Ionic-Liquid-Based Nanofluids and Their Heat-Transfer Applications: A Comprehensive Review

Due to the improved thermophysical characteristics of ionic liquids (ILs), such as their strong ionic conductivity, negligible vapor pressure, and thermal stability at high temperatures, they are being looked at viable contender for future heat transfer fluids. Additionally, the dispersing nanoparticles can further improve the thermophysical characteristics and thermal performance of ionic liquids, which is one of the emerging research interests to increase the heat transfer rates of the thermal devices. The latest investigations about the utilization of ionic liquid nanofluids as a heat transfer fluid is summarized in this work. These summaries are broken down into three types: (a) the thermophysical parameters including thermal conductivity, viscosity, density, and specific heat of ionic liquids (base fluids), (b) the thermophysical properties like thermal conductivity, viscosity, density, and viscosity of ionic liquids based nanofluids (IL nanofluids), and (iii) utilization of IL nanofluids as a heat transfer fluid in the thermal devices. The techniques for measuring the thermophysical characteristics and the synthesis of IL nanofluids are also covered. The suggestions for potential future research directions for IL nanofluids are summarized.     

Calculation of isentropic compressibility and sound velocity in two-phase fluids

Derivative properties from equations of state (EoS) are well defined for homogeneous fluid systems. However, some of these properties, such as isothermal and isentropic (or adiabatic) compressibilities and sound velocity need to be calculated at conditions for which a homogeneous fluid splits into two (or more) phases, liquid or vapor. The isentropic compressibility and sound velocity of thermodynamically equilibrated fluids exhibit important discontinuities at phase boundaries, as noticed long ago by Landau and Lifschitz in the case of pure fluids. In this work, the two-phase isentropic compressibility (or inverse bulk modulus) is expressed in terms of the two-phase isothermal compressibility, two-phase thermal expansivity and an apparent heat capacity, defined as the partial derivative of total enthalpy with respect to temperature at constant pressure and composition. The proposed method is simple (simpler than previous approaches), easy to implement and versatile; it is not EoS-dependent and it requires only a flash routine and the expression of total enthalpy at given pressure, temperature and composition. Our approach is applied to a variety of fluid systems representative of reservoir applications and geophysical situations, including petroleum fluids (oil and gas condensate) and mixtures of water and gas (methane or CO₂). For low gas content in the two-phase fluid, i.e., near bubble point conditions, we obtain significantly lower bulk moduli and sound velocities than predicted within Wood's conventional approach, in which the liquid and gas phases are considered to be “frozen” at the passage of the acoustic wave.     

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.     

The partial solubility parameters: An equation-of-state approach

The division of the well-known solubility parameter into its dispersion, polar, and hydrogen-bonding components has significantly upgraded its capacity and usefulness in the screening and selection of the appropriate solvents in Industry and in Laboratory. This work presents a new statistical thermodynamic approach for the estimation of these partial components over a broad range of temperature and pressure. Key to this approach is the development of explicit expressions for the contribution of dispersion, dipolar, and hydrogen-bonding interactions to the potential energy of the fluid. The approach is applicable to ordinary solvents, to supercritical fluids, as well as to high polymers. Information on various thermodynamic properties of fluids is used in order to estimate the three solubility parameter components. Extensive tables with the key parameters are presented. On the other hand, available information on these separate components is exploited in order to extract information for the thermodynamic behaviour of the fluids over an extended range of external conditions.     

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems.     

Modified PT-LJ-SAFT Density Functional Theory: I. Prediction of surface properties and phase equilibria of non-associating fluids

A new modified version of a Perturbation Density Functional Theory (PT-DFT) based on the Statistical Association Fluid Theory (SAFT) with a Lennard–Jones interaction potential is proposed to model the vapor–liquid phase equilibrium and to predict the interfacial behavior of non-associating hydrocarbon fluids. In the interaction model for the Helmholtz free energy functional the molecules are separated into m spherical segments interacting via a Lennard–Jones potential. The segments form chains of tangent spheres. In the perturbation approximation to Density Functional Theory the interaction potential is split according to WCA and the attractive term to the free energy functional consists of a suitable modification of the perturbation expression. This modification to PT-DFT yields surface tensions for the Lennard–Jones sphere fluid (m = 1.0) which are in perfect agreement with simulation data.The new PT-DFT model combines the high flexibility of the SAFT free energy functional with a modified density functional approach that enables to perform accurate calculations of interfacial properties. To take into account the contributions to surface tension resulting from mesoscale thermal fluctuations a semiempirical model is proposed that allows to correct the microscopic intrinsic surface tension.The model is used to describe the phase equilibrium of lower alkanes and aromatics. The results demonstrate the capability to fit vapor–liquid equilibrium data and to predict very accurately the surface properties of these fluids within the uncertainties of the experimental data.     

Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

Equation of state and liquid-vapor equilibrium of polarizable Stockmayer fluids

In this work we develop the concept of an effective potential to obtain the equation of state of polarizable Stockmayer (PSM) fluids. This potential consists of a Lennard-Jones function with appropriate energy and distance parameters that depend on the reduced dipolar moment μ(?) and polarizability α(?). The approach deals accurately with polarizable SM fluids with μ(?)≤2.0 and α(?)≤0.1. However, prediction of second virial coefficients is reliable up to μ(?)≤4.0. When the low-density sphericalized potential is used at moderate and large densities, the effect of the dipole-dipole attraction is overestimated in agreement with an effect previously found in the literature. This effect can be traced back to a frustration mechanism due to the interaction between three and more dipoles. We propose a model to account for this frustration effect and are able to reproduce the vapor-liquid equilibrium of polarizable SM fluids in agreement with simulated results from the literature. Molecular dynamics simulations were carried out to show that the effective SM fluid has a radial distribution function very close to that of the true SM system.     

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.     

Determination of nanolayer thickness and effective thermal conductivity of nanofluids

Nanofluids having high thermal conductivity enhancement relative to conventional pure fluids are fluids engineered by suspending solid nanoparticles into base fluids. In the present study, calculating the Van der Waals interaction energy between a nanoparticle and an ordered liquid nanolayer around it, the nanolayer thickness was determined, the average velocity of the Brownian motion of nanoparticles in a fluid was estimated, and by taking into account both the aggregation of nanoparticles and the presence of a nanolayer a new thermal conductivity model for nanofluids was proposed. It has been shown that the nanolayer thickness in nanofluids is independent on the radius of nanoparticles when the radius of the nanoparticles is much greater than the nanolayer thickness and determines by the specific interaction of the given liquid and solid nanoparticle through the Hamaker constant, the surface tension and the wetting angle. It was proved that the frequency of heat exchange by fluid molecules is two orders of magnitude higher than the frequency of heat transfer by nanoparticles, so that the contribution due to the Brownian motion of nanoparticles in the thermal conductivity of nanofluids can be neglected. The predictions of the proposed model of thermal conductivity were compared with the experimental data and a good correlation was achieved.     

Calorimetric Studies and Structural Aspects of Ionic Liquids in Designing Sorption Materials for Thermal Energy Storage

The thermal properties of a series of twenty‐four ionic liquids (ILs) have been determined by isothermal titration calorimetry (ITC) with the aim of simulating processes involving water sorption. For eleven water‐free ILs, the molecular structures have been determined by X‐ray crystallography in the solid state, which have been used to derive the molecular volumes of the ionic components of the ILs. Moreover, the structures reveal a high prevalence of hydrogen bonding in these compounds. A relationship between the molecular volumes and the experimentally determined energies of dilution could be established. The highest energies of dilution observed in this series were obtained for the acetate‐based ILs, which underlines their potential as working fluids in sorption‐based thermal energy storage systems.     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

Thermodynamic pressure of simple fluids confined in cylindrical nanopores by isothermal-isobaric Monte Carlo: influence of fluid/substrate interactions

The thermodynamic pressure or grand potential density is calculated by isobaric-isothermal Monte Carlo algorithm for simple Lennard-Jones fluid confined in cylindrical pores presenting chemical heterogeneities along their axis. Heuristic arguments and simulation results show that the thermodynamic pressure of the confined fluid contains two contributions. The first term is the usual pressure of the bulk fluid for a density equal to the confined fluid density defined as the total number of confined particles divided by the accessible volume due to thermal agitation. A second term has to be added, which is empirically shown to be proportional to the fluid/wall interface area and almost constant along the adsorption and desorption branches. This interfacial contribution, calculated for various pore models, has small variations reminiscent of the fluid adsorption/desorption properties calculated in the various pores. In particular, it is shown that this interfacial quantity is maximum for a fluid/substrate interaction intensity of the same order as the fluid/fluid one, while the thermodynamic pressure at which rapid desorption occurs presents a minimum. Stronger or weaker fluid/wall affinity favors gas state nucleation on the desorption of confined fluids.     

Performance analysis and multi-objective optimization of an organic Rankine cycle with binary zeotropic working fluid employing modified artificial bee colony algorithm

From a thermal point of view, zeotropic mixtures are likely to be more efficient than azeotropic fluids in low-temperature power cycles for reduction in exergy destruction occurring during heat absorption/rejection processes due to their suitable boiling characteristics. In this study, comprehensive energetic and exergetic analyses are mathematically performed for an organic Rankine cycle (ORC) system employing a potential binary zeotropic working fluid, namely R717/water. For this purpose, initially mass, energy, and exergy balance equations are derived. With regard to the similarity in molar mass of R717 (17.03 g mol^?1) and water (18.01 g mol^?1), there is no need to alter the size of the ORC components such as turbine and pump. In order to achieve the optimal thermal and exergy efficiencies of the ORC system, modified version a powerful and relatively new optimization algorithm called artificial bee colony (ABC) is used taking into account different effective constraints. The main motivation behind using ABC lies on its robustness, reliability, and convergence rate speed in dealing with complicated constrained multi-objective problems. Convergence rates of the algorithm for optimal calculation of the efficiencies are presented. Subsequently, due to the importance of exergy concept in ORC systems, exergy destructions occurring in the components are computed. Finally, the impacts of pressure, temperature, mass fraction, and mass flow rate on the ORC thermal and exergy efficiencies are discussed.

     

Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.     

Sedimentation equilibrium of colloidal suspensions in a planar pore based on density functional theory and the hard-core attractive Yukawa model

The sedimentation equilibrium of colloidal suspensions modeled by hard-core attractive Yukawa (HCAY) fluids in a planar pore is studied. The density profile of the HCAY fluid in a gravitational field and its distribution between the pore and uniform phases are investigated by a density functional theory (DFT) approach, which results from employing a recently proposed parameter-free version of the Lagrangian theorem-based density functional approximation (Zhou, S. Phys. Lett. A 2003, 319, 279) for hard-sphere fluids to the hard-core part of the HCAY fluid, and the second-order functional perturbation expansion approximation to the tail part as was done in a recent partitioned density functional approximation (Zhou, S. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 061201). The resultant DFT approach is, thus, the first adjustable parameter-free DFT for HCAY fluids. The validity of the present DFT for HCAY fluids of reduced range parameter z(red) = 1.8 under various external potentials is established in the first of the papers cited previously. The present DFT for HCAY fluids can predict the radial distribution function for the bulk HCAY fluid accurately in the colloidal limit (large value of z(red)), and in the hard-sphere limit, its prediction for the density profile of the hard-sphere fluid in a gravitational field is in very good agreement with the existing simulation data. The dependence of the density profile and distribution coefficient on the magnitude of the interparticle attraction, gravitational field, and degree of confinement is investigated in detail by the present DFT approach. Intuitive and qualitative analyses are also compared with the quantitative DFT calculational results.     

The 1/N expansion and nonrelativistic potential problems with several expansion parameters — Applications to the rotating harmonic oscillator,Zeeman effect and helium-like atoms

Many Hamiltonians contain more than one parameter which can be used for making perturbation expansions. Lagrangian or other suitable interpolations of these perturbation series can incorporate all known analytic results and often considerably enlarge the domain of accuracy in parameter space. We point out that many physically interesting nonrelativistic potential problems fall into this class since 1/N (N=number of spatial dimensions) is very often available as one parameter, and large-N expansions are generally very successful. We apply this philosophy of combining the 1/N series with other more standard expansions to find the energy levels of the rotating harmonic oscillator and the ground state energies of the Zeeman Hamiltonian and the helium isoelectronic sequence.     

Microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces: A hybrid density functional approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.