Abstract

The field of liquid-metal (LM) catalysts is attracting significant attention, owing to their unique properties and their exceptional ability to support homogeneous and heterogeneous catalysis. Nevertheless, LM chemistry is still in its infancy and substantial contributions are required to make the most of these catalysts. This review presents an overview of the fundamental properties of LMs that govern the applicability of these state-of-the-art catalysts. Due to the close association between catalytic activity and the phase and structure of the catalyst, current characterization and modeling methods that are available for LM-based process analysis are outlined. Moreover, the use of both supported and unsupported LM catalysts in thermal and electrochemical catalytic processes for energy applications is showcased, and factors underlying their efficacy are explored. To date, the most common reaction design approach in LM thermal catalysis involves the use of bubbling-column reactors. The dependence of current investigations on a single-design model instigates the need to reassess this approach and evaluate other attractive reactor models, such as spraying or pulsing. Future advancements in LM catalysis and progress toward commercialization in this field necessitate research on several fronts, including the development of new LM-characterization methods, to enable characterization of the LM bulk that is currently lacking and facilitate in situ analysis; deploying innovative reactor designs to maximize liquid-gas interactions; and refining catalyst design to improve catalytic activity and increase application specificity through alloying. To keep up with the fast-paced transitioning of the global energy sector, which is constantly thriving to enable reliable, economic, and sustainable energy production, catalysis research has been required to continuously evolve in response. The challenges in the existing systems are predominantly due to dependencies on heterogeneous solid catalysts that are susceptible to coking. In this respect, liquid-metal (LM) catalysts have been demonstrated to have a critical advantage over conventional catalysts. Recently, LMs acquired a place in catalysis, with a reputation often synonymous with interesting properties and a remarkable ability to break trade-offs between homogeneous and heterogeneous catalysis. This review bridges the fundamental principles of LM research and the recent advances in LM-based thermal and electrochemical catalysis for energy applications. Moreover, emerging approaches for the improved utilization of LMs are outlined, and the concepts requiring greater research attention that could enable the development of exciting energy solutions are highlighted. To keep up with the fast-paced transitioning of the global energy sector, which is constantly thriving to enable reliable, economic, and sustainable energy production, catalysis research has been required to continuously evolve in response. The challenges in the existing systems are predominantly due to dependencies on heterogeneous solid catalysts that are susceptible to coking. In this respect, liquid-metal (LM) catalysts have been demonstrated to have a critical advantage over conventional catalysts. Recently, LMs acquired a place in catalysis, with a reputation often synonymous with interesting properties and a remarkable ability to break trade-offs between homogeneous and heterogeneous catalysis. This review bridges the fundamental principles of LM research and the recent advances in LM-based thermal and electrochemical catalysis for energy applications. Moreover, emerging approaches for the improved utilization of LMs are outlined, and the concepts requiring greater research attention that could enable the development of exciting energy solutions are highlighted. Catalysis is at the core of technological advancement and is a key enabler of future energy development. The current state of socioeconomic pressures, 21st-century energy demands, and the challenges encountered developing sustainable energy solutions have inspired a resurgence in the investigation of innovative new catalysts. The infrastructure of today’s energy catalysis scene is mainly built on the deployment of heterogeneous solid catalysts,1Descorme C. Gallezot P. Geantet C. George C. Heterogeneous catalysis: a key tool toward sustainability.ChemCatChem. 2012; 4: 1897-1906Crossref Scopus (48) Google Scholar which are greatly limited by coking effects and short lifetime.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar The use of liquid metals (LM), as heat-transfer media and catalysts has recently gained significant research attention. The main aim of LM-based liquid-phase catalysis is to capitalize on the ability of LMs to facilitate conversion in their liquid state, while eliminating coking and coarsening limitations that are commonly associated with the use of solid catalysts in these applications.3Taccardi N. Grabau M. Debuschewitz J. Distaso M. Brandl M. Hock R. Maier F. Papp C. Erhard J. Neiss C. et al.Gallium-rich Pd–Ga phases as supported liquid metal catalysts.Nat. Chem. 2017; 9: 862-867Crossref PubMed Google Scholar A number of properties make LMs appealing candidates as catalysts, including high thermal and electrical conductivities, relatively low viscosities, and an ability to retain their liquid-phase state over a wide range of temperatures (i.e., relatively low melting points and considerably higher boiling points).4Haynes W.M. CRC Handbook of Chemistry and Physics: a Ready-Reference Book of Chemical and Physical Data. CRC Press, 2016Crossref Google Scholar Moreover, LMs possess an exceptional potential to promote development on several fronts, including liquid-phase catalysis and advancing electro- and photocatalysis. Some of the most notable LMs are gallium (Ga) based due to their low toxicity and the ability of Ga to dissolve a wide range of other metals, therefore facilitating application specificity through alloying.5Dickey M.D. Emerging applications of liquid metals featuring surface oxides.ACS Appl. Mater. Interfaces. 2014; 6: 18369-18379Crossref PubMed Scopus (262) Google Scholar The use of LM catalysts signifies a paradigm shift away from reliance on solid catalysts and low-boiling-point solvents. This review provides an overview of the fundamental properties of LMs and elucidates the correlation to their effectiveness in catalysis. Moreover, the deployment of LM catalysts in thermal and electrochemical catalysis is detailed with special emphasis on creating and controlling the system architecture from catalyst selection to reactor design. Furthermore, this review sheds light on prospective concepts that could advance exciting opportunities away from conventional catalysis. This review additionally identifies some fundamental aspects of LMs that remain underexplored necessitating further investigation to unlock further inspiring opportunities. What distinguishes LMs from all other liquids or solvents is their characteristic metallic bonding. Metal atoms in the molten state provide electrons to a generated electron cloud shared by the bulk metal, surrounding positively charged metal ions and forming metallic bonds. The delocalized electrons can freely interact with electric fields, thermal energy, and light. This bestows LMs with high electric and thermal conductivities despite the absence of a lattice structure. The term LM is conventionally used to refer to the bulk of a molten metal while intuitively implying its presence in the liquid state. The term, however, is multidimensional and its interpretation is considerably more involved. In fact, many of the more attractive properties, functionalities, and applications are predicated on the multicomponent nature of LMs, and an oversimplified single-component representation of these materials tends to underestimate their potential value. By contrast, LMs represent four main components as illustrated in Figure 1: (1) the metallic core (molten LM bulk) comprising metallic bonding is present in the zero-valence state and is highly conductive making for an excellent reaction medium in thermal and electrocatalysis;6Armbrüster M. Behrens M. Cinquini F. Föttinger K. Grin Y. Haghofer A. Klötzer B. Knop-Gericke A. Lorenz H. Ota A. et al.How to control the selectivity of palladium-based catalysts in hydrogenation reactions: the role of subsurface chemistry.ChemCatChem. 2012; 4: 1048-1063Crossref Scopus (0) Google Scholar, 7Geißler T. Abánades A. Heinzel A. Mehravaran K. Müller G. Rathnam R.K. Rubbia C. Salmieri D. Stoppel L. Stückrad S. et al.Hydrogen production via methane pyrolysis in a liquid metal bubble column reactor with a packed bed.Chem. Eng. J. 2016; 299: 192-200Crossref Scopus (31) Google Scholar, 8Geißler T. Plevan M. Abánades A. Heinzel A. Mehravaran K. Rathnam R.K. Rubbia C. Salmieri D. Stoppel L. Stückrad S. et al.Experimental investigation and thermo-chemical modeling of methane pyrolysis in a liquid metal bubble column reactor with a packed bed.Int. J. Hydr. Energy. 2015; 40: 14134-14146Crossref Scopus (30) Google Scholar (2) the outer interface formed in the presence of air or an oxygen-containing environment includes oxygen sites and ionized metal atoms and can contribute to redox, protonation, and chelation functions;9Chen S. Wang H.-Z. Zhao R.-Q. Rao W. Liu J. Liquid metal composites.Matter. 2020; 2: 1446-1480Abstract Full Text Full Text PDF Scopus (5) Google Scholar, 10Zavabeti A. Ou J.Z. Carey B.J. Syed N. Orrell-Trigg R. Mayes E.L.H. Xu C. Kavehei O. O’Mullane A.P. Kaner R.B. et al.A liquid metal reaction environment for the room-temperature synthesis of atomically thin metal oxides.Science. 2017; 358: 332-335Crossref PubMed Scopus (213) Google Scholar, 11Martin A. Du C. Chang B. Thuo M. Complexity and opportunities in liquid metal surface oxides.Chem. Mater. 2020; https://doi.org/10.1021/acs.chemmater.0c02047Crossref Google Scholar, 12Khan H. Mahmood N. Zavabeti A. Elbourne A. Rahman M.A. Zhang B.Y. Krishnamurthi V. Atkin P. Ghasemian M.B. Yang J. et al.Liquid metal-based synthesis of high performance monolayer SnS piezoelectric nanogenerators.Nat. Commun. 2020; 11: 3449Crossref PubMed Scopus (4) Google Scholar (3) the existence of a pristine metal interface, as an extension of the metallic core, formed between the metal and injected gas bubbles or preserved in inert oxygen-free environments, mirrors the metallic core functions in catalysis applications;7Geißler T. Abánades A. Heinzel A. Mehravaran K. Müller G. Rathnam R.K. Rubbia C. Salmieri D. Stoppel L. Stückrad S. et al.Hydrogen production via methane pyrolysis in a liquid metal bubble column reactor with a packed bed.Chem. Eng. J. 2016; 299: 192-200Crossref Scopus (31) Google Scholar,13Palmer C. Upham D.C. Smart S. Gordon M.J. Metiu H. McFarland E.W. Dry reforming of methane catalysed by molten metal alloys.Nat. Catal. 2020; 3: 83-89Crossref Scopus (5) Google Scholar,14Upham D.C. Agarwal V. Khechfe A. Snodgrass Z.R. Gordon M.J. Metiu H. McFarland E.W. Catalytic molten metals for the direct conversion of methane to hydrogen and separable carbon.Science. 2017; 358: 917-921Crossref PubMed Scopus (87) Google Scholar and (4) solid suspended particles present in the metallic mixtures can constitute the active region of the catalyst alloy, rendering the internal morphology to be a controlling factor in catalytic performance and enhance the thermal conductivity of the alloy.15Zhang Q. Liu J. Nano liquid metal as an emerging functional material in energy management, conversion and storage.Nano Energy. 2013; 2: 863-872Crossref Scopus (40) Google Scholar These LM components are characteristically distinct and can be individually tailored, providing greater flexibility for catalysis applications and necessitating further investigation. The distinctive properties of LMs, including tailor-made flexibility through alloying, ease of separation, their existence in the liquid state over a wide range of temperatures, negligible vapor pressure, and low toxicity, make LMs a real technological asset. These remarkable properties, summarized in Figure 2, offer unprecedented advantages over other conventional liquid systems and set them apart as promising materials for advanced energy and catalysis applications. Moreover, the expansive use of LMs in a wide range of applications mirrors their unique physical properties, as listed in Table 1. Therefore, a thorough understanding of metal and gas solubilities, fluidity, and the characterization methods associated with LMs is imperative for making the best use of this new class of catalysts.Table 1Physical Properties of Prominent LMsLMTmelt (°C)Density (g/cm3)Electrical Conductivity ×106 (S/cm)Specific Heat Capacity (J/g K)Thermal Conductivity (W/m K)Ga29.76aData from Haynes45.91 (at 25°C)aData from Haynes40.074 (at 25°C)aData from Haynes40.373aData from Haynes440.60 (at 27°C)aData from Haynes4In156.60aData from Haynes47.31 (at 25°C)aData from Haynes40.125 (at 25°C)aData from Haynes40.233aData from Haynes481.60 (at 27°C)aData from Haynes4Sn (white)231.93aData from Haynes47.29 (at 25°C)aData from Haynes40.087 (at 25°C)aData from Haynes40.227aData from Haynes466.60 (at 27°C)aData from Haynes4EGaIn15.00aData from Haynes46.28 (at 20°C)bData from Liu et al.160.034 (at 22°C)eData from Yu and Kaviany190.404bData from Liu et al.1626.43 (at 37°C)eData from Yu and Kaviany19Galinstan−19.00aData from Haynes46.44 (at 20°C)bData from Liu et al.160.035 (at 20°C)cData from Karcher et al.170.296dData from Hodes et al.1825.41 (at 37°C)eData from Yu and Kaviany19Bi271.40aData from Haynes49.79 (at 25°C)aData from Haynes40.009 (at 25°C)aData from Haynes40.122aData from Haynes47.87 (at 27°C)aData from Haynes4Hg−38.83aData from Haynes413.53 (at 25°C)aData from Haynes40.010 (at 25°C)aData from Haynes40.140aData from Haynes48.51 (at 27°C)aData from Haynes4a Data from Haynes4Haynes W.M. CRC Handbook of Chemistry and Physics: a Ready-Reference Book of Chemical and Physical Data. CRC Press, 2016Crossref Google Scholarb Data from Liu et al.16Liu S. Sweatman K. McDonald S. Nogita K. Ga-based alloys microelectronic interconnects: a review.Materials (Basel). 2018; 11: 1384Crossref Scopus (19) Google Scholarc Data from Karcher et al.17Karcher C. Kocourek V. Schulze D. Experimental investigations of electromagnetic instabilities of free surfaces in a liquid metal drop.International Scientific Colloquium, Modelling for Electromagnetic Processing. 2003; : 105-110Google Scholard Data from Hodes et al.18Hodes M. Zhang R. Lam L.S. Wilcoxon R. Lower N. On the potential of Galinstan-based minichannel and minigap cooling.IEEE Trans. Compon. Packaging Manuf. Technol. 2014; 4: 46-56Crossref Scopus (0) Google Scholare Data from Yu and Kaviany19Yu S. Kaviany M. Electrical, thermal, and species transport properties of liquid eutectic Ga-In and Ga-In-Sn from first principles.J. Chem. Phys. 2014; 140: 064303Crossref PubMed Scopus (37) Google Scholar Open table in a new tab LMs can be used as single-element, pure liquid-metal (PLM) or as alloyed liquid-metal (ALM) catalysts, depending on the target reaction. LM alloying can be achieved through several established techniques, including an electrochemical approach, acid-facilitated suspension, and mechanical mixing of solid catalytic particles in an LM base. The electrochemical process of LM-alloy synthesis is analogous to the biological phagocytosis process, wherein the LM “engulfs” the metal particles.20Tang J. Zhao X. Li J. Zhou Y. Liu J. Liquid metal phagocytosis: intermetallic wetting induced particle internalization.Adv Sci (Weinh). 2017; 4: 1700024Crossref PubMed Scopus (43) Google Scholar This is typically done by coating the LM with the metal precursor particles and immersing the mixture in an electrolyte as illustrated in Figure 3A. The choice of electrolyte can vary in its basicity, such that the solvent used can either be alkaline or neutral in nature. The mixture is then subjected to a substantial electrical potential. The reducing potentials diminish the existing interfacial oxides and enable the wetting of the metal particles. Another LM-alloying method involves the suspension of metal particles into the LM bulk using an acid, such as hydrochloric acid, as illustrated in Figure 3B. The acid helps to break the metal-oxide bonds on the metal particles and in the LM. The method is suggested to be capable of integrating larger metal particles that are greater than 1 μm in size into the LM. It is demonstrated that the high density of the relatively larger particles and the wetting effect are responsible for the effective alloying.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar These methods enable alloying based on the ability of LMs to wet the metal particles. Therefore, efficient alloying of, for instance, Ga-based LMs is limited to a selection of metals such as copper.21Cui Y. Liang F. Yang Z. Xu S. Zhao X. Ding Y. Lin Z. Liu J. Metallic bond-enabled wetting behavior at the liquid Ga/CuGa2 interfaces.ACS Appl. Mater. Interfaces. 2018; 10: 9203-9210Crossref PubMed Scopus (20) Google Scholar Moreover, metals can also be dissolved into the LM base by mechanical grinding, which can be done manually in a mortar and pestle as shown in Figure 3C. Grinding increases the surface area of the metal by breaking up the particles and disrupts the prevailing interfacial oxides. These metal oxides form a barrier to the solid metal particles and prevent the metal particles from entering the LM, effectively impeding the alloying process.22Carle F. Bai K. Casara J. Vanderlick K. Brown E. Development of magnetic liquid metal suspensions for magnetohydrodynamics.Phys. Rev. Fluids. 2017; 2: 013301Crossref Scopus (27) Google Scholar This means that for efficient alloying the metal oxides must be eliminated. The aim is to ensure complete insertion of the metal precursor into the bulk of LM instead of having it weakly adhered to its surface. Typically, alloying is considered complete when the alloy appears to be uniformly shiny, indicating that there are no residual metal particles left in the mixture.10Zavabeti A. Ou J.Z. Carey B.J. Syed N. Orrell-Trigg R. Mayes E.L.H. Xu C. Kavehei O. O’Mullane A.P. Kaner R.B. et al.A liquid metal reaction environment for the room-temperature synthesis of atomically thin metal oxides.Science. 2017; 358: 332-335Crossref PubMed Scopus (213) Google Scholar The grinding method is particularly useful for reactive metals, since it does not require solvents and may be carried out in an inert atmosphere.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar LMs can form monophasic or biphasic alloys, producing homogeneous liquid-phase or distinctive solid-liquid mixed-phase ALMs.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar Moreover, LMs can accommodate the integration of noble and transition metals, often in small quantities (typically below 1 wt %), that are incorporated to gain enhanced chemical properties or improved catalytic performance. These elements are often referred to as “active metals” in LM-based catalysis studies. Figure 3D highlights the various LM-base and active-metal elements with special emphasis on the elements used in energy-related catalysis applications. Their solubility in an LM base is heavily dependent on temperature and the nature of the metal.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar The relative concentration at which the alloy remains in the liquid state can be determined by its respective phase diagram.23Okamoto H. Schlesinger M.E. Mueller E.M. Binary alloy phase diagrams.in: Alloy Phase Diagrams. ASM International, 2016: 79-624Crossref Google Scholar Common stable and high melting point of precious- or transition-metal catalysts, such as copper (Cu), nickel (Ni), silver (Ag), palladium (Pd), and platinum (Pt), can therefore all be effectively dispersed in an LM base to form intermetallic compounds.3Taccardi N. Grabau M. Debuschewitz J. Distaso M. Brandl M. Hock R. Maier F. Papp C. Erhard J. Neiss C. et al.Gallium-rich Pd–Ga phases as supported liquid metal catalysts.Nat. Chem. 2017; 9: 862-867Crossref PubMed Google Scholar,24Liang S.T. Wang H.Z. Liu J. Progress, mechanisms and applications of liquid-metal catalyst systems.Chemistry. 2018; 24: 17616-17626Crossref PubMed Scopus (0) Google Scholar The nonuniformity present in ALMs alters their chemical and physical properties and fundamentally impacts their catalytic performance in various applications. The properties attained for an ALM are not distinctive for a specific concentration, but rather for a range of concentrations, i.e., ALMs do not abide by the law of definite proportions.2Daeneke T. Khoshmanesh K. Mahmood N. de Castro I.A. Esrafilzadeh D. Barrow S.J. Dickey M.D. Kalantar-zadeh K. Liquid metals: fundamentals and applications in chemistry.Chem. Soc. Rev. 2018; 47: 4073-4111Crossref PubMed Google Scholar The ability of LMs to dissolve other metals is a critical factor in the fluid handling and design of chemical processes due to the well-known corrosiveness of LMs to metals constituting common materials of construction.7Geißler T. Abánades A. Heinzel A. Mehravaran K. Müller G. Rathnam R.K. Rubbia C. Salmieri D. Stoppel L. Stückrad S. et al.Hydrogen production via methane pyrolysis in a liquid metal bubble column reactor with a packed bed.Chem. Eng. J. 2016; 299: 192-200Crossref Scopus (31) Google Scholar Nevertheless, the high metal solubility in LMs and the inherent formation of alloyed catalysts with tunable features render LMs highly flexible and enable the tailoring to a variety of applications. The morphologies of the supported LM catalysts remain mostly spherical due to the high surface tension of the LM, with surface coverage ranging from full surface to sparse nanosized features, depending on loading.25Hoshyargar F. Khan H. Kalantar-zadeh K. O'Mullane A.P. Generation of catalytically active materials from a liquid metal precursor.Chem. Commun. 2015; 51: 14026-14029Crossref PubMed Google Scholar,26Hoshyargar F. Crawford J. O’Mullane A.P. Galvanic replacement of the liquid metal galinstan.J. Am. Chem. Soc. 2017; 139: 1464-1471Crossref PubMed Scopus (38) Google Scholar In addition, the dissolution and amalgamation of otherwise reactive pyrophoric elements becomes possible due to the oxygen-free environment within the bulk LM.27Esrafilzadeh D. Zavabeti A. Jalili R. Atkin P. Choi J. Carey B.J. Brkljača R. O’Mullane A.P. Dickey M.D. Officer D.L. et al.Room temperature CO2 reduction to solid carbon species on liquid metals featuring atomically thin ceria interfaces.Nat. Commun. 2019; 10: 865Crossref PubMed Scopus (44) Google Scholar This strategy has historically been proven to be successful for the development of electrocatalysts, as exemplified by the sodiation of liquid mercury, which consists of a Hg–Na amalgam to form a reactive and electroactive material.28Crook J. Mousavi A. The chlor-alkali process: a review of history and pollution.Environ. Forensics. 2016; 17: 211-217Crossref Scopus (21) Google Scholar In an LM catalysis framework the solubility of gaseous reactants in a liquid-phase catalyst impacts the dynamics and possibly the reaction pathways, with effects potentially attributable to the degree of homogeneity of the catalysis, such as in the case of slurry-bubble reactors. Since LMs readily oxidize upon exposure to air,10Zavabeti A. Ou J.Z. Carey B.J. Syed N. Orrell-Trigg R. Mayes E.L.H. Xu C. Kavehei O. O’Mullane A.P. Kaner R.B. et al.A liquid metal reaction environment for the room-temperature synthesis of atomically thin metal oxides.Science. 2017; 358: 332-335Crossref PubMed Scopus (213) Google Scholar and hydrogen is a common method of LM reduction, oxygen and hydrogen solubility are regarded as the most essential in existing LM-catalysis applications. The solubility of gases in LMs is principally endothermic in nature, such that the solubility increases with temperature. In general, the solubility of gases is higher in LMs than in their solid-phase counterparts. The solubility of hydrogen,29Sacris E.M. Parlee N.A.D. The diffusion of hydrogen in liquid Ni, Cu, Ag, and Sn.Metall. Trans. 1970; 1: 3377-3382Google Scholar,30Schumacher R. Weiss A. Hydrogen solubility in the liquid alloys lithium-indium, lithium-lead, and lithium-tin.Ber. Bunsen ges. Phys. Chem. 1990; 94: 684-691Crossref Scopus (18) Google Scholar oxygen,31Alcock C.B. Jacob K.T. Solubility and activity of oxygen in liquid gallium and gallium-copper alloys.J. Less Common Met. 1977; 53: 211-222Crossref Scopus (27) Google Scholar and inert gases32Reed, E.L., and Droher, J.J. (1970). Solubility and diffusivity of inert gases in liquid sodium, potassium, and NaK. pp. 32, https://doi.org/10.2172/4181890.Google Scholar in various pure LMs are well modeled. However, correlations depicting solubility trends have been found to be only achievable by sophisticated thermodynamics, increasing the complexity of any solubility prediction.33Austin Chang Y. Fitzner K. Zhang M.-X. The solubility of gases in liquid metals and alloys.Prog. Mater. Sci. 1988; 32: 97-259Crossref Scopus (60) Google Scholar The evaluation of the degree of solubility of gases in LM matrices is still not well established, and its influence on the pragmatic realization of catalytic processes that successfully manipulate solubilities to tune degrees of homogeneity remains underexplored. LM viscosity is associated with reaction rates in catalytic systems. This is due to the viscosity- dependent rate of diffusion and number of collisions of particles present in the fluid. There is an established systematic relation between viscosity, diffusivity, and temperature that can be extended to LMs, formulated as follows:ηD∝kTa,(Equation 1) where η is the viscosity of the liquid, D is the self-diffusion coefficient, k is Boltzmann’s constant, T is the absolute temperature, and a is the atomic size parameter.34Poirier J.P. Transport properties of liquid metals and viscosity of the Earth's core.Geophys. J. Int. 1988; 92: 99-105Crossref Scopus (143) Google Scholar Since viscosity is one of the factors that dictate the motion and deformation of bubbles flowing through the liquid catalyst, it is a critical parameter for gas-liquid processes and reactor design. LMs exhibit relatively low viscosities in the order of 1 mPa·s.35Dinsdale A.T. Quested P.N. The viscosity of aluminium and its alloys--a review of data and models.J. Mater. Sci. 2004; 39: 7221-7228Crossref Scopus (99) Google Scholar To put this in context, liquid gallium has a viscosity of 2.037 mPa‧s36Spells K.E. The determination of the viscosity of liquid gallium over an extended nrange of temperature.Proc. Phys. Soc. 1936; 48: 299-311Crossref Scopus (0) Google Scholar at its melting point (29.76°C), which is only twice that of water (0.798 mPa·s).37Ma K. Liu J. Liquid metal cooling in thermal management of computer chips.Front. Energy Power Eng. China. 2007; 1: 384-402Crossref Scopus (116) Google Scholar When compared with many other commonly used heat-media fluids such as heavy oils, LMs have up to three orders of magnitude lower viscosity.38Alomair O. Jumaa M. Alkoriem A. Hamed M. Heavy oil viscosity and density prediction at normal and elevated temperatures.J. Petrol. Explor. Prod. Technol. 2016; 6: 253-263Crossref Scopus (12) Google Scholar This property highlights a fundamental advantage of developing LM-based catalysts that can also facilitate heat transfer while ensuring fast kinetics.39Bennett J.W. Horton K.E. Materials requirements for liquid metal fast breeder reactors.Metall. Trans. A. 1978; 9: 143-149Crossref Scopus (6) Google Scholar Viscosity of PLMs is inversely proportional to temperature.40Yakymovych A. Plevachuk Y. Mudry S. Brillo J. Kobatake H. Ipser H. Viscosity of liquid Co–Sn alloys: thermodynamic evaluation and experiment.Phys. Chem. Liq. 2014; 52: 562-570Crossref PubMed Scopus (15) Google Scholar Moreover, metals can undergo viscosity change as temperature increases induced by liquid-liquid phase transitioning.41Wei S. Yang F. Bednarcik J. Kaban I. Shuleshova O. Meyer A. Busch R. Liquid–liquid transition in a strong bulk metallic glass-forming liquid.Nat. Commun. 2013; 4: 2083Crossref PubMed Scopus (0) Google Scholar Extending this relationship to ALMs, however, is significantly more involved due to the strong dependency on alloy composition. Moreover, the presence of intermetallic compounds, which are defined as solid particles with specific stoichiometry and crystal structure, is shown to significantly increase viscosity.22Carle F. Bai K. Casara J. Vanderlick K. Brown E. Development of magnetic liquid metal suspensions for magnetohydrodynamics.Phys. Rev. Fluids. 2017; 2: 013301Crossref Scopus (27) Google Scholar,35Dinsdale A.T. Quested P.N. The viscosity of aluminium and its alloys--a review of data and models.J. Mater. Sci. 2004; 39: 7221-7228Crossref Scopus (99) Google Scholar,4

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