Role of particle size on the cohesive behavior of limestone powders at high temperature

Role of particle size on the cohesive behavior of limestone powders at high temperature M. J. Espina, F. J. Duran-Olivenciab, J. M. Valverdeb,∗ aDepartamento de Fisica Aplicada II, Universidad de Sevilla. Avenida Reina Mercedes s/n, 41012 Sevilla, Spain bFacultad de Fisica, Universidad de Sevilla. Avenida Reina Mercedes s/n, 41012 Sevilla, Spain Abstract Thermal Energy Storage (TES) using granular solids is gaining momentum in the last years. With no degradation up to very high temperatures and very low price the use of some granular materials such as sand or SiC would be feasible for storing sensible heat at large scale. A further step beyond TES is thermochemical energy storage (TCES) wherein the granular solids undergo a highly endothermic reaction at high temperature. Energy can be in this way more efficiently stored in the long term and released on demand by means of the reverse exothermic reaction. The Calcium Looping process, based on the calcination/carbonation of CaCO3, is being actively investigated for this purpose. However, a caveat of using granular solids for energy storage is the possible increase of interparticle adhesive forces with temperature which would severely hamper the flowability of the solids in the ∗Corresponding author Email addresses: [email protected] (M. J. Espin), [email protected] (F. J. Duran-Olivencia), [email protected] (J. M. Valverde) Preprint submitted to Chemical Engineering Journal September 4, 2019 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ You can view the Version of Record for this article at: https://doi.org/10.1016/j.cej.2019.123520 process. The cohesiveness of granular materials is essentially determined by particle size. In this paper we investigate the dependence of the tensile yield strength and compressibility of CaCO3powders on temperature and consolidation stress using samples of narrow particle size distribution in the relevant range between ∼30 and ∼80 µm particle size and temperatures up to 500◦C. Our experimental results show that powder cohesiveness is greatly increased with temperature especially in the case of the finest powders whose tensile yield strength can be increased by up 2 orders of magnitude. The increase of cohesiveness with temperature is further enhanced with a previously applied consolidation stress, which is particularly relevant for applications wherein large amounts of solids are to be stored at high temperature. Experimental data are consistent with the predictions by a contact mechanics model assuming that the solids deform plastically at interparticle contacts. A main conclusion from our work is that some mechanical properties of the solids, specially the mechanical hardness, and how they change with temperature, play a critical role on the flowability of the solids as affected by an increase of temperature. Keywords: Granular Materials, Energy Storage, Calcium Looping, Fluidization, Flowability 2 1. Introduction The commercial expansion of renewable energy at large scale is urgently needed for mitigating global warming. Renewable energy sources have the potential to supply clean, affordable and sufficient power to replace fossil fuels in the medium term while simultaneously satisfy the ever growing energy demands [1]. However, increasing the degree of penetration of the main renewable energies, such as solar and wind, in the power grid will not be possible until large-scale energy storage is incorporated to power generation plants to cope with the intermittent nature of these clean energy resources [2–5]. Thermal energy storage (TES) in sensible form has already reached a commercial stage in concentrating solar power (CSP) plants with central tower technology enabling electricity generation when sunlight is not available or during low radiation hours [6–9]. These CSP plants with energy storage basically consist of a set of heliostats orientated to concentrate solar radiation in a solar receiver at the top of a tower where a heat transfer fluid can be heated to temperatures up to 1000◦C [10–12]. Sensible heat storage (SHS) fluids or solids store/release sensible heat during the process of heating/cooling. Their main working requirements are an extended temperature range to avoid phase change and degradation, high thermal conductivity for efficient heat transfer, low viscosity (for SHS fluids) to avoid large pressure drops during pumping, high heat capacity, safety, non-corrosiveness and low cost [13–15]. Commonly used SHS materials in 3 commercial CSP plants are water/steam and molten salts. Water/steam [16] seems to be the best option available because of its low cost, high specific heat capacity, wide availability and chemical stability. A limited temperature range (≤100◦C at atmospheric pressure) is yet an important drawback for its large-scale application. This issue may be overcome by increasing steam pressure (even up to 35 bar for industrial purposes) which adds however excessive costs [13]. Nowadays, most commercial CSP plants with integrated energy storage use solar salts (usually a binary sodium-potassium nitrate compound in a molten state [17]) as SHS fluid [11, 18]. Main advantages of these solar salts are their high heat capacity and relative low cost. However, molten salts degrade at temperatures beyond ∼560◦C and solidify below 200◦C which limits their working temperature range [19, 20]. Corrosiveness of solar salts poses also a main inconvenient as it raises operation and maintenance costs [21, 22]. Solid materials such as sand, SiC, concrete or fire bricks [6, 23] are being investigated as good alternatives to molten salts [6, 24–27]. SHS solids are not corrosive nor environmentally unfriendly and may operate at much higher temperatures than molten salts without degradation. Nevertheless their heat capacity is appreciably lower which makes necessary the use of very large units to store sufficient energy [28]. Latent heat storage (LHS) relies on the heat stored/released when materials undergo a phase transition [28]. Phase change materials (PCMs) for TES applications should have an adequate phase transition temperature, 4 high thermal conductivity, long-term chemical stability, safety, low cost and, overall, their volume change during the phase transition should be as small as possible to avoid storage problems [29]. Phase changes yielding the highest latent heat are solid-gas and liquid-gas transitions but they involve large volume changes which causes excessive complexity and economic cost [30]. Thus, most industrial efforts have been focused on PCMs that undergo solidliquid phase changes in the typical range of temperatures taking place in CSP plants [30]. These PCMs suffer a small volume change during the phase transition but the associated latent heat is low [13, 29, 31]. Paraffin, fatty acids and salt hydrates are some of the most widespread used PCMs [32]. For the same temperature range, LHS systems have larger heat storage capacity than SHS materials and heat is stored in a nearly isothermal process. Degradation by dehydration, chemical decomposition and maintenance costs are the principal disadvantages of PCMs with respect to fluids and solids used in SHS systems [29, 33]. In addition, most PCMS are operated in low temperature ranges (up to ∼90◦C) which makes them suitable for residential applications [28, 33] but not for CSP with tower technology. The less mature but highly promising technology for heat storage in CSP plants with tower technology consists of thermochemical energy storage (TCES) [34–37]. TCES systems are based on the storage/release of heat by means of reversible chemical reactions with high enthalpy [38–40]. The high temperatures achievable in the solar receiver of CSP plants can supply the required heat to drive highly endothermic chemical reactions. The 5 by-products of the endothermic reaction are stored separately and brought together on demand. Then, at suitable reaction conditions, the previously used heat is released in the reverse exothermic reaction. TCES systems can store energy with a theoretically high density and are suitable to work at higher temperatures compared to SHS and LHS systems [33, 41–43]. A main potential benefit of TCES is the possibility of long-term storage, including long-distance transport of the reactants (and, hence, the heat stored), at ambient temperature without significant losses. Till the date, the majority of works at laband pilot-scale on TCES have been focused on redoxbased systems [44–46]. Another interesting option to integrate TCES in CSP plants is the Calcium-Looping process (CaL) based on the reversible calcination/carbonation reaction of CaCO3/CaO [47–51] CaCO3(s) CaO(s) + CO2(g); ∆Hr0= 178kJ/mol.(1) The CaCO3/CaO system presents several advantages as compared to other TCES systems. These compounds are non-toxic, non-corrosive, environmentally friendly, abundant, cheap and naturally occurring as raw minerals [38, 47]. The reversible calcination/carbonation reaction has been thoroughly investigated and technically developed at large pilot-scale (1 −2 MWth) to capture CO2in fossil fuel power plants [52–57] and cement and lime manufactures [58–62] with successful results [56, 63–66]. Lab-scale experiments and simulations using limestone powder (almost 6 pure CaCO3) demonstrate a number of advantages of the CaL process to store energy in chemical form [11, 34–37]. Mainly, high energy storage densities can be potentially achieved (theoretically up to 3.26 GJm−3vs. 0.5 GJm−3 for molten salts [47, 67–70]). These materials present also a high thermal conductivity (around 1.5 Wm−1K−1, which is about three times higher than solar salts [71]). The integration of the CaL process into CSP plants with central tower technology for energy storage is being currently tested at the small pilot scale in Europe within the SOCRATCES project [72] and in USA (DOE) under the APOLLO [73] and ELEMENTS programs [74]. Direct solar irradiation provided by an heliostats field would be used to calcine the CaCO3particles in a solar calciner reactor [51]. In the SOCRATCES project Sensible heat of the subsequent products of the calcination reaction (CaO and CO2) are recovered by heat exchangers before storing them separately at ambient temperature [51]. Alternatively, the solids can be stored at high temperature for shortterm use to increase the overall efficiency [69]. When required, the reaction byproducts are recirculated and mixed in a carbonator reactor where the reversible carbonation reaction takes place at high temperature and high CO2partial pressure. The released heat from this exothermic reaction is transported to a gas turbine by the excess CO2over the stoichiometric ratio not intervening in the carbonation reaction to produce electricity by means of a Joule–Brayton cycle [47]. Thus, tailoring the calcination/carbonation reaction of CaCO3/CaO would enable electric power generation on demand. 7 The CaL process would be likely carried out in circulating fluidized bed reactors, where the high gas-solid contact efficiency would enhance the performance of the calcination/carbonation reactions [24, 47, 50, 57, 72]. Moreover, the mixture of solid particles and gas in fluidized beds promotes temperature uniformity and heat transfer between reagents [75]. However, a key property that may compromise the efficiency of fluidized bed reactors as well as the transport of particles within the system is the cohesive behavior of the granular material which depends critically on particle size [76]. Recent studies on the role of particle size on the CaL process have been focused on thermogravimetric tests targeting the multicycle reactivity of limestone derived CaO when cycled under calcination/carbonation conditions for CO2capture [77–80] and for TCES [81]. To the best of authors’ knowledge, the role of particle size on the flowability of CaCO3/CaO powders at high temperatures remains unexplored. As particle size is decreased, the gas-solid contact efficiency is increased but also the cohesiveness of the powder [82]. Fine particles in cohesive powders (belonging to the Geldart C type [83]) form large agglomerates impermeable to the gas flow. As a consequence, stable gas channels are usually developed in the bulk of the powder through which most of the gas flow bypasses the bed, which hinders the gas-solid contact efficiency in fluidized beds. Moreover, the flow of cohesive powders becomes severely impaired as stable arches are prone to be developed and jamming is promoted [84]. Typically, powder cohesiveness becomes significant when particle size is de8 creased below ∼50 µm [82]. Blockage of stand-pipes and discontinuous flow are prone to occur in cement plants for Ca-based powders of particle size below ∼30 µm [85]. Moreover, poor flowability is usually enhanced after powders are stored for a long period of time, which may promote interparticle adhesive forces [86, 87]. Since powder cohesiveness may be also enhanced as the temperature increases, free flowing powders at ambient temperature could turn into cohesive at high temperatures [88]. Thus, the influence of particle size and temperature on powder flowability must be taken under consideration for solids transport and storage [89]. Knowing how temperature and particle size may affect limestone flowability may help understand the governing mechanism behind the increase of powder cohesiveness with temperature. This basic knowledge would be useful for applications based on the CaL process such as CO2capture and energy storage in CSP plants. Other applications currently under research and development that might benefit from this fundamental research are solar irradiated rotary kilns [90] and sensible heat storage where other solid granular materials must flow and be transported at high temperatures [28]. In this work, we have investigated the cohesiveness of a set of CaCO3 powders as affected by particle size at high temperatures and previously subjected to a range of relatively low consolidation stresses between ∼100 Pa and a few kPa which are relevant to powder flow. The average particle size of the tested CaCO3powders ranges between ∼30 and ∼80 µm which belongs to the range of interest for industrial purposes in the integration of the CaL 9 behavior of the powder. At a given temperature and consolidation stress, the tensile yield strength σtis increased as particle size is decreased. Interestingly, the slope salso depends markedly on dp. As particle size increases from dp∼30 µm to dp∼60 µm, the slope sis progressively diminished. The reduction of sbecomes more pronounced for powder beds of larger particle size (dp∼80 µm). As will be seen below this dependence of the slope son particle size is a consequence of the variation of the particle volume fraction of the settled powders with particle size. Gas pressure drop measurements also serve to investigate the role of temperature Ton the fluidization behavior of the powder. Figure 5 exemplifies data obtained of ∆p(normalized by the powder’s weight per unit area W) vs. the gas flow rate for the CaCO3powder of particle size dp∼60 µm previously subjected to a consolidation stress σc= 1500 Pa and for tests carried out at different temperatures. As may be observed in Figure 5, the tensile yield strength of the powder is appreciably increased as the temperature is increased. The initial slope sis also clearly dependent on T. Thus, the values of sincrease significantly when Traises from 25 to 300◦C. However, at temperatures beyond 300◦C, the enhancement of swith Tbecomes less marked. Figure 6 illustrates the effect of the previously imposed consolidation stress on the fluidization behavior of the tested CaCO3powders. The values of σtincrease considerably as the powder is subjected to increasing values of σc. However, the influence of σcon the initial slope sis less noticeable as 16 compared to the effects of dpand T. At this point, it is worth wondering whether these results are also dependent on the period of time during which the powder beds were subjected to a given consolidation stress. This effect is well-known in powder technology (caking) and consists of the enhancement of powder cohesiveness of loaded powders with time due to the viscoplastic nature of interparticle contacts for some materials [82, 87, 110]. Caking is particularly relevant when powders are allowed to settle for relatively long periods of time between successive uses, as might occur for CaCO3powders in TCES systems or for CO2capture where large masses of limestone would be stored in silos [47, 70, 72, 111]. The modified STP used in this work is also able to measure σtas a function of the consolidation time τ(time of application of σc). Figure 7 shows data on the average values of σtmeasured for CaCO3samples (dp∼45 µm) subjected to a consolidated stress σcequal to their own weight per unit area W and for increasing periods of time. Consolidation time ranges between just 10 seconds to one hour. The experiments were performed at different temperatures. As clearly observed, within the accuracy of our measurements, σt does not change appreciably with the consolidation time regardless of temperature, which indicates that caking in CaCO3powders is not relevant even at the high temperatures and for the time lags employed in our work. Data shown in Figure 7 serve also to demonstrate the reproducibility of the results obtained in our experimental tests. 17 3.2. Effect of temperature, particle size and consolidation stress on the tensile yield strength Figure 8 shows data of the measured tensile yield strength of CaCO3 powders as a function of σc,T, and dp. First, we will analyze the effect of σcfor powders with a given particle size and tests carried out at a fixed temperature. As expected from Figure 6, increasing consolidation stresses lead to higher tensile yield strengths. In agreement with previous studies carried out at ambient temperature on diverse types of fine powders [68, 100], the rate of increase of σtwith σcfollows a sublinear trend, σt=aσb cwith b/1 (Table 2). At a given particle size dp, the tensile yield strength of the powders is clearly increased when Traises from 25 to 500◦C as was inferred from the fluidization curves (Figure 5). This effect is appreciable in the whole range of temperatures tested in our work but becomes more marked for T≥300◦C. It must be also underlined that the increase of σtwith Tis influenced by the previously imposed consolidation stress. As σcincreases, the effect of T becomes remarkable giving rise to an increase in σtof up to two orders of magnitude for the highest consolidation stress tested (σc≈2000 Pa) when the temperature is increased from 25◦C to 500◦C. This cross effect of Tand σccan be also observed in the exponent of the power law σt=aσb c. As the temperature of the powder bed becomes higher, bgradually increases from ∼0.3 to ∼0.9 (Table 2). Finally, we will describe the role of dpon the tensile yield strength as 18 affected by temperature and the consolidation stress. At a given temperature, the tensile yield strength of the powder increases with the consolidation stress in a less pronounced manner the larger the particle size (as was inferred from Figure 4). The decrease of σtwith dpis not gradual yet. When dpis decreased from ∼80 µm to ∼45 µm, σtincreases smoothly but from ∼45 µm to ∼30 µm the enhancement of σtis neatly more marked. The influence of T on σtis also affected by particle size. There is an appreciable increase in the tensile yield strength for temperatures as low as ∼100◦C when particle size is small (dp∼30 µm). However, higher temperatures are required to cause a significant enhancement of σtas particle size increases. For instance, for dp∼45 µm, there is no relevant effect of Ton the tensile yield strength until the temperature is increased over 200◦C whereas this threshold is increased to 300◦C in the case of dp∼60 µm and dp∼80 µm. As a preliminary conclusion, our results demonstrate that the particle size of CaCO3powders employed in industrial applications determines critically the flow behavior of these powders as depending on temperature. Thus, a decrease of dpbelow ∼80 µm yields a significant enhancement of powder cohesiveness as the temperature is increased over ∼100◦C at relatively small consolidation stresses relevant to powder flow. Since the storage of CaCO3powders in industrial-scale plants may lead to consolidation stresses well above 1 kPa at temperatures higher than 300◦C [72], it is a foregone conclusion that the flowability of CaCO3powders will be severely hindered at the high temperatures typical of the CaL process. 19 3.3. Influence of temperature, particle size and consolidation stress on the micro-structure of CaCO3powder beds Information on the micro-structure of the tested CaCO3powders can be inferred from the particle volume fraction after the powder has been consolidated under a stress σc. Using Equation 2, φcan be calculated from the initial slope s= ∆p/qm(Figure 4). All the parameters involved in this equation are known with the exception of the ratio E/ψ2 p, which depends on particle shape. To estimate it, we will use experimental data for samples of dp∼30 µm which were initially subjected to a consolidation stresses σc in the range between Wand ∼5 kPa at room temperature. In these tests, the particle volume fraction could be obtained from direct measurements of the height hof the consolidated powder bed (φ=mp/(ρphS)) by means of an ultrasonic sensor mounted on top of the bed using the original setup of the SPT [98, 102] (at high temperatures the use of the ultrasonic sensor was not possible due to technical limitations). The initial slope s= ∆p/qm was also obtained in these tests at ambient temperature from the fluidization curve. Figure 9 shows the values of svs. η d2 pρ h S φ2 (1−φ)3which has been calculated from the direct measurements of φusing the ultrasonic sensor. Fitting the Carman-Kozeny equation (Equation 2) to the data yields the ratio E/ψ2 p≈272 which is close to the value reported for other irregularly shaped beads [112]. SEM images (Figure 1) demonstrate that CaCO3particles used in this work have a similar shape regardless of particle size. Thus, we will consider E/ψ2 p≈272 as the reference value for all the samples. More20 over, heating the particles up to T= 500◦C has no appreciable effect on their shape (see SEM pictures in Figures 10 and 11), thus we will also assume also E/ψ2 p≈272 for the whole range of temperatures employed in our work. Data on the particle volume fraction obtained as explained above are plotted in Figure 12 as a function of the previously imposed consolidation stress, average particle size and temperature. As would be expected for irregularly shaped adhesive particles subjected to relatively low consolidation stresses [113], the values of φare well below the theoretical limit corresponding to the random loose packing of uniform, non-cohesive spheres (φRLP ∼0.55) [114]. Regarding the evolution of φwith σc(for a given particle size and temperature), the powder bed becomes more compacted (φincreases) the larger the applied consolidation stress as would be expected. However, the influence of σcis less accused as the degree of compaction increases. Larger changes in φ are observed for σc≤1000 Pa whereas φincreases only slightly beyond this consolidation stress. This behavior can be satisfactorily described by a logarithmic law φ=c+dln σcas also found for other powders tested at ambient temperature under similar ranges of consolidation stresses [115, 116]. Concerning the role of temperature (for a given dp), Figure 12 shows that the increase of temperature raises the powder compressibility (as measured by the slope d= ∆φ/ ln σc). Thus, increasing values of Tyield more porous (smaller φ) powder beds. This change in the micro-structure of the bed with Tmagnifies the effect of σcon φ. For the same range of consolidation stresses, the increase of φbecomes more pronounced as Tincreases. For 21 instance, for powders of dp∼45 µm, φincreases by around a 3% in the range W≤σc/1000 Pa for T= 25◦C whereas it is increased over a 14% if the bed is heated up to 500◦C in the same range of consolidations. Let us now focus on the effect of particle size on the compressibility of the powder. At a given temperature and consolidation stress, particles rearrange in more compact structures as dpis increased. On the other hand, there exists a cross effect of dpand Ton φ. For example, for σc≈1000 Pa, and when Tis increased from 25 to 500◦C, φis reduced by a ∼11% for dp∼80 µm, by a ∼18% for dp∼60 µm, by a ∼20% for dp∼45 µm, and by a ∼36% for dp∼30 µm. This empirical observation can be quantified by the change of the values of din the relationship φ=c+dln σc(see Table 3). As Tis diminished, ddecreases more markedly the smaller the particle size. In summary, our experimental measurements show that CaCO3powders become less cohesive (smaller σt) and pack in closer structures (larger φ) more difficult to compress as dpis increased. Conversely, as the cohesiveness of the powders increases because of a reduction of dp, particles rearrange in more porous structures (smaller φ) which can be easily compressed even under low consolidation stresses. The increase of temperature magnifies these trends. As Traises, the powders become more cohesive and particles rearrange in more porous and easier to be compressed structures. 22 4. Discussion 4.1. Flowability of powders under small consolidations at room temperature We will begin the discussion of our experimental results by analyzing the results on the tensile yield strength of CaCO3powder beds previously subjected to the small consolidation stress just given by their own weight per unit area (σc=W) at ambient temperature (Figure 4). Under these conditions, the flowability of powders depends mainly on the ratio of the attractive interparticle force Fat to particle weight mg, so-called cohesive granular Bond number [117], Bog=Fat mg (3) When the attractive force between particles is smaller than particle weight (Bog<1), the powder flows freely. By contrast, powder flowability is hindered by the aggregative behavior of particles when the attractive interaction between them overcome their own weight (Bog>1). The attractive force between particles may be of capillary, magnetic, electrostatic and/or van der Waals nature [82, 118–120]. In our dry samples, capillary forces that would arise from water condensation on the particles surface [121] may be neglected. For non-charged fine powders, as our tested samples, the electrostatic force can be also dismissed as compared to the van der Waals force [122–124]. Nor our samples exhibit a magnetic behavior. Therefore, the attractive interaction between CaCO3particles is mainly due 23 to the short ranged van der Waals force Fat =FvdW which arises from the interaction between the fluctuating molecular dipoles of neighbor particles. If dipole-dipole interaction is assumed pairwise and retardation effects are considered as negligible, the maximum van der Waals force between two unloaded particles at contact can be approximated by [125]: FvdW ≈AD∗ 20z2 0 .(4) where Ais the Hamaker constant, whose typical values are on the order of 10−19 J for most solids in vacuum [126], z0denotes the distance of closest approach between two molecules and ranges from 3 to 4 ˚ A [122, 123, 127, 128], and D∗= 2R∗, being R∗the reduced local radius of curvature of the particles surfaces at contact. For smooth spherical beads of diameter dpthe reduced diameter is equal to D∗=dp/2. The van der Waals force is however a short ranged interaction. Consequently, the magnitude of the van der Waals force is mainly determined by the roughness of the particles surface. Thus, dpmust be replaced by the typical size of the asperities dasp (D∗≈d∗ asp =dasp/2). For particles of size on the order of tens of microns, a typical value of dasp is ∼0.2µm [129, 130]. Taking into account these considerations in Equation 4, the granular Bond number can be rewritten as Bog≈3Adasp 20πgz2 0ρpd3 p .(5) The above expression suggests that the cohesiveness of powders increases 24 greatly as dpdecreases as indicated by our measurements of the tensile yield strength (Figures 4 and 8). To quantify this observation, we have calculated Bogassuming A≈1.01 ×10−19 J for CaCO3[131] and z0≈4˚ A, which give Bog∼0.3, Bog∼1, Bog∼3 and Bog∼7 for dp∼80 µm, dp∼ 60 µm, dp∼45 µm, and dp∼30 µm, respectively. As dpis decreased from ∼80 to ∼30 µm, the magnitude of the attractive force between particles gradually increases until it overcomes the particle weight. Thus, the increase of Bogyields an appreciable increase of cohesiveness of the CaCO3powders in this range of particle size as observed empirically therefore hindering their flowability. The van der Waals force does not reflect however the remarkable increase of the tensile yield strength of the powder after it has been subjected to a consolidation stress as seen from our measurements (Figures 6 and 8). This effect is crucial for applications such as the CaL process where powder flow is to be resumed after the material has been consolidated under storage and at conditions possibly involving high temperatures [69]. Experimental results shown in the present work demonstrate that consolidation and high temperatures enhance significantly the powder tensile strength. Understanding the mechanisms that govern this undesirable behavior may provide us with useful methods to mitigate it. The next section is aimed at this purpose. 25 cohesiveness of the material changes with temperature as it may determine crucially the flowability of the solids in the process. As the cohesiveness of the powder is increased particles rearrange in more porous structures which can be easily compressed. As well known from industrial applications using granular solids, poor flowability caused by particle aggregation and jamming may cause serious problems in practice. In this work we have measured the tensile yield strength and packing fraction of CaCO3powders with well-defined particle size in the range between ∼30 and ∼80 µm of interest for the integration of the CaL process in CSP plants to store energy in thermochemical form. The results demonstrate that particle size determines critically the flow behavior of these powders as depending on temperature. As particle size is decreased below ∼80 µm powder cohesiveness is markedly promoted when temperature is increased above 100◦C. Cohesiveness is significantly enhanced with temperature when the powders are subjected to relatively small consolidation stresses especially in the case of the finest samples. In our work we have also analyzed the physical mechanisms by which the cohesive behavior of granular solids is enhanced with temperature. To this end the average forces of consolidation and adhesion between individual particles have been estimated from the measured bulk stresses and particle volume fraction. The results show that the interparticle force of adhesion Ftscales proportionally to the square root of the interparticle consolidation force Fcin agreement with a contact model based on the assumption that the 32 solid near the interparticle contact zone yields plastically. As temperature increases, the rate of increase of Ftwith √Fcis progressively increased which may be explained by a decrease of the mechanical hardness of the solid as measured elsewhere. A main conclusion from our work is that the change of flowability of granular materials with temperature is not only affected critically by particle size but also by the variation of the solid mechanical properties with temperature. The results presented here would be useful in general for applications involving the storage and transport of granular solids at high temperature. They may help develop methods for mitigating the possible significant increase of powder cohesiveness with temperature (as found in our work for CaCO3powders) for example by preparing functional particles with enhanced mechanical hardness at high temperature. Acknowledgements This work was supported by Spanish Goverment Agency Ministerio de Economia y Competitividad (contract No. CTQ2017-83602-C2-2-R). The Microscopy service of the Innovation, Technology and Research Center of the University of Seville (CITIUS) is gratefully acknowledged. 33 References References [1] O. Edenhofer, R. P. Madruga, Y. Sokona, K. Seyboth, P. Eickemeier, P. Matschoss, G. Hansen, S. Kadner, S. Schlmer, T. Zwickel, C. von Stechow (Eds.), Renewable Energy Sources and Climate Change Mitigation. Special Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 2012. [2] S. Chu, A. Majumdar, Opportunities and challenges for a sustainable energy future, Nature 488 (2012) 294–303. doi:https://doi.org/10.1038/nature11475. [3] G. Crabtree, Perspective: The energy-storage revolution, Nature 526 (2015) S92. doi:https://doi.org/10.1038/526S92a. [4] D. Lindley, Smart grids: The energy storage problem, Nature 463 (2010) 18–20. doi:https://doi.org/10.1038/463018a. [5] M. Z. Jacobson, Review of solutions to global warming, air pollution, and energy security, Energy Environ. Sci. 2 (2009) 148–173. doi:https://doi.org/10.1039/B809990C. [6] Y. Tian, C. Zhao, A review of solar collectors and thermal energy storage in solar thermal applications, Appl. Energy 104 (2013) 538– 553. doi:https://doi.org/10.1016/j.apenergy.2012.11.051. 34 [7] M. Romero, A. Steinfeld, Concentrating solar thermal power and thermochemical fuels, Energy Environ. Sci. 5 (2012) 9234–9245. doi:https://doi.org/10.1039/C2EE21275G. [8] J. T. Hinkley, J. A. Hayward, B. Curtin, A. Wonhas, R. Boyd, C. Grima, A. Tadros, R. Hall, K. Naicker, An analysis of the costs and opportunities for concentrating solar power in Australia, Renew. Energ. 57 (2013) 653–661. doi:https://doi.org/10.1016/j.renene.2013.02.020. [9] V. S. Reddy, S. Kaushik, K. Ranjan, S. Tyagi, State-of-the-art of solar thermal power plants - A review, Renew. Sust. Energ. Rev. 27 (2013) 258–273. doi:https://doi.org/10.1016/j.rser.2013.06.037. [10] S. Kuravi, J. Trahan, D. Y. Goswami, M. M. Rahman, E. K. Stefanakos, Thermal energy storage technologies and systems for concentrating solar power plants, Prog. Energy Combust. Sci. 39 (4) (2013) 285–319. doi:https://doi.org/10.1016/j.pecs.2013.02.001. [11] H. L. Zhang, J. Baeyens, J. Degreve, G. Caceres, Concentrated solar power plants: Review and design methodology, Renew. Sust. Energ. Rev. 22 (2013) 466–481. doi:https://doi.org/10.1016/j.rser.2013.01.032. [12] A. Henry, R. Prasher, The prospect of high temperature solid state energy conversion to reduce the cost of concen35 trated solar power, Energy Environ. Sci. 7 (2014) 1819–1828. doi:https://doi.org/10.1039/C4EE00288A. [13] S. Pintaldi, C. Perfumo, S. Sethuvenkatraman, S. White, G. Rosengarten, A review of thermal energy storage technologies and control approaches for solar cooling, Renew. Sust. Energ. Rev. 41 (2015) 975– 995. doi:https://doi.org/10.1016/j.rser.2014.08.062. [14] M. Becker, Comparison of heat transfer fluids for use in solar thermal power stations, Electr. Pow. Syst. Res. 3 (3) (1980) 139–150. doi:https://doi.org/10.1016/0378-7796(80)90001-2. [15] M. J. Bignon, The influence of the heat transfer fluid on the receiver design, Electr. Pow. Syst. Res. 3 (1) (1980) 99–109. doi:https://doi.org/10.1016/0378-7796(80)90026-7. [16] D. Barlev, R. Vidu, P. Stroeve, Innovation in concentrated solar power, Sol. Energy Mater. Sol. Cells 95 (10) (2011) 2703–2725. doi:https://doi.org/10.1016/j.solmat.2011.05.020. [17] G. J. Janz, C. B. Allen, N. P. Bansal, R. M. Murphy, R. P. T.Tomkins, Physical properties data compilations relevant to energy storage. II. Molten salts: data on single and multi-components salt systems, Tech. rep., National Standard Reference Data System (1979). doi:https://doi.org/10.6028/NBS.NSRDS.61p2. 36 [18] A. G. Fernandez, S. Ushak, H. Galleguillos, F. J. Perez, Development of new molten salts with LiNO3 and Ca(NO3)2 for energy storage in CSP plants, Appl. Energy 119 (2014) 131–140. doi:https://doi.org/10.1016/j.apenergy.2013.12.061. [19] J. Ortega, J. Burgaleta, F. M. Tellez, Central Receiver System Solar Power Plant Using Molten Salt as Heat Transfer Fluid, ASME. J. Sol. Energy Eng. 130 (2) (2018) 024501–6. doi:https://doi.org/10.1115/1.2807210. [20] R. I. Dunn, P. J. Hearps, M. N. Wright, Molten-salt power towers: Newly commercial concentrating solar storage, Proc. IEEE 100 (2) (2012) 504–515. doi:https://doi.org/10.1109/JPROC.2011.2163739. [21] K. Vignarooban, X. Xu, A. Arvay, K. Hsu, A. M. Kannan, Heat transfer fluids for concentrating solar power systems A review, Appl. Energy 146 (2015) 383–396. doi:https://doi.org/10.1016/j.apenergy.2015.01.125. [22] E. Pihl, D. Kushnir, B. Sanden, F. Johnsson, Material constraints for concentrating solar thermal power, Energy 44 (1) (2012) 944–954. doi:https://doi.org/10.1016/j.energy.2012.04.057. [23] S. Khare, M. Dell’Amico, C. Knight, S. McGarry, Selection of materials for high temperature sensible energy stor37 age, Sol. Energy Mater. Sol. Cells 115 (2013) 114–122. doi:https://doi.org/10.1016/j.solmat.2013.03.009. [24] G. Flamant, Theoretical and experimental study of radiant heat transfer in a solar fluidized-bed receiver, AIChE J. 28 (4) (1982) 529–535. doi:https://doi.org/10.1002/aic.690280402. [25] D. M. Bachovchin, D. H. Archer, D. H. Neale, Heat transfer in a fluidized-bed solar thermal receiver, AIChE Symp. Ser. (1983) 222. [26] I. Haddad, M. Elsayed, Transient performance of fluidized bed solar receiver at various parametric conditions, Solar & Wind Technol. 5 (6) (1988) 653–659. doi:https://doi.org/10.1016/0741-983X(88)90063-X. [27] S. Ayyappan, K. Mayilsamy, V. Sreenarayanan, Performance improvement studies in a solar greenhouse drier using sensible heat storage materials, Heat Mass Transf. 52 (3) (2016) 459–467. doi:https://doi.org/10.1007/s00231-015-1568-5. [28] I. Sarbu, C. Sebarchievici, A Comprehensive Review of Thermal Energy Storage, Sustainability 10 (1) (2018) 1–32. doi:https://doi.org/10.3390/su10010191. [29] A. Sharma, V. Tyagi, C. Chen, D. Buddhi, Review on thermal energy storage with phase change materials and applications, Renew. Sust. Energ. Rev. 13 (2) (2009) 318–345. doi:https://doi.org/10.1016/j.rser.2007.10.005. 38 [30] S. M. Hasnain, Review on sustainable thermal energy storage technologies, Part I: heat storage materials and techniques, Energy Convers. Manag. 39 (11) (1998) 1127–1138. doi:https://doi.org/10.1016/S01968904(98)00025-9. [31] U. Herrmann, D. W. Kearney, Survey of Thermal Energy Storage for Parabolic Trough Power Plants, ASME. J. Sol. Energy Eng. 124 (2) (2002) 145–152. doi:https://doi.org/10.1115/1.1467601. [32] A. Kasaeian, L. Bahrami, F. Pourfayaz, E. Khodabandeh, W.-M. Yan, Experimental studies on the applications of PCMs and nano-PCMs in buildings: A critical review, Energy Build. 154 (2017) 96–112. doi:https://doi.org/10.1016/j.enbuild.2017.08.037. [33] P. Tatsidjodoung, N. L. Pierres, L. Luo, A review of potential materials for thermal energy storage in building applications, Renew. Sust. Energ. Rev. 18 (2013) 327–349. doi:https://doi.org/10.1016/j.rser.2012.10.025. [34] P. Pardo, A. Deydier, Z. Anxionnaz-Minvielle, S. Rouge, M. Cabassud, P. Cognet, A review on high temperature thermochemical heat energy storage, Renew. Sust. Energ. Rev. 32 (2014) 591–610. doi:https://doi.org/10.1016/j.rser.2013.12.014. [35] H. O. Paksoy, Thermal energy storage for sustainable energy consup39 tion, Springer: Netherlands, 2007. doi:https://doi.org/10.1007/978-14020-5290-3. [36] K. E. N’Tsoukpoe, H. Liu, N. L. Pierres, L. Luo, A review on long-term sorption solar energy storage, Renew. Sust. Energ. Rev. 13 (9) (2009) 2385–2396. doi:https://doi.org/10.1016/j.rser.2009.05.008. [37] T. M. I. Mahlia, T. J. Saktisahdan, A. Jannifar, M. H. Hasan, H. S. C. Matseelar, A review of available methods and development on energy storage; technology update, Renew. Sust. Energ. Rev. 33 (2014) 532– 545. doi:https://doi.org/10.1016/j.rser.2014.01.068. [38] C. Prieto, P. Cooper, A. I. Fernandez, L. F. Cabeza, Review of technology: Thermochemical energy storage for concentrated solar power plants, Renew. Sust. Energ. Rev. 60 (2016) 909–929. doi:https://doi.org/10.1016/j.rser.2015.12.364. [39] I. Dincer, M. A. Rosen, Thermal Energy Storage: Systems and Applications, 2nd Edition, John Wiley & Sons, 2010. [40] P. Pinel, C. A. Cruickshank, I. Beausoleil-Morrison, A. Wills, A review of available methods for seasonal storage of solar thermal energy in residential applications, Renew. Sust. Energ. Rev. 15 (7) (2011) 3341– 3359. doi:https://doi.org/10.1016/j.rser.2011.04.013. [41] Y. Kato, Thermal Energy Storage for Sustainable Energy Consumption. NATO Science Series (Mathematics, Physics and Chem40 istry), Vol. 234, Springer, Dordrecht, 2007, Ch. Chemical energy conversion technologies for efficient energy use, pp. 377–391. doi:https://doi.org/10.1007/978-1-4020-5290-3. [42] A. H. Abedin, M. A. Rosen, A Critical Review of Thermochemical Energy Storage Systems, Open Renew. Energy J. 4 (2011) 42–46. doi:http://dx.doi.org/10.2174/1876387101004010042. [43] L. F. Cabeza, C. Sole, A. Castell, E. Oro, A. Gil, Review of solar thermal storage techniques and associated heat transfer technologies, Proc. IEEE 100 (2) (2012) 525–538. doi:https://doi.org/10.1109/JPROC.2011.2157883. [44] K. J. Albrecht, G. S. Jackson, R. J. Braun, Thermodynamically consistent modeling of redox-stable perovskite oxides for thermochemical energy conversion and storage, Appl. Energy 165 (2016) 285–296. doi:https://doi.org/10.1016/j.apenergy.2015.11.098. [45] L. F. Cabeza, A. Sole, X. Fontanet, C. Barreneche, A. Jove, M. Gallas, C. Prieto, A. I. Fernandez, Thermochemical energy storage by consecutive reactions for higher efficient concentrated solar power plants (CSP): Proof of concept, Appl. Energy 185 (2017) 836–845. doi:https://doi.org/10.1016/j.apenergy.2016.10.093. [46] S. Tescari, A. Singh, C. Agrafiotis, L. de Oliveira, S. Breuer, B. Schlgl-Knothe, M. Roeb, C. Sattler, Experimental evalua41 [78] G. S. Grasa, J. C. Abanades, M. Alonso, B. Gonzalez, Reactivity of highly cycled particles of CaO in a carbonation/calcination loop, Chem. Eng. J. 137 (3) (2008) 561–567. doi:https://doi.org/10.1016/j.cej.2007.05.017. [79] G. Grasa, R. Murillo, M. Alonso, J. C. Abanades, Application of the random pore model to the carbonation cyclic reaction, AIChE J. 55 (5) (2009) 1246–1255. doi:https://doi.org/10.1002/aic.11746. [80] I. Martinez, C. Grasa, R. Murillo, B. Arias, J. C. Abanades, Kinetics of Calcination of Partially Carbonated Particles in a Ca-Looping System for CO2 Capture, Energy Fuels 26 (2) (2012) 1432–1440. doi:https://doi.org/10.1021/ef201525k. [81] M. Benitez-Guerrero, B. Sarrion, A. Perejon, P. E. Sanchez-Jimenez, L. A. Perez-Maqueda, J. M. Valverde, Large-scale high-temperature solar energy storage using natural minerals, Sol. Energy Mater. Sol. Cells 168 (2017) 14–21. doi:https://doi.org/10.1016/j.solmat.2017.04.013. [82] A. Castellanos, The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders, Adv. Phys. 54 (4) (2005) 263–376. doi:https://doi.org/10.1080/17461390500402657. [83] D. Geldart, Types of gas fluidization, Powder Technol. 7 (5) (1973) 285–292. doi:https://doi.org/10.1016/0032-5910(73)80037-3. 48 [84] J. M. Valverde, M. A. S. Quintanilla, A. Castellanos, Jamming threshold of dry fine powders, Phys. Rev. Lett. 92 (2004) 258303. doi:https://doi.org/10.1103/PhysRevLett.92.258303. [85] B. Arias, M. Alonso, C. Abanades, CO2 Capture by Calcium Looping at Relevant Conditions for Cement Plants: Experimental Testing in a 30 kWth Pilot Plant, Ind. Eng. Chem. Res. 56 (10) (2017) 2634–2640. doi:https://doi.org/10.1021/acs.iecr.6b04617. [86] A. Castellanos, J. M. Valverde, M. A. S. Quintanilla, Aggregation and sedimentation in gas-fluidized beds of cohesive powders, Phys. Rev. E 64 (2001) 041304. [87] U. Zafar, V. Vivacqua, G. Calvert, M. Ghadiri, J. A. S. Cleaver, A review of bulk powder caking, Powder Technol 313 (2017) 389–401. doi:https://doi.org/10.1016/j.powtec.2017.02.024. [88] I. Tomasetta, D. Barletta, M. Poletto, The Effect of Temperature on Flow Properties of Fine Powders, Chem. Eng. Trans. 24 (2011) 655– 660. doi:https://doi.org/10.3303/CET1124110. [89] H. Purutyan, B. H. Pittenger, J. W. Carson, Six steps to designing a storage vessel that really works, Powder Bulk Eng. 13 (1999) 56–67. [90] G. Moumin, S. Tescari, P. Sundarraj, L. de Oliveira, M. Roeb, C. Sattler, Solar treatment of cohesive particles in a di49 rectly irradiated rotary kiln, Sol. Energy 182 (2019) 480–490. doi:https://doi.org/10.1016/j.solener.2019.01.093. [91] [link]. URL https://www.ksl-staubtechnik.de/en/pruefentesten/fractions/ [92] H. Shi, R. Mohanty, S. Chakravarty, R. Cabiscol, M. Morgeneyer, H. Zetzener, J. Y. Ooi, A. Kwade, S. Luding, V. Magnanimo, Effect of Particle Size and Cohesion on Powder Yielding and Flow, KONA Powder Part. J. (2018) 226–250doi:10.14356/kona.2018014. [93] L. Riester, P. Blau, E. Lara-Curzio, K. Breder, Nanoindentation with a Knoop indenter, Thin Solid Films 377-378 (2000) 635–639. doi:https://doi.org/10.1016/S0040-6090(00)01298-0. [94] L. Zheng, A. W. Schmid, J. C. Lambropoulos, Surface effects on Youngs modulus and hardness of fused silica by nanoindentation study, J. Mater. Sci. 42 (2007) 191–198. doi:https://doi.org/10.1007/s10853006-1051-2. [95] W. C. Oliver, G. M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (6) (1992) 1564–1583. doi:https://doi.org/10.1557/JMR.1992.1564. [96] J. M. Valverde, A. Castellanos, A. Ramos, A. T. Perez, M. A. Morgan, P. K. Watson, An automated apparatus for 50 measuring the tensile strength and compressibility of fine cohesive powders, Rev. Sci. Instrum. 71 (7) (2000) 2791–2795. doi:https://doi.org/10.1063/1.1150694. [97] J. Schwedes, Review on testers for measuring flow properties of bulk solids, Granul. Matter 5 (1) (2003) 1–43. doi:https://doi.org/10.1007/s10035-002-0124-4. [98] A. Castellanos, J. M. Valverde, M. A. S. Quintanilla, The Sevilla Powder Tester: A Tool for Characterizing the Physical Properties of Fine Cohesive Powders at Very Small Consolidations, KONA Powder Part. J. 22 (2004) 66–81. doi:https://doi.org/10.14356/kona.2004011. [99] U. Zafar, C. Hare, G. Calvert, M. Ghadiri, R. Girimonte, B. Formisani, M. A. S. Quintanilla, J. M. Valverde, Comparison of cohesive powder flowability measured by Schulze Shear Cell, Raining Bed Method, Sevilla Powder Tester and new Ball Indentation Method, Powder Technol. 286 (2015) 807–816. doi:https://doi.org/10.1016/j.powtec.2015.09.010. [100] Y. Chen, M. A. S. Quintanilla, J. Yang, J. M. Valverde, R. N. Dave, Pull-off force of coated fine powders under small consolidation, Phys. Rev. E 79 (2009) 041305. doi:https://doi.org/10.1103/PhysRevE.79.041305. [101] D. Barletta, M. Poletto, A. C. Santomaso, Chapter 4 Bulk Pow51 der Flow Characterisation Techniques, in: A. Hassanpour, C. Hare, M. Pasha (Eds.), Powder Flow: Theory, Characterisation and Application, The Royal Society of Chemistry, 2019, pp. 64–146. doi:https://doi.org/10.1039/9781788016100-00064. [102] J. M. Valverde, A. Castellanos, P. K. Watson, The effect of particle size on interparticle adhesive forces for small loads, Powder Technol. 118 (3) (2001) 236–241. doi:https://doi.org/10.1016/S0032-5910(00)00382-X. [103] H. Schubert, Capillary forces - modeling and application in particulate technology, Powder Technol. 37 (1) (1984) 105–116. doi:https://doi.org/10.1016/0032-5910(84)80010-8. [104] J. M. Valverde, F. Raganati, M. A. S. Quintanilla, J. M. P. Ebri, P. Ammendola, R. Chirone, Enhancement of CO2 capture at Ca-looping conditions by high-intensity acoustic fields, Appl. Energy 111 (2013) 538– 549. doi:https://doi.org/10.1016/j.apenergy.2013.05.012. [105] J. M. Valverde, A. Castellanos, M. A. S. Quintanilla, The memory of granular materials, Contemp. Phys. 44 (5) (2003) 389–399. doi:https://doi.org/10.1080/0010751031000155939. [106] P. C. Carman, Fluid flow through granular beds, Trans. Inst. Chem. Eng. 15 (1937) 150–166. [107] R. M. Nedderman, Statics and Kinematics of Gran52 ular Materials, Cambridge University Press, 1992. doi:https://doi.org/10.1017/CBO9780511600043. [108] S. C. Tsinontides, R. Jackson, The mechanics of gas fluidized beds with an interval of stable fluidization, J. Fluid Mech. 255 (1993) 237–274. doi:https://doi.org/10.1017/S0022112093002472. [109] J. M. Valverde, A. Ramos, A. Castellanos, P. K. Watson, The tensile strength of cohesive powders and its relationship to consolidation, free volume and cohesivity, Powder Technol. 97 (3) (1998) 237–245. doi:https://doi.org/10.1016/S0032-5910(98)00025-4. [110] M. A. S. Quintanilla, J. M. Valverde, A. Castellanos, Adhesion force between fine particles with controlled surface properties, AIChE J. 52 (5) (2006) 1715–1728. doi:https://doi.org/10.1002/aic.10770. [111] Y. A. Criado, B. Arias, J. C. Abanades, Calcium looping CO2 capture system for back-up power plants, Energy Environ. Sci. 10 (2017) 1994– 2004. doi:http://dx.doi.org/10.1039/C7EE01505D. [112] M. J. Espin, M. A. S. Quintanilla, J. M. Valverde, Effect of particle size polydispersity on the yield stress of magnetofluidized beds as depending on the magnetic field orientation, Chem. Eng. J. 277 (2015) 269–285. doi:https://doi.org/10.1016/j.cej.2015.04.124. [113] J. M. Valverde, A. Castellanos, Random loose packing of cohesive 53 granular materials, Europhysics Letters (EPL) 75 (6) (2006) 985–991. doi:https://doi.org/10.1209/epl/i2006-10208-4. [114] D. Bideau, A. Hansen, Disorder and Granular Media, North-Holland, Amsterdam, 1993. [115] P. K. Watson, J. M. Valverde, A. Castellanos, The tensile strength and free volume of cohesive powders compressed by gas flow, Powder Technol. 115 (1) (2001) 45–50. doi:https://doi.org/10.1016/S00325910(00)00275-8. [116] K. H. Roscoe, A. N. Schofield, C. P. Wroth, On The Yielding of Soils, Gotechnique 8 (1) (1958) 22–53. doi:http://doi.org/10.1680/geot.1958.8.1.22. [117] S. T. Nase, W. L. Vargas, A. A. Abatan, J. J. McCarthy, Discrete characterization tools for cohesive granular material, Powder Technol. 116 (2) (2001) 214–223. doi:https://doi.org/10.1016/S00325910(00)00398-3. [118] J. Visser, Van der Waals and other cohesive forces affecting powder fluidization, Powder Technol. 58 (1) (1989) 1–10. doi:https://doi.org/10.1016/0032-5910(89)80001-4. [119] J. P. K. Seville, C. D. Willett, P. C. Knight, Interparticle forces in fluidisation: a review, Powder Technol. 113 (3) (2000) 261–268. doi:https://doi.org/10.1016/S0032-5910(00)00309-0. 54 [120] S. J. Antony, W. Hoyle, Y. Ding (Eds.), Granular Materials: Fundamentals and Applications, The Royal Society of Chemistry, 2004. doi:https://doi.org/10.1039/9781847550996. [121] S. Herminghaus, Dynamics of wet granular matter, Adv. Phys. 54 (3) (2005) 221–261. doi:https://doi.org/10.1080/00018730500167855. [122] H. Krupp, Particle adhesion theory and experiment, Adv. Colloid Interface Sci. 1 (2) (1967) 111–239. doi:https://doi.org/10.1016/00018686(67)80004-6. [123] K. Rietema, The Dynamics of Fine Powders, Springer Netherlands, 1991. doi:https://doi.org/10.1007/978-94-011-3672-3. [124] B. Gady, D. Schleef, R. Reifenberger, D. Rimai, L. P. DeMejo, Identification of electrostatic and van der Waals interaction forces between a micrometer-size sphere and a flat substrate, Phys. Rev. B 53 (1996) 8065–8070. doi:https://doi.org/10.1103/PhysRevB.53.8065. [125] H. C. Hamaker, The London-van der Waals attraction between spherical particles, Physica 4 (10) (1937) 1058–1072. doi:https://doi.org/10.1016/S0031-8914(37)80203-7. [126] S. Ross, L. D. Morrison, Colloidal Systems and Interfaces, WileyInterscience, New York, USA, 1988. [127] J. Israelachvili, Intermolecular and Surface Forces, Academic Press, New York, USA, 1992. 55 [128] N. Yu, A. A. Polycarpou, Adhesive contact based on the LennardJones potential: a correction to the value of the equilibrium distance as used in the potential, J. Colloid Interface Sci. 278 (2) (2004) 428–435. doi:https://doi.org/10.1016/j.jcis.2004.06.029. [129] L. Massimilla, G. Dons, Cohesive forces between particles of fluid-bed catalysts, Powder Technol. 15 (2) (1976) 253–260. doi:https://doi.org/10.1016/0032-5910(76)80054-X. [130] E. R. Beach, G. W. Tormoen, J. Drelich, R. Han, Pull-off Force Measurements between Rough Surfaces by Atomic Force Microscopy, J. Colloid Interface Sci. 247 (1) (2002) 84–99. doi:https://doi.org/10.1006/jcis.2001.8126. [131] L. Bergstrom, Hamaker constants of inorganic materials, Adv. Colloid Interface Sci. 70 (1997) 125–169. doi:https://doi.org/10.1016/S00018686(97)00003-1. [132] S. D. Mesarovic, N. A. Fleck, Spherical indentation of elasticplastic solids, Proc. R. Soc. Lond. A 455 (1987) (1999) 2707–2728. doi:https://doi.org/10.1098/rspa.1999.0423. [133] S. D. Mesarovic, N. A. Fleck, Frictionless indentation of dissimilar elastic-plastic spheres, Int. J. Solids Struct. 37 (46) (2000) 7071–7091. doi:https://doi.org/10.1016/S0020-7683(99)00328-5. 56 [134] S. D. Mesarovic, K. L. Johnson, Adhesive contact of elasticplastic spheres, J. Mech. Phys. Solids 48 (10) (2000) 2009–2033. doi:https://doi.org/10.1016/S0022-5096(00)00004-1. [135] J. Q. Feng, Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius, J. Colloid Interface Sci. 238 (2) (2001) 318–323. doi:https://doi.org/10.1006/jcis.2001.7532. [136] L. Kogut, I. Etsion, Adhesion in elastic-plastic spherical microcontact, J. Colloid Interface Sci. 261 (2) (2003) 372–378. doi:https://doi.org/10.1016/S0021-9797(03)00071-7. [137] D. Maugis, H. M. Pollock, Surface forces, deformation and adherence at metal microcontacts, Acta Metallurgica 32 (9) (1984) 1323–1334. doi:https://doi.org/10.1016/0001-6160(84)90078-6. [138] K. L. Johnson, Contact Mechanics, Cambridge University Press, 1985. doi:https://doi.org/10.1017/CBO9781139171731. [139] D. Tabor, Surface forces and surface interactions, J. Colloid Inteface. Sci. 58 (1) (1977) 2–13. doi:https://doi.org/10.1016/00219797(77)90366-6. [140] B. V. Derjaguin, V. M. Muller, Y. P. Toporov, Effect of contact deformations on the adhesion of particles, J. Colloid Interface Sci. 53 (2) (1975) 314–326. doi:https://doi.org/10.1016/0021-9797(75)90018-1. 57 Table 3: Best fitting parameters (S. I. units) of the equation φ=c+dln σcto data in Figure 12. The fitting correlation factor is ρ2. dp= 32 ±1µmdp= 42.5±0.8µm T(◦C) c d ρ2c d ρ2 25 0.377 ±0.008 0.014 ±0.001 0.981762 0.42 ±0.01 0.010 ±0.002 0.911592 100 0.33 ±0.01 0.019 ±0.002 0.974538 0.383 ±0.005 0.0114 ±0.0008 0.985863 200 0.27 ±0.02 0.025 ±0.002 0.97092 0.33 ±0.01 0.017 ±0.0.002 0.975466 300 0.23 ±0.03 0.028 ±0.005 0.927938 0.26 ±0.02 0.025 ±0.0.002 0.974871 400 0.04 ±0.05 0.051 ±0.007 0.940588 0.21 ±0.02 0.029 ±0.003 0.968876 500 −0.4±0.1 0.10 ±0.02 0.871666 0.11 ±0.06 0.038 ±0.008 0.876716 dp= 59.3±0.8µmdp= 88.2±0.7µm T(◦C) c d ρ2c d ρ2 25 0.446 ±0.006 0.0080 ±0.0009 0.96668 0.511 ±0.002 0.0025 ±0.0003 0.95278 100 0.435 ±0.007 0.006 ±0.001 0.92688 0.477 ±0.007 0.005 ±0.001 0.889436 200 0.353 ±0.003 0.0149 ±0.0004 0.997859 0.452 ±0.007 0.008 ±0.0.0001 0.961141 300 0.30 ±0.01 0.020 ±0.002 0.981252 0.434 ±0.009 0.009 ±0.001 0.957253 400 0.27 ±0.02 0.023 ±0.003 0.954567 0.418 ±0.009 0.0.010 ±0.001 0.953974 500 0.19 ±0.01 0.032 ±0.002 0.986809 0.38 ±0.02 0.013 ±0.004 0.82149 64 Table 4: Slope mexp =Ft/√Fcof the best linear fitting of estimated data of the pull-off force and the square root of the compressive force from experimental measurements of the bulk tensile yield strength and consolidation stress, respectively (Figure 13). The fitting correlation factor is ρ2. T(◦C) mexp (√nN)ρ2 25 2.4±0.2 0.933621 100 3.9±0.3 0.921107 200 5.6±0.3 0.93635 300 15.5±0.5 0.983518 400 37.8±0.9 0.988935 500 69 ±3 0.968318 65 (a) (b) (c) (d) Figure 1: Scanning electron microscopy (SEM) pics of the tested CaCO3particles with an average particle size of (a) dp= 32 ±1µm –Eskal30–; (b) dp= 42.5±0.8µm –Eskal45–; (c) dp= 59.3±0.8µm –Eskal60–; and (d) dp= 88.2±0.7µm –Eskal80– as measured from laser diffractometry (Figure 2). 66 0 20 40 60 80 100 1 10 100 1000 (a) Cumulative volume distribution (%) dp (µm) Eskal30 Eskal45 Eskal60 Eskal80 0 10 20 30 40 50 60 1 10 100 1000 (b) Frequency distribution (%) dp (µm) Eskal30 Eskal45 Eskal60 Eskal80 Figure 2: Cumulative volume distribution (a) and number distribution (b) of particle sizes dpfor the tested CaCO3powders. Lines between dots are a guide to the eye. 67 Air compressor Air dryer & filters Differencial manometer Mass flow controller Silicone elastic membrane Acoustic waveguide Valve 1 Valve 2 Valve 3 Valve 4 Low frequency loudspeaker Electric amplifier Electric signal generator G Furnace temperature controller T Powder bed Quartz reactor Quartz fritted filter Furnace Teflon adapter Data acquistion and control C Pipeline Electric connection Figure 3: Sketch of the experimental set-up used in the experiments reported in this paper. 68 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.00 0.20 0.40 0.60 0.80 1.00 T=25°C; σc=W Pa σ t /W σ t /W σ t /W σ t /W qmf qmf qmf qmf s/W s/W s/W s/W ∆p/W (−) qm (g/min) dp∼30 µm dp∼45 µm dp∼60 µm dp∼80 µm Figure 4: Experimental curves of the gas pressure drop across the powder bed ∆p(normalized by the powder’s weight per unit area W) as a function of the gas flow rate qm for samples of CaCO3powders of different particle size dp(indicated). The vertical lines indicate the minimum fluidization gas flow rate qmf ; the tensile yield strength of the bed σt; and the initial slope sbetween ∆pand qm(before fracture of the bed). In these tests, samples were previously consolidated to σc=WPa at room temperature. 69 0.00 0.50 1.00 1.50 2.00 2.50 3.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 dp∼60 µm; σc=1500 Pa σ t /W σ t /W σ t /W σ t /W σ t /W σ t /W ∆p/W (−) qm (g/min) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C Figure 5: Examples of gas pressure drop curves across the CaCO3powder bed (made non dimensional with the powder’s weight per unit area) ∆p/W versus the gas flow rate qmfor samples of average particle size dp= 59.3±0.8µm previously subjected to a consolidation stress of σc= 1500 Pa. The inset shows the temperatures at which the experiments were performed. Vertical lines indicate the measured tensile yield strength for each temperature. 70 0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 0.00 0.20 0.40 0.60 0.80 1.00 dp∼80 µm; T=500°C σ t /W σ t /W σ t /W σ t /W σ t /W ∆p/W (−) qm (g/min) σc=W Pa σc=500 Pa σc=1000 Pa σc=1500 Pa σc=2000 Pa Figure 6: Normalized gas pressure drop across the powder bed ∆p/W as a function of the gas flow rate qmfor CaCO3samples of average particle size dp= 88.02 ±0.7µm. These experiments were carried out at T= 500◦C at different consolidation stresses σcas indicated which were applied to the beds previously to breaking. 71 0 50 100 150 200 250 300 350 400 450 10 100 1000 dp∼45 µm; σc=W Pa σ t (Pa) τ (s) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C Figure 7: Measured tensile yield strength σtas a function of the period of time τduring the powder bed was subjected to a consolidation stress σc=WPa before breaking for the indicated temperatures. The solid lines represent average values of the experimental data. Particle size of the tested sample was dp= 42.5±0.8µm. 72 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 (d) dp∼30µm σ t (Pa) σ c (Pa) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 (c) dp∼30µmdp∼45µm σ t (Pa) σ c (Pa) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 (b) dp∼30µmdp∼45µm dp∼60µm σ t (Pa) σ c (Pa) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 (a) dp∼30µmdp∼45µm dp∼60µmdp∼80µm σ t (Pa) σ c (Pa) T=25°C T=100°C T=200°C T=300°C T=400°C T=500°C Figure 8: Tensile yield strength of the powder bed σtas a function of the previously applied consolidation stress σcand temperature Tfor CaCO3samples of different particle size: (a) dp= 88.2±0.7µm; (b) dp= 59.3±0.8µm; (c) dp= 42.5±0.8µm; and (d) dp= 32 ±1µm. The solid lines represent the best fittings of the equation σt=aσb cto the experimental data. Best fitting parameters are reported in Table 2. 73