT depends on the aspect ratio  270   
Ag (25–38.5 nm)  Polyvinylpyrrolidone–water  3.4 × 10−3  DT increases when the particle sizes increase  282   
Ag  Ethylene glycol–water  1.6 × 10−4  DT and effusivity (by PA) measured, conductivity calculated (5% and 3% enhancement)  244   
Ethanol–water 
Cu  Polyvinylpyrrolidone–water  5 × 10−2  DT increases with the addition of NPs  272   
TiO2  Water  4.7 × 10−2  DT and effusivity (by PPE) measured, conductivity calculated (12% enhancement)  227   
SiO2 (100–600 nm)  Water  6.2 × 10−3  DT increases when the particle sizes increase  209   
TiO2  4.7 × 10−2  DT increases with the addition of NPs 
TiO2  Water  No information  DT increases with the particle size and the calcination temperature  283   
Fe3O4 (6–63 nm)  Water  1.7 × 10−11  DT increases when the particle sizes increase  284   
Na2C2  Water  2.9 × 10−3  DT enhanced by 87%  285   
CdTe quantum dots  Water  2.1 × 10−4  DT is less than that of water and decreases when the particle sizes increase  57   
A mixture of carbon allotropes  Acetone  0.2 mg/ml  DT enhanced by 95% with soot annealed at 300 °C  286   
Silicone  Ethanol  4.5 mg/ml  DT is less than that of ethanol and decreases with the addition of NPs  287   

Nevertheless, inconsistencies in thermal-lens assessment of NFs may result from incorrect data processing; two-phase systems require either a correction in standard homogeneous models of the thermal-lens signal or brand-new approaches. If for homogeneous systems, transient curves are largely symmetric, for disperse systems, the local heating at the initial time is located around absorbing particles followed by the heat transfer to the bulk, which leads to much more rapid heating and reduction of the characteristic time of the thermal lens. On the contrary, dissipation of the thermal lens changes less significantly because for small heating (10–2 K, which is characteristic for solutions used in thermal-lens spectrometry), it is possible not to consider the dispersion medium.

As an example, studies of fullerene C60 solutions in toluene (no aggregate formation, molecular solutions), n-methylpyrrolidone (NMP, C60 aggregates), and water (aggregates are formed and are stabilized by charge-transfer complexes) show that the aggregation and stabilization processes change thermooptical parameters (Fig. 11).

FIG. 11.

Transient thermal-lens curves (a) fullerene C60, blue line and a molecular dye (Sudan) in toluene, red line; (b) for fullerene C60, blue line and a molecular dye (ferroin) in n-methylpyrrolidone, red line; (c) for fullerene C60, blue line and a molecular dye (ferroin) in water, red line; and (d) for ND (1.0 mg/ml, NanoAmando), blue line and a molecular dye (ferroin) in water, red line; 532 nm, 150 mW. I r e l ( t ) = ( I p ( 0 ) I p ( t ) ) / ( I p ( 0 ) I p ( ) ).

FIG. 11.

Transient thermal-lens curves (a) fullerene C60, blue line and a molecular dye (Sudan) in toluene, red line; (b) for fullerene C60, blue line and a molecular dye (ferroin) in n-methylpyrrolidone, red line; (c) for fullerene C60, blue line and a molecular dye (ferroin) in water, red line; and (d) for ND (1.0 mg/ml, NanoAmando), blue line and a molecular dye (ferroin) in water, red line; 532 nm, 150 mW. I r e l ( t ) = ( I p ( 0 ) I p ( t ) ) / ( I p ( 0 ) I p ( ) ).

Close modal

In toluene [Fig. 11(a)], the transient curves, Eq. (5) (normalized values of Irel, the inital probe-beam intensity is set to 1, the equilibrium, to 0) for fullerene C60 and a dye of approximately the same molecule size (1 nm), are nearly identical. This correlates well with the theory of thermal lensing, and the estimation of the characteristic time [Eq. (6)] shows that the values for fullerene and the dye differ insignificantly from one another and from the value calculated using the reference data for toluene.197 However, in NMP [Fig. 11(b)], the situation changes drastically: the curve for fullerene C60 shows a slower heat transfer (a less steeper transient curve) and differs from the characteristic curve of a molecular dye. This is accounted for by the formation of a coarse dispersion of fullerene in NMP, which significantly decreases the rate of heat propagation. This is confirmed by the same effect of the second part of the curve (dissipation after a mechanical chopper switches off the excitation beam). In water [Fig. 11(c)], the result is contrary to the case of NMP: the curve for a fullerene solution shows a characteristic time lower than a molecular solution of a dye (ferroin) and a quicker decrease in the probe laser intensity due to thermal-lens effect. This can be attributed to the formation of a finely dispersed solution with a cluster size of 50–150 nm,288 which exhibits short overheating near the clusters followed by a longer period of thermal equilibration of the whole solution.289 The same behavior, though with larger changes, is characteristic to nanodiamond aqueous dispersions [Fig. 11(d)]. It is interesting that the behavior of the dissipation part of the curve for fullerene is nearly the same as for a molecular dye, which is contrary to the behavior of the ND dispersions. Overall, this cannot be predicted using the generic theory for homogeneous thermal lensing, and the new approach should be based upon, e.g., single-point approaches.41,290 This area has not been fully studied; however, it is crucial for thermophysical characterization of nanofluids as the majority of information is not used in full or may be inaccurate.

The advantage of TLS in NF assessment is the simplicity of equipment relative to other photothermal methods (for liquids, only a cuvette is needed). There are no restrictions on the range of determination of the thermal diffusivity; due to high accuracy and precision (1% and 5%), it is possible to determine small differences (of the order of 2%–3%)288 in the thermal diffusivity, which is especially important in the analysis of nanofluids. There is a possibility of measurements at different temperatures and the time range (milliseconds) makes it possible to simultaneously record the uneven heating of the dispersion medium and the dispersed phase. The method is non-contact, and the effect of convection is minimal due to low heating per cycle (10–2 K).30 

The disadvantage of TLS for NFs is that any thermal-lens spectrometer is characterized by a certain concentration region in which the signal linearity is observed; therefore, to work with highly concentrated (highly scattering) solutions, it is necessary either to reduce the length of the optical path (it is impossible to infinitely decrease the thickness of the cell) or to decrease the power of the exciting laser. The processing of the time-resolved curves is time-consuming and, in the case of heterogeneous media, requires significant improvements in the theory. Also, while absorbance measurements by thermal lensing are calibration based and linear, thermophysical characterization, even for one-point calibration using a reference solvent, requires several conditions (cell length, cell wall length, measurement time, excitation beam radius) to be selected carefully as incorrect parameters may lead to deviations from the one-dimensional heat-transfer model;291–300 thus, the use of this model for estimation of thermophysical parameters may lead to rather serious errors.

These techniques belong to the group of fast (micro-, nanosecond, or shorter timescales) photothermal methods: transient-grating (TG) methods,301–303, optical heterodyne detection, or impulsive stimulated scattering (ISS)157,304,305 and related techniques.306 These fast transient modalities of PTS are used for investigating dynamics of charge transfer,307,308 thermoelastic properties,304 or ultrafast heat transfer inside nanoparticles.309–311 

Thermoreflectance techniques (time-domain, TDTR and frequency-domain, FDTR) have been typically used to measure the thermal conductivity of both bulk and thin films along with interfacial thermal conductance.213 The excitation laser focused on the sample generates a periodic temperature change through the sample, which is detected by changes in probe-beam reflectivity. The sample must be covered by a thin metallic layer highly reflecting at the wavelength of the probe laser. The obtained phase signals are fitted with the heat-transfer model to extract thermophysical properties of solid samples.312 TDTR measures the thermoreflectance response as a function of the time delay between the arrival of the probe and the excitation pulses at the sample surface. In FDTR, the thermoreflectance change is a function of the excitation modulation frequency.312 

Only a few studies have been made for liquids and they are based on the transient-grating technique.313,314 This time-domain method relies on the thermal decay of a periodic variation in the refractive index generated by the interference of two picosecond light pulses. Optical absorption also causes thermal expansion, which launches acoustic waves (within a few hundred nanoseconds) into the sample; thus, the sound velocity can be measured. From the signal decay (Fig. 12) at longer times (tens or hundreds of microseconds), thermal diffusivity is determined.315 

FIG. 12.

Typical signal from a TG measurement. The acoustic response (inset) is finished within 400 ns. The slower exponential response can be fit to extract the thermal diffusivity of the sample. Reproduced with permission from Schmidt et al., J. Appl. Phys. 103, 083529 (2008). Copyright 2008 AIP Publishing LLC.

FIG. 12.

Typical signal from a TG measurement. The acoustic response (inset) is finished within 400 ns. The slower exponential response can be fit to extract the thermal diffusivity of the sample. Reproduced with permission from Schmidt et al., J. Appl. Phys. 103, 083529 (2008). Copyright 2008 AIP Publishing LLC.

Close modal

An impulsive stimulated scattering technique in a heterodyne diffraction detection configuration was used to study the dependence of the speed of sound and the thermal diffusivity on the concentration of silver nanoparticles in water with a precision better than 1%.157 Al2O3 particles suspended in decane and isoparaffinic poly(alpha-olefin) were assessed by TG for thermal diffusivity determination, and thermal conductivity was calculated using theoretical effective volume heat capacity.315 The results on thermal conductivity were compared with data obtained by THW (Sec. III A) , and good agreement between these two dissimilar techniques was observed.

An interesting, though not fully implemented idea is the use of fast techniques such as ISS or TG with thermal-lens measurements for NF characterization. This would provide a simultaneous use of the fast technique for the assessment of thermophysical parameters of the base fluid and building the whole timescale for heat transfer using ISS by acoustic and photothermal responses in the nanosecond–microsecond range (Fig. 12) followed by thermal lensing in the microsecond–second range.

Forced Rayleigh scattering is an approach that shares similarity to the TG technique but takes place on a slower (millisecond) timescale; the amplitude of the temperature modulation is small as well (≤10 mK). The technique was applied for thermal diffusivity measurements in a citrate-stabilized Au NP suspension in water and an Al2O3 NP suspension in a petroleum oil at a temperature range of 25–75 °C. The sample (should be transparent) was contained between optical windows separated by a Teflon spacer having a nominal thickness of 1 mm. The samples were mounted in an aluminum block through which oil from a temperature-controlled bath was circulated maintaining the sample within ±0.1 K of the desired temperature. In contrast to experimental results obtained using THW, forced Rayleigh scattering shows that a small (2%) thermal conductivity enhancement is independent of temperature and is consistent with effective medium theory predictions.316 

Thus, the interest in nanofluids as advanced heat-conducting and heat-accumulating materials is growing constantly. The effect of nanofluids in the advanced heat-transfer applications is significant, and particles of different nature are considered dispersed phases for nanofluids tailored for industrial, fast-transfer, or biomedical applications. The impact of carbon and hybrid NFs combining the advantages of nanoparticles of various types of nanoparticles and CNFs is increasing due to several advantages over NFs of metals and metal oxides.

The well-developed technology of nanofluids is reflected in several established production technologies of the fabrication and characterization of common and tailored nanoparticles and nanofluids. This is reflected in the appearance of the innovative market and several R&D and production companies such as PLiN Nanotechnology (Greece), Synano (the Netherlands), JJ Bioenergy Ltd. (UK), TCT Nanotech (Italy), Advanced Thermal Solutions, Inc. (USA), Meliorum Technologies, Inc. (USA), and others. Notable is the “Nanouptake” action initiative (the European Cooperation in Science and Technology, http://www.nanouptake.eu/is-it-possible-to-overcome-all-the-barriers-to-nanofluids-market-uptake/), a Europe-wide network of research, development, and industrial institutions, which get together to develop and foster the use of nanofluids to increase the efficiency of heat-exchange and thermal-storage systems.

However, all this progress and relevance of nanofluids makes the problems in NF research and production that remained unsolved or not fully unsolved rather topical. These challenges may be summarized as follows.

  • In many studies, empirical approaches to the estimation of the working parameters of NFs prevail, with primary attention being paid to the “front row” of characteristics, i.e., thermophysical parameters. The chemical and physicochemical properties of nanofluids have been studied to a much lesser extent. However, the knowledge of such properties (exact chemical composition, size, shape, surface properties and limiting concentrations of nanoparticles, temperature dependences of physicochemical parameters, etc.), along with the information on thermophysical properties, will make it possible to purposefully design and create new nanofluid systems and increase their efficiency. The development of approaches to the production of new types of nanofluids with tailored properties is rather topical.

  • Noteworthy is that the proposed models of NF action do not give a whole description of the thermal properties of nanofluids and, in most cases, are adapted for the description of systems containing metal rather than carbon nanoparticles.122,123 Also, to date, there is no working model for the change in specific heat during the production of nanofluids. Thermal effusivity, though playing an important part in the NF action, is not considered in full.

  • The necessity for new technologies of nanofluids with better cost efficiency and reliable upscaling is still required. With increasing volumes of produced nanofluids and their limited lifetime, the questions of costs become more and more serious and are a concern of many industrial and production R&D initiatives.

  • Increasing amounts of nanofluids in an increasing number of cooling circuits of various scale inevitably raise the problem of NF wastes or restoration. This requires studies on the environmental impacts of nanofluids, which include but are not limited to biocompatibility, biodegradability, the impact on soils and marine environments, and long-term effects on nanoparticle accumulation. Certainly, the progress in issues of engineering nanoparticles and their biohazards is studied for a long time,317–319 but nanofluids as a specific type of nanoscale systems requires certain work especially for hybrid and core-and-shell particles.12,16,320,321

  • Of all the dispersed systems based on carbon nanoparticles, the most studied are systems with carbon nanotubes due to their extremely high values of thermal conductivity; however, other CNFs, especially hydrophilic ones based on nanodiamonds, graphene, and graphene oxide, are probably more versatile and promising; however, the values of thermal conductivity of CNFs and carbon hybrid NFs are contradictory and must be estimated with a standardized technology and high accuracy. Also, the stability of CNFs is an important and not fully resolved problem.

As a whole, nanofluids require both precise measurement and constant monitoring techniques, and the development of methods for their comprehensive characterization becomes crucial. The accuracy and precision of the existing data suffer from the errors in calculation, changes in the sample by the measurement system,11,119 and convective effects. Thus, measurement techniques for thermal conductivity of NFs are continuously developed or improved. Among those, non-contact heating methods are of importance as they bypass a frequent source of errors characteristic to contact-based thermal measurements and thermal-contact resistances, which can be dominating in nanoscale materials. A standardized methodology for nanofluid measurement is on demand.

The progress in the development of photothermal and photoacoustic methods and the results obtained for the last 10–15 years show that they are fairly promising for such non-contact thermal measurements when heating is generated by incident UV/vis/IR radiation.213 Apart from high sensitivity, accuracy, reproducibility, small required quantities or volumes of the test sample, and relative simplicity of the detection cells and laboratory instrumentation are other advantages of photothermal techniques, as compared to classical thermophysical methods.35 In addition, being both thermal and optical techniques, photothermal methods provide an extended pool of information with a small influence from a scattering matrix. As the density and thermal expansion coefficients of nanofluids are determined by the base fluid, it is possible to find especially important features of the test object connected with the heterogeneity effect of NFs. The latter is particularly important as the majority of classical thermophysical methods can provide average characteristics of the sample only,37,288 thus forcing empirical approaches in designing nanofluids mentioned above.

The advantages of photothermal spectroscopy are not limited to the information on the base fluid and the possibility to assess the disperse phase more accurately. In many cases, including NFs and their biomedical applications, the actual spatial heterogeneity and the mechanism of heat transfer are quite important. Here, various microspectroscopic photothermal modalities can be of serious value. They provide images of tissues,31,322 cells,197,323 and single and assembled nanoparticles206,324 with a high resolution challenging the diffraction limit due to joint use of optical as well as thermal imaging governed by the characteristic rates of nonradiative heat transfer.33,207,325 This provides both thermal and optical sample nondestructive quantitative mapping with a nanoscale locality.30,34,175,177,326 Recent results show that photothermal microspectroscopy is capable of non-destructive characterization of carbon nanomaterials and nanoparticle dispersions.209,228,327–333

Photothermal imaging and microscopy techniques are closely related with another state-of-the-art trend in photothermics, the development of single particle photothermal modalities. These methods include photothermal difference interference contrast,334,335 photothermal heterodyne microspectroscopy,311,336,337 and photothermal correlation microspectroscopy32,338,339 and are capable of measuring single submicrometer particles. Nowadays, these techniques mainly target biomedical research but may be even more relevant for nanoparticle systems with multiple phase composition (like hybrid NFs) or complex structural properties (like microencapsulated phase-change materials).340 

In these microspectroscopic modalities, the photothermal effect upon the absorption of an excitation beam by a single nano-object (a heated large molecule or a nanoparticle) causes the scattering of a probe beam, which can be detected as a fluctuation of its power due to the interference of the initial beam and scattered radiation around.341 Photothermal heterodyne microspectroscopy was introduced as imaging310,311,342,343 and spectroscopy344,345 of nano-size particles. Photothermal correlation microspectroscopy, an advanced technique based on photothermal heterodyne spectroscopy,32,338,339 is based on building an autocorrelation function G ( τ ) for time-resolved photothermal signal S ( t ),
which provides characteristic times τ of the heat-releasing processes of the underlying photothermal phenomena. As the photothermal processes for nanoparticle solutions depend on the thermal and optical properties of nanoparticles and their motion velocity, this provides detecting, monitoring, and characterizing such objects. In the simplest concept related to thermal lensing (Sec. IV E) and correlation spectroscopy,324,346,347 a single absorber particle acts like an analog of a “macro” thermal lens, a nanolens, which can be detected using a scattering pattern of the probe radiation from a “halo” of the thermally induced field around the heated particle. The combination of the nanolens concept and a differential mode-mismatched excitation-probe schematics30,291,348,349 is a very promising microscopic technique called twin-focus photothermal correlation spectroscopy.350 This technique detects two spatially separated volumes of the sample and reference building two autocorrelation functions for each of the volumes separately. It provides a tool for precise measurements of a slow motion along the beam axis or very slight changes in heterogeneities at nanometer scales in the sample. Such measurements beyond the diffraction limit can be used for probing nanoparticles tailored to NFs from the viewpoint of the mechanism of heat transfer.

Finally, as we showed in Sec. IV, nondestructive and fast character of many photothermal techniques such as photoacoustic modalities and thermal lensing along with relative simplicity of instrumentation make them very robust monitoring techniques. This is currently used in biomedical studies, both in vitro and ex vivo (flow cytometry)192,351–353 and in vivo.246,354,355 Such modalities can be very valuable for monitoring the workability of nanofluids in industrial scale (such as nuclear and solar energy), while the development of compact photothermal instruments356,357 may be of value for small-scale and widespread NF applications in computers, appliances, etc.

Certainly, photothermal spectroscopy is not free from some drawbacks and limitations. First, as major photothermal methods (thermal lensing, optical beam deflection, photothermal radiometry) are based on thermal diffusivity, to assess the thermal conductivity coefficient of NFs, other methods for the density and specific heat are required. These are no single measurements, as these values are required for each concentration in the desired range at all the working temperature range of a NF or rely on some detailed preliminary data or precise regularities. This certainly degrades or at least questions both accuracy and precision of the final values of thermal conductivity by photothermics. Certainly, this is a disadvantage of all the methods for NFs based on thermal diffusivity and may be a reason behind differing data for the same nanofluids in the literature. Thus, it seems expedient to use several complementary photothermal techniques based on thermal conductivity and thermal diffusivity229,230 or thermal effusivity and thermal diffusivity. In principle, this can be implemented in a single setup; therefore, it would provide all the key parameters of a nanofluid (as we discussed above, in two-modality PTS measurements, thermal conductivity can be assessed or calculated from photothermal experiments only, without external data).

As we have shown in the main body of this paper, the application of the methods of photothermal spectroscopy to determine the thermal properties of liquids and, moreover, dispersed systems have many merits. Still, a reader may say that they are rather scarce still, and they demonstrate the possibilities for a rather limited set of nanofluids. In our opinion, this is caused by two main reasons: (a) lack of methodology and (b) lack of standardized photothermal instruments.

The analysis of the data shows that building a methodology for nanofluids requires solving the following issues.

  • In many photothermal modalities, the theory is based on either homogeneous media or a single nanoscale object.30 Thus, it necessitates either to develop a theory of the generation of the photothermal signal in complex objects or correct the existing theories. This is especially important for ensemble-based slow techniques such as thermal lensing and optical beam deflection.

  • The issues related to the experiment planning also require considering new factors both connected with nanofluids and the possible operation modes. Therefore, the setups should be based on flow techniques and should provide both transient and steady-state measurements. Thermal-lens spectrometry would require a minimum change; for other photothermal techniques and modalities, some work is in order.

Instrumentation issues are more general as such a situation is characteristic for any types of photothermal applications. In our opinion, it requires the following:
  • The first important issue is the unification of photothermal apparatuses. Despite several companies in the market and industrial applications and many excellent prototypes,357–362 many photothermal apparatuses are home-built for certain research applications. This results in difficulty in comparing apparatuses, even those based on the same principle. This in turn results in the lack of standard samples and no detailed uncertainty data in photothermics.

  • As the measurements of dispersed systems require a special set of time, concentration, and excitation powers, the specialized setups built for specific types of nanofluids are probably required. The techniques such as photoacoustic modalities, optical beam deflection, and PTR require special cells or compartments for liquid media.

  • A broader comment is appropriate here. The serious progress in photothermal methods in many branches of industry and research already demands a special initiative—alike “Nanouptake” action for nanofluids—to photothermal market-uptake due to large possibilities for photothermal instrumentation.

Despite rather difficult and serious tasks of methodology and instrumentation, they are resolvable, and they are required for nanofluid research in photothermal spectroscopy. Witnessing the boom in multi-spectral optoacoustic tomography (MSOT),193,194,200,203,355,363–373 the area neighboring to photothermal techniques, we believe that it will be made in the nearest future.

Moreover, our experience in photothermal spectroscopy allow us to state that the complex character of photothermal techniques makes them a valuable tool, and disadvantages could be turned to advantages. The examples below can possibly serve as other featured applications of photothermal spectroscopy in nanofluids and related research:

  • Detection of the Soret effect, which is usually a negative factor in NFs and may be the cause of their deterioration, can be assessed using photothermal techniques in the same run of the experiment.

  • As nanofluid thermophysical properties are used in other applications such as thermally resistant lubricants and fuels (a nanoparticle-filled biodiesel mentioned above212), photothermal methods may be used for testing the two-phase thermally conductive liquids with the same type and concentration of the disperse phase but with a varying composition of the base fluid.

  • As photothermal spectroscopy may provide the spectra of thermal properties,186,356,374–376 this could be especially valuable for photothermally induced NFs, e.g., in solar energetics.

All these features of photothermics may be combined in developing areas of nanofluid research. In our opinion, new types of nanofluids will be a subject of research. They are NFs based on natural nanoparticles such as clay minerals377 and core–shell nanoparticles. Also, double-action heat-accumulating nanofluids such as microencapsulated phase-change materials should be mentioned,340 which are introduced into building materials but may be extended to many heat-transfer applications.

Other promising NF-related materials for photothermal methods are thermal slurries and thermally conductive pastes that are used in various industries such as computers and energy storage. Microencapsulated phase-change material slurries improve the value of critical heat flux by as much as 100%–200% as a result of nanoparticle deposition on the surface of the component.378 Also, nanolayers formed at nanoparticle–liquid interfaces,122,379 nanoparticle clustering, and some other mechanisms of heat transfer that improve the workability of NFs in addition to the primary increase in thermal conductivity are interesting concepts that await instrumental control and evaluation. A combination of thermal-lens and mirage modalities can be a concept of controlling both the solution and the surface.

Anyway, the complex problem of nanofluid design, development, and application will undoubtedly advance and progress in the nearest future, and it will find many new ideas and concepts. By the phenomena beneath, abilities, and the current status as well as the theory and instrumentation, photothermal spectroscopy undoubtedly provides very promising tools for nanofluids.

L.O.U., M.V.K., and M.A.P. contributed equally to this work.

This work was supported by the Russian Foundation for Basic Research (Grant Nos. 18-33-00586mol_a and 19-08-00498 a).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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