Nanosilica to improve the flowability of fine limestone powders in thermochemical storage units

Chemical Engineering Journal 426 (2021) 131789 Available online 20 August 2021 1385-8947/© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej Nanosilica to improve the flowability of fine limestone powders in thermochemical storage units R. Gannouna, J.M.P. Ebría, A.T. Péreza, M.J. Espínb, F.J. Durán-Olivenciaa, J.M. Valverdea,∗ aFacultad de Física, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Seville, Spain bDpto. de Física Aplicada II, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Seville, Spain ARTICLE INFO Keywords: Powder flowability Thermochemical energy storage Concentrated solar power Cohesive granular media Granular flows Fluidization ABSTRACT Fine powders are the cornerstone of new energy storage solutions to assist concentrated solar power plants. Though, their ability to behave like fluid can be seriously affected at high temperatures. This work investigates the use of nanosilica in fine limestone (calcium carbonate, CaCO3) powders to mitigate the promotion of cohesion forces at high temperatures. Experiments were conducted over limestone powder samples with particle sizes around 45 μm. The analysis was performed monitoring the tensile yield strength as the samples were subjected to different temperatures and consolidation stresses while varying the nanosilica content up until 0.82wt%. Temperatures reached a maximum of 500◦C (close to the Tamman temperature in limestone), whereas consolidation stresses were increased up to 2kPa. Results show that nanosilica coating is an efficient solution to inhibit the enhancement of powder cohesiveness at high temperatures and consolidations. A solution that offers better control to smooth the granular flow regimes in production environments. 1. Introduction Limestone powders, nearly 100% calcium carbonate (CaCO3), are used to operate new thermochemical energy storage technology [1]. A solution devised to assist concentrated-solar-power (CSP) plants channeling the solar energy from the receiver to the storage unit [2–4]. It is in these two extremes of the storage circuit where granular-based solutions surpass the performance of their molten salt counterparts [5]. However, liquid-based solutions are unbeatable when it comes to transport the material from end to end. Certainly, granular flows may exhibit jamming and other issues that eventually may lead to intermittent flow regimes. This is especially relevant in fine powders, which would be the best candidates in gas–solid reactive flows that require large contact areas, if not for such issues. Fine powders are usually cohesive, and their cohesiveness is often enhanced significantly at high temperatures [6]. This is one of the most controversial features of new granular-based storage designs. Unlike coarser granular media like sand, in fine powders delimiting the turning point from which adhesion forces govern the powder flowability is a challenge. In contrast to coarser granular materials, in fine powders adhesion forces can be much higher than their weight at ambient temperature [7]. Surface deformation at particles contact, interparticle diffusion, reactivity between grains, or atomic/ion mobility at surface level are some factors that may well unbalance the adhesion/weight ∗Corresponding author. E-mail addresses: [email protected] (R. Gannoun), [email protected] (J.M.P. Ebrí), [email protected] (A.T. Pérez), [email protected] (M.J. Espín), [email protected] (F.J. Durán-Olivencia), [email protected] (J.M. Valverde). relationship favoring the clustering among grains. Thus, fine powders are much more prone to suffer significant variation in their flowability as all these factors intertwined as temperature raises [6,8,9]. Indeed, characterizing and controlling the flowability in fine powders is still one of the most critical issues in many industries, such as flour [10,11] or cement industries [12]. Therefore, a better understanding of the granular flow regimes is of paramount importance within the European research project (H2020) developed by the authors [13]. The main goal of this project is to prove the feasibility of thermochemical energy storage solutions to assist CSP plants via fine limestone powders. The first CSP pilot plant assisted by thermochemical storage units in the EU (currently under construction [13]) implements the calcium looping (CaL) process devised by Shimizu et al. [14]. The CaL cycle [15–17] is governed by a reversible solid–gas reaction [18]. The endothermic part of this reaction —the calcination process— absorbs the solar radiation collected at the receiver. As a result, the heat is stored in the form of chemical potential. Later the exothermic reaction —the carbonation process— unleashes all this heat during the discharge phase at the generator. The heat released in this sector maps the high temperatures reached at the receiver. As it turns out, higher temperatures lead to more efficient thermodynamic cycles. Certainly, heat transfer or chemical reactivity are central factors to keep the overall performance [19]. But, the transport of the granular material https://doi.org/10.1016/j.cej.2021.131789 Received 2 April 2021; Received in revised form 22 June 2021; Accepted 25 July 2021 Chemical Engineering Journal 426 (2021) 131789 2 R. Gannoun et al. from both ends is by far the most critical aspect of this technology. Production environments demand uninterrupted granular flows, which, in turn, requires more precise control of powder flowability. Particle size is very essential in this matter [9,20]. It modulates (1) the amount of material exposes to react and (2) the relation between surface and volume forces shaping the intensity of cohesion forces. Thus, the smaller the particle size, the more important the attractive forces (cohesion) between particles become compared to their weight. As a result, as the particle size decreases, the granular flow regime shifts from the free-flowing area to the cohesive region, where the airflow drag is no longer enough to fall apart the aggregates. At the working conditions in thermochemical storage units in CSP plants, the pore plugging effect severely limits the carbonation reaction for particle size above 50 μm, approximately [19,21–25]. At ambient temperature, 50 μm particle size delimits a fuzzy boundary depending on the material [7] that serves to differentiate between free-flowing and cohesive behaviors. Fluidization promoted by fine particles not only favors the transport but also enhances the kinetics in entrained flow reactors. A reactor design [13,17,18,26,27] that has proven to be the optimal architecture for the calcination process at the receiver in CSP facilities. Though, these reactors involve short solid residence time—the reason why, they require fine powders to boost the chemical activity [28,29]. The downside of fine powders within the context of thermochemical storage units is that their flowability is more vulnerable to the impact of temperature [20,30,31]. In fact, around the 50 μm particle size boundary at ambient temperature, van der Waals attraction forces between particles balance their weight [20]. The increase in temperature quickly unbalances this situation; temperature favors particle mobility and reactivity, which eventually leads to larger powder cohesiveness. As it has been reported, fine limestone powders are critically affected by temperature [6,8,9]. Limestone flowability decreases significantly as the temperature approaches the Tamman temperature (545◦C [32,33]); the temperature at which atoms or ions mobility in solids becomes appreciable, favoring thus the sintering process. Recent studies with fine limestone powders measured an increment up to one order of magnitude in the tensile yield strength at 500◦C [6,8]. The authors used particles size around 45 μm, applying a consolidation stress of 2kPa before fluidizing the sample and monitoring its tensile yield strength. Authors showed that the consolidation stress enhances the cohesion forces significantly, worsening thus the effect of temperature on the limestone flowability. These results align with the softening that occurs at the contact between solids at high temperatures [20]. With a larger contact area, adhesion forces increase, and powder flowability declines accordingly. Nanosilica has shown to be an additive able to reduce the power cohesiveness at ambient temperature [34–38]. These results apply if nanosilica eventually coat powder particles after the mixing process. The coating acts as an armor layer that increases the mechanical hardness of the modified powder particle [39–41]. Furthermore, as particles are less prone to deform at the contact, the effective interaction area is reduced considerably. Thus, shielding powder particles with nanosilica tend to deplete attractive forces at the contact. Recent experimental studies confirmed the effectiveness of the nanosilica coatings in limestone at ambient temperature [42]. More importantly, the shielding effect has also been reported to be effective in limestone at high temperatures [6]. Within this context, this work aims at investigating the optimal amount of nanosilica coating to mitigate flowability issues in CSP facilities assisted with thermochemical storage units. To that end, this work analyzes the evolution of cohesion forces in limestone as the amount of nanosilica increases gradually up to 0.82wt%. Experiments monitored the tensile yield strength of the limestone powder as the temperature increased up to 500◦C (close to the Tamman temperature in limestone). To clarify the nanosilica shielding effect (increasing the hardness of the material), powder samples were consolidated up to 2kPa before monitoring the tensile yield strength through the fluidization regime. The results confirm that nanosilica is an excellent candidate to ease the limestone cohesiveness at high temperatures. For instance, in the worst scenario analyzed in this work (at 500◦C with powder sample subjected to a previous consolidation stress of 2kPa), the tensile yield strength was reduced by roughly 50%. Thus, modified particles behave as if they operated 200◦C below the actual temperature (500◦C). An outcome that might be critical to alleviate flowability issues when limestone powders must operate near the Tamman temperature while transporting the granular material from the calciner to the storage unit. This work has been carried out within the framework of the H2020 European project SOCRATCES [13] coordinated by the University of Seville, whose goal is to demonstrate at the pilot scale the suitability of the Calcium Looping process to store energy using fine limestone powders. 2. Materials and experimental setup In what follows, the materials and the experimental setup used in this work are introduced in detail. 2.1. Materials Experiments were performed on fine limestone powders (99.1% CaCO3), supplied by KSL Staubtechnik Gmbh (Eskal45). The average particle size was about 𝑑𝑝= 41.5 μm. More importantly, particle size exhibited a very sharp distribution around the average [8], which is essential to control potential size effects throughout the experiments. Two types of powder samples were used in the experiments: (1) the raw samples and (2) samples coated with fumed nanosilica (Aerosil R974 from Evonik) at different wt%. The coating process was undertaken via simple dry-mixing in a rotating drum [36,43]. This method layers limestone particles uniformly with nanosilica aggregates, whose size is around 100nm (Fig. 1,2) [44]. Table 1 outlines the mechanical properties of the materials studied in this work. According to the literature, there exists no clear consensus about the values of these mechanical properties. Data vary broadly among different studies, partly because of the use of different procedures and settings. 2.2. Experimental setup The experimental setup used in this work is based on the Sevilla Powder Tester (SPT), which was originally proposed by Valverde et al. [62]. During the last years, the SPT design has been extensively used in powder characterization studies [44,63–68]. This work used an upgraded version of the SPT setup to measure the tensile yield strength at high temperatures [6,8] (Fig. 3). The test cell consisted of a vertical cylindrical quartz tube of 4.5cm diameter. Wall effects are negligible [39] as the height of the powder bed (about 2.8cm) is always kept below the diameter of the cell. At the bottom of the cell, a porous ceramic plate was used to distribute the airflow across the bed uniformly. Before pumping the airflow through the bed, it was filtered and dried. The cleaning sequence eliminates both potential pollutants and moisture, which could have an impact on powder cohesiveness. This was achieved by a set of filters and an air dryer (model SMC IDFA3E). Dried and purified, the air stream was passed across the bed using a mass flow controller (Omega model FMA-2606 A, 2000sccm). A set of electric valves enable a bidirectional flow through the bed. Upward, for breaking the powder bed through a fluidization cycle. And, downward, to impose a given consolidation stress on the sample. In both cases, the pressure drop across the bed was measured by a differential pressure transducer (MKS model 220CD, 10Torr full scale). A sound generation system was used to produce a low-frequency sound wave driven by a PVC pipe to the top of Chemical Engineering Journal 426 (2021) 131789 3 R. Gannoun et al. Fig. 1. Scanning electron microscopy (SEM) images of the limestone particles used in this work mixed with silica at different weight ratios: (a-c) 0wt%; (d-f) 0.42wt%; (g-i) 0.82wt%. Fig. 2. Scanning electron microscopy (SEM) images of limestone particles coated with nanosilica (0.42wt%): (a-c) sample at 30◦C before the tests, and (d-f) after the tests carried out at 500◦C. Chemical Engineering Journal 426 (2021) 131789 4 R. Gannoun et al. Table 1 Material properties at room temperature reported in the literature for the powders tested in this work. Materials Density Diameter Young’s modulus Mechanical hardness Poisson ratio Surface energy 𝜌p(kg/m3)𝑑p(μm)𝐻(GPa) 𝐸(GPa) 𝛾(J/m2)𝜈(-) CaCO32700a41.52a(25, 88.19)b(0.75,5.11)c(0.21, 0.34)d(0.32, 0.347)e SiO2 (fumed silica) 2200a≈0.1a74f6f0.17g0.025h aData provided by the supplier. b[45–52]. c[46,49,50,53,54]. d[45–48,55–58]. e[58,59]. f[44]. g[60]. h[61]. Fig. 3. Schematic representation of the experimental setup. More details about the method, procedure, and protocol can be found in Refs. [6,8,62]. the bed. This pipe was endowed with a silicone membrane to avoid contamination by elutriated particles in the sound generation system and keep the cell sealed. The whole measuring process was controlled and automated using a protocol devised in LabView [6,8]. Before performing any test, the effect of the porous ceramic plate used for gas distribution was calibrated measuring the pressure drop in the absence of material. This pressure drop must be subtracted from the total one when the measure was performed with the powder sample, 𝛥𝑝. To initialize the powder in a reproducible state, the bed was fluidized by imposing a gas velocity much higher than the minimum fluidization velocity. The resulting bubbling regime was held for 30s. During the first 5 s of this initialization period, an acoustical excitation of 150dB at 130Hz was applied to aid the fluidization of strongly cohesive samples. Then the gas flow was stopped, and the bed let to settle for 30s. To heat the samples up to the target temperature, the testing cell was placed inside an electric furnace controlled by a PID temperature controller (Eurotherm 3126). A thermal stabilization time of 1h was set after reaching the desired temperature (ranging between ambient and 500◦C). Afterward, the sample was consolidated by a downwarddirected gas flow to a target consolidation stress that varied between the powder weight per unit area (in the absence of consolidating air flow) and 2kPa. The consolidating gas flow was kept fixed for 10s. When the target consolidation stress was reached, the gas flow was withdrawn gradually. In the final step, an upward-directed gas flow increased gradually to fluidize and break the powder bed under tension. As detailed in the result section, the tensile yield strength of the powder can be inferred from the pressure drop across the bed during the breaking process. Each test was repeated 3 times to assess the reproducibility of the results. 3. Results Fig. 4 shows typical examples of the evolution of the pressure drop through the powder bed 𝛥𝑝 (expressed as a non-dimensional ratio to the powder weight per unit area, 𝑊) as the gas velocity was increased. Lines represent different experiments where powder samples were subjected to pre-consolidation stresses (𝜎𝑐) up to 2 kPa. Initially, the gas pressure drop increases at a constant rate with the superficial gas velocity (𝑠=𝛥𝑝∕𝑣𝑔). As captured in the Carman–Kozeny relation, the passage of a viscous fluid through a granular bed induces a pressure drop proportional to the gas velocity at low Reynolds numbers [69]: 𝛥𝑝 ℎ=𝐸𝜂 𝜓2 𝑝𝑑2 𝑝 𝜙2 (1 − 𝜙)3𝑣𝑔,(1) where 𝐸stands for the Ergun’s empirical constant (𝐸≈ 180), 𝜂refers to the gas dynamic viscosity, 𝜓𝑝is the particle’s sphericity, ℎis the bed height, and 𝜙is the particle volume fraction. The point at which the pressure drop across the bed balances its weight per unit area (𝛥𝑝∕𝑊= 1) defines the minimum gas fluidization velocity, 𝑣𝑚𝑓 . Beyond this critical point, the increase in the gas velocity would lead to a bubbling fluid-like regime in a noncohesive granular material. In these conditions, as the airflow drag matches the powder weight, particles lift, and the pressure drop would fluctuate around the weight per unit area. Fig. 4 reveals then the cohesive character of limestone powders since the pressure drop exhibits a linear trend that overcomes the 𝑣𝑚𝑓 threshold. Interparticle adhesive forces are strong enough to hold particles together, even when the pressure drop is larger than the powder weight. As this linear rate goes further, the competition between adhesion and drag forces tensions the powder progressively. As a result, powders break eventually when the overpressure is equivalent to the tensile yield strength of the powder. Throughout the experiments, the fracture was triggered in a horizontal Chemical Engineering Journal 426 (2021) 131789 5 R. Gannoun et al. Fig. 4. Gas pressure drop, 𝛥𝑝, measured through the powder bed (expressed as a nondimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed in fine limestone powder (raw, CaCO3) at 𝑇= 400 ◦C. Powder samples were subjected to different consolidation stresses previous to the fluidization cycle used to measure the tensile yield strength, 𝜎𝑡. The pressure overshoot above the weight per unit area is used as a measure of the tensile yield strength of the powder. plane close to the bottom of the bed where the tensile stress reaches its maximum, as predicted theoretically [70–72]. After the peak, 𝛥𝑝 falls abruptly to a value of around the weight per unit area. The overshoot in the pressure drop determines the tensile yield strength of the powder: 𝜎𝑡=𝛥𝑝max −𝑊(Fig. 4). This approximation assumes that wall retention effects do not introduce a significant contribution to the pressure drop. To control these effects, experiments were performed with a bed height always below its diameter [39]. Fig. 4 details the consolidation effect at 400◦C. Samples were subjected to different pre-loads by a downward-directed gas flow rate. According to Fig. 4, higher consolidation stresses lead to larger slopes through the linear stage 𝛥𝑝∕𝑣𝑔, which indicates that particles were packed in tighter structures of higher particle volume fraction. Furthermore, as consolidation increased, the tensile yield strength registered a significant increase too. As it shall be discussed later, loading particles enhance adhesion forces, which promotes the rise observed in the tensile yield strength. Similar trends have been reported in previous works on fine limestone at high temperatures [6,8], detailing how the cross-effect between temperature and consolidation modulates the tensile yield strength. Fig. 5 shows the effect of temperature in the tensile yield strength when the samples were previously subjected to a consolidation stress of 𝜎𝑐= 1500 Pa. As it may be observed, the tensile yield strength increased significantly as temperature raised, which indicates that attractive forces between particles were increased accordingly. Besides, the initial slope, 𝛥𝑝∕𝑣𝑔, increased with temperature too. Gas viscosity could explain this rise in the slope since it goes from 16.08 ⋅10−6 m2/s at ambient temperature to 78.06 ⋅10−6 m2/s at 500◦C. A factor that might conceal the reduction in the particle volume fraction, as observed in previous studies [9,42]. In addition, Fig. 5 can be compared with Fig. 6, where the isotherm series were performed in limestone coated with nanosilica at 0.82wt%. Both figures exhibit similar trends, though the peaks were shifted to lower velocity in those samples coated with Fig. 5. Gas pressure drop, 𝛥𝑝, measured through the powder bed (expressed as a nondimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed in fine limestone powders (raw, CaCO3) at different temperatures ranging from 30◦C to 500◦C. Powder samples were previously subjected to a consolidation stress of 𝜎𝑐= 1500 Pa. nanosilica. This shift evidences that nanosilica eases the fluidization regime in fine limestone powders. Fig. 7 outlines the effect of the nanosilica content in the tensile yield strength for a given isotherm, 𝑇= 400 ◦C. These experiments were conducted pre-loading the powder samples at 𝜎𝑐= 1 kPa. Interestingly, even when the samples were coated with a small amount of nanosilica, the tensile yield strength declined significantly. The largest drop is observed for nanosilica content above 0.6wt%, which would arguably yield a sufficiently high nanosilica coating level on the surface of the host limestone particles [20,42]. With particles coated uniformly, the contact between particles mostly happens via nanosilica aggregates. Regarding the initial slope 𝛥𝑝∕𝑣𝑔, it increased with the nanosilica content as the peaks shifted to lower velocities. According to Eq.(1), a reduction of interparticle attractive forces may explain this effect. As cohesion is reduced, particles could settle in tighter structures with larger particle volume fractions. Fig. 8 shows how nanosilica can buffer the effect of the consolidation stress applied to the sample. In contrast to Fig. 4, doubling the consolidation stress at 400◦C had no impact in the tensile yield strength when the nanosilica content was above 0.6wt%. At 500◦C (Fig. 9), the nanosilica effect appears slightly less sharp than what is observed at 400◦C. Even though, nanosilica still reduced the tensile yield strength significantly compared to those values registered in raw limestone powders (Fig. 5). The interested reader may check in the supplementary information a video showing the breaking of the bed with an animation on the simultaneous evolution of the gas pressure drop with the gas velocity at different temperatures. These videos illustrate the breaking of the bed near the bottom while the pressure drop falls abruptly. The notable increase of cohesiveness with temperature can be appreciated. Chemical Engineering Journal 426 (2021) 131789 6 R. Gannoun et al. Fig. 6. Gas pressure drop, 𝛥𝑝, across the powder bed (expressed as a non-dimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed on fine limestone powder coated with nanosilica at 0.82wt%. Coated samples were subjected to a consolidation stress of 𝜎𝑐= 2000 Pa previous to the fluidization cycle used to measure the tensile yield strength. Each line represents an isotherm series ranging from 30◦C to 500◦C. Fig. 7. The gas pressure drop, 𝛥𝑝, measured through the powder bed (expressed as a non-dimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed on fine limestone powder coated with nanosilica at different weight ratios from 0wt% to 0.82 wt%. Samples were subjected to a consolidation stress of 𝜎𝑐= 1000 Pa at 𝑇= 400 ◦C previous to the fluidization cycle used to measure the tensile yield strength. Fig. 8. Gas pressure drop, 𝛥𝑝, measured through the powder bed (expressed as a non-dimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed on fine limestone powder coated with nanosilica at different weight ratios from 0wt% to 0.82 wt%. Samples were subjected to a consolidation stress of 𝜎𝑐= 2000 Pa at 𝑇= 400 ◦C previous to the fluidization cycle used to measure the tensile yield strength. Fig. 9. Gas pressure drop, 𝛥𝑝, measured through the powder bed (expressed as a non-dimensional ratio to the powder weight per unit area, 𝑊) as a function of the gas velocity, 𝑣𝑔. Experiments were performed on fine limestone powder coated with nanosilica at different weight ratios from 0wt% to 0.82 wt%. Samples were subjected to a consolidation stress of 𝜎𝑐= 1500 Pa at 𝑇= 500 ◦C previous to the fluidization cycle used to measure the tensile yield strength. Chemical Engineering Journal 426 (2021) 131789 7 R. Gannoun et al. Fig. 10. Tensile yield strength of the powder bed, 𝜎𝑡, as a function of the preconsolidation stress, 𝜎𝑐, for different isotherms. Raw sample of fine limestone powder were used in these series. Solid lines represent a linear fitting, although a more accurate regression model detailing the interaction between consolidation and temperature can be found in the Refs. [6,8]. 3.1. Effect of temperature, pre-consolidation stress, and nanosilica content in the tensile yield strength Fig. 10 represents the tensile yield strength as a function of the consolidation stress in the range of temperatures between ambient (𝑇= 30 ◦C) and 𝑇= 500 ◦C. Data were derived from the fluidization curves for limestone samples. Fig. 10 maps the evolution of the peak in Fig. 4, showing that the tensile yield strength raised as the consolidation stress was increased. A similar trend can be inferred for the relationship between the tensile yield strength and the temperature mapping the evolution in Fig. 5. Both parameters, temperature and consolidation, led to an increase in 𝜎𝑡, but interestingly they seem to reinforce each other from 300◦C. Fig. 10 shows a good agreement regarding how the interaction of these two parameters modulate the tensile yield strength as reported in the literature [6,8]. As described in previous works, from 300◦C consolidation shapes better contacts in fine limestone powders. Analyzing the experimental data in Fig. 10, the tensile strength fits a linear regression model with the consolidation stress for a given isotherm: 𝜎𝑡(𝑇) = 𝑎(𝑇)𝜎𝑐+𝑏(𝑇),(2) where 𝑏(𝑇)represents the tensile strength in the absence of previous consolidation at a given temperature, which results in a negligible value compared to the powder weight per unit area (𝑊). The constant rate in Eq.(2),𝑎(𝑇), increases as the temperature raises, revealing higher degree of cohesion for similar consolidation stresses at high temperatures. In fact, 𝜎𝑡exhibited an increase of two orders of magnitude for 𝜎𝑐= 2000 Pa when the temperature was raised from 30◦C to 500◦C. Fig. 11 outlines the central issue of this work, namely, how the use of nanosilica can alleviate the impact of temperature and consolidation in the tensile strength of fine limestone. At higher temperature, close to the Tamman temperature in limestone (Fig. 11,right), a nanosilica coating of 0.82wt% induced a reduction factor around 3. The effect is equivalent to an effective temperature in the material of 200◦C below the actual one, as it can be inferred contrasting the graphs at 300◦C and 500◦C in Fig. 11. Therefore, nanosilica coating offers an effective route to mitigate the impact of temperature and consolidation at high temperatures, even when added in small amounts (less than 1wt%). These outcomes can be of interest in applications where limestone powders must be transported and stored at high temperatures such as the CaL process. So far, the results have shown that coating limestone particles with nanosilica reduces cohesion forces significantly, although its impact on the powder flowability is not quantified yet. To that end, the so-called flow factor (𝑓𝑓) is used in the next analysis. This factor is commonly employed in the powder technology literature [73,74]. The flow factor is usually defined using unconfined yield strength data from shear testers; it prescribes the ratio between the consolidation stress used to pre-load the sample and the unconfined yield strength of the powder. A value of 𝑓𝑓 < 4is considered as representative of a poorly flowing cohesive powder, whereas for 𝑓𝑓 < 2the powder behaves as very cohesive. Admittedly, this work measured the tensile yield strength while the powder samples were subject to uniaxial tensile stresses. It is expected, though, that these measurements present similar values to those registered in yield stresses under shear for the same consolidations [75,76]. In these circumstances, an effective flow factor 𝑓𝑓∗ can be defined as the ratio between the consolidation stress imposed previously to the sample and the tensile yield strength of the powder (𝑓𝑓∗=𝜎𝑐∕𝜎𝑡). According to the linear trend shown by the experimental data (Eq.(2)), the flow factor result in 𝑓𝑓 ∗≈ 1∕𝑎for the range of consolidation stresses explored in this work. Fig. 12 shows how the content of nanosilica (wt%) alters the powder flowability throughout different isotherms. In the absence of additive, the limestone powder tested in this work (average particle size 𝑑𝑝= 45 μm) exhibited a free flowing behavior at ambient temperature. However, above 300◦C approximately, the free flowing behavior was turned into cohesive in the absence of nanosilica. At 𝑇= 500 ◦C with 0wt% content of nanosilica, the flow factor reached similar values to those observed in very cohesive fine limestone powders with particle size around 𝑑𝑝= 4.6 μm at ambient temperature (reported elsewhere [77]). Therefore, Fig. 12 indicates how the use of nanosilica in fine limestone powder boosts the limestone flowability at high temperatures, keeping the samples within the free-flowing regime when nanosilica content is above 0.6wt%. 3.2. Effect of temperature, pre-consolidation stress, and nanosilica content in the packing fraction The particle volume fraction (or packing fraction 𝜙) for a consolidated bed can be measured at room temperature using ultrasonic sensors (original SPT device [71,72]). This technique consists primarily of measuring the height of the bed, which is used to calculate the particle volume fraction. Unfortunately, this technique introduces a technical limitations as the sensor cannot operate at high temperatures. The Carman–Kozeny equation (Eq.(1)) offers an alternative for an indirect measurement of the particles volume fraction. In effect, from the linear stage in the fluidization curves, the slope 𝛥𝑝∕𝑣𝑔relates to the unknown parameter: the ratio 𝐸∕𝜓2 𝑝, which depends on the particles’ shape. This factor, however, is not sensitive to temperature [78] and could be estimated using the volume fraction at ambient temperature obtained by ultrasonic sensors. Thus, fitting the linear stage of the experimental data to the Carman– Kozeny equation, the ratio resulted in 𝐸∕𝜓≈ 272, which is close to values reported in the literature [78] for particles with irregular shapes. In fact, SEM images (Fig. 1,2) show that (1) limestone particles used in this work exhibit irregular shapes, and (2) shapes are not visibly affected by temperature. As a result, the ratio 𝐸∕𝜓2 𝑝can be considered constant for limestone below 500◦C, which makes possible to estimate the particle volume fraction of the pre-consolidated bed by a linear fitting through the pre-peak region. Chemical Engineering Journal 426 (2021) 131789 8 R. Gannoun et al. Fig. 11. Effect of nanosilica coating in tensile yield strength, 𝜎𝑡, as temperature increases from 30◦C to 500◦C. Solid lines fit the experimental data according to the interaction between consolidation and temperature [6,8]. Fig. 12. Effective flow factor, 𝑓𝑓∗, as a function of the nanosilica content, wt%, throughout different isotherms. Fig. 13 illustrates the effect of nanosilica coating in the volume fraction through different isotherms ranging from 30◦C to 500◦C. The volume fractions, 𝜙, were considerably below the theoretical limit for the random loose packing of hard non-cohesive spheres even in the absence of consolidation stresses (𝜙RLP ≈ 0.55 [79]). This because of the limestone powder cohesiveness and the irregular shapes of the particles. Data fits to the type logarithmic law 𝜙=𝑐+𝑑ln 𝜎𝑐used in previous studies [9,42] for other fine cohesive powders. On the other hand, Fig. 13 highlights that temperature reduced the particle volume fraction. This effect maps the increase in the powder cohesiveness, which hinders the particles mobility preventing thus tighter structures. The increase of 𝜙with 𝜎𝑐becomes more prominent at higher temperatures. Variations were more steep in fine limestone powders without additives (Fig. 13, left). For instance, for consolidation stresses in the interval between 𝑊and 1000Pa, 𝜙registered an increase around 3%, approximately at 𝑇= 30 ◦C, whereas 𝜙increased by a 14% at 500◦C. Fig. 13 shows how the use of nanosilica leads to larger values of 𝜙(Fig. 13, right). This is because of nanosilica reduces interparticle attractive forces, easing then that particles pack in closer arrangements. For a 0.82wt% of nanosilica, the particle volume fraction was decreased significantly only when coated samples were heated up to 500◦C. In contrast, below 500 ◦C the variations in 𝜙 were negligible, indicating that nanosilica help to set a stable internal powder structure for a broad range to temperatures (Fig. 13, right). 4. Discussion 4.1. Powder cohesiveness at small consolidation stresses Cohesive Bond number [80] compares attractive forces 𝐹at between particles with their weight 𝑚𝑔: Bo𝑔=𝐹at 𝑚𝑔 .(3) If Bo𝑔≪1, adhesion forces between particles are negligible. Particles, then, may flow freely if the drag is strong enough to lift them up. As attractive forces between the particles prevail over their weight, powder cohesiveness becomes appreciable. Flowability is then hindered due to particle aggregation [7]. In the absence of humidity and external fields, attractive interparticle forces are determined mainly by the ubiquitous van der Waals force. By neglecting retardation effects and assuming pairwise dipole–dipole interaction, the van der Waals force between two unloaded particles at contact is given by [81]: 𝐹vdW ≈𝐴𝐷∗ 20𝑧2 0 ,(4) where 𝐴refers to the Hamaker constant, whose typical value for most solids in vacuum is about 10−19 J; 𝑧0is the minimum distance between the solids which ranges from 3 to 5Å ; and 𝐷∗= 2𝑅∗, where 𝑅∗is the reduced local radius of curvature of the surfaces at contact. Since the van der Waals force is a short-ranged interaction, its magnitude is very sensitive to the roughness of the contact surfaces. Thus, for particles with irregular shapes, as those used in this study, the typical size of asperities must be employed for 𝐷∗in Eq.(4) [81]. Chemical Engineering Journal 426 (2021) 131789 9 R. Gannoun et al. Fig. 13. Particle volume fraction of the powder bed, 𝜙, as a function of the consolidation stress, 𝜎𝑐. Nanosilica content varies from 0 (raw samples) to 0.82wt% for each isotherm series where temperatures ranges from 30◦C to 500◦C. The solid lines represent the fitting according to the equation 𝜙=𝑑+ ln 𝜎𝑐. This parameter has a typical value 𝑑asp ≈ 0.2 μm for most powders [75]. Hence, the granular Bond number may be expressed as: Bo𝑔=3𝐴𝑑asp 20𝜋𝑔𝑧2 0𝜌𝑝𝑑3 𝑝 .(5) According to Eq.(5), powder cohesiveness increases rapidly as particle size decreases. In particular, for the fine limestone powder used in this work (𝑑𝑝= 45 μm)Bo𝑔≈ 1. Thus, the cohesiveness of this powder at low consolidations and ambient temperature is not relevant as observed experimentally. Moreover, it would not be critically affected by the increase of temperature since the van der Waals force increases only weakly with temperature [78] through the Hamaker constant. As seen in Fig. 10, extrapolation of the experimental data to very low consolidations yields accordingly very low values of the tensile yield strength. Moreover, there is not a relevant effect of temperature as expected. However, the tensile yield strength measured in this work, which is an average measure of the interparticle attractive forces, is notably increased as the powder was subjected to larger consolidation stresses. As the powder cohesiveness increases, its flowability reduces which is a serious issue to transport the granular material through the storage unit. This issue would be aggravated as temperature gets closer to the Tamman temperature in limestone (∼ 545 ◦C) [82]. These observations are relevant within the context of the Ca-looping process, where the powder may be subjected to high consolidation stresses during storage at conditions that may involve temperatures on this order or even higher [83]. The experimental results presented above demonstrate that nanosilica coverage serves to mitigate the increase of the powder tensile yield strength with consolidation and temperature, improving the powder flowability. However, Eq.(4) cannot explain the appreciable increase of the tensile yield strength with consolidation and temperature because when interparticle contacts are loaded the adhesion between particles is not determined anymore by the van der Waal force between unloaded particles. It is therefore necessary to assess the physical mechanisms that govern the adhesion between particles under load in order to devise possible solutions to mitigate the augmentation of powder cohesiveness with consolidation and temperature. 4.2. Adhesion force between particles under load The cohesiveness of pre-consolidated powders and, consequently, their flowability is ultimately determined by the microscopic forces required to separate the loaded particles 𝐹𝑡(so-called pull-off or interparticle adhesion force). If the particles are subjected to small loads, the contact is usually elastic [84,85]. In this regime, the imposed external load has no remarkable effect on the adhesion forces. The elastic limit is exceeded when the load force reaches a critical value that depends on the solid physical properties. Then, a region of the solid in the vicinity of the contact point deforms plastically. As the load force is raised above the threshold value, the plastic zone spreads inside the bulk of the solid until, eventually, reaches the contact surface and propagates along it [20]. The interparticle adhesion force in the elastic–plastic regime is determined by the indentation and decohesion stages [20]. During the indentation stage, the solid deforms plastically as the external load force 𝐹𝑐is applied. In the following decohesion stage, it arrives a point at which the attractive force between the solids at contact is overcome. Then, the particles recover their profile when the contact is broken. The critical value of the pull-off force to break the contact 𝐹𝑡depends on the previously applied load force and on the mechanical properties of the solids at contact [86–88]. For a frictionless contact between an elastic–plastic sphere and a rigid flat surface, Mesarovic and Johnson obtained 𝐹𝑡as: 𝐹𝑡=𝑠𝐸𝑃 √𝐹𝑐=𝜆2𝑤𝐸∗ (𝜋𝐻3)1∕2 √𝐹𝑐,(6) Here 𝐻is the solid hardness (when dissimilar materials are at contact the relevant hardness is that of the softer material) [44], 𝑤is the work of adhesion between the solid surfaces defined as the work required to separate two half-spaces to infinity in vacuum (𝑤= 2𝛾 for two surfaces of the same material where 𝛾is the particle surface energy), 𝐸∗denotes the reduced Young’s modulus, 𝐸∗=[1 − 𝜈2 1 𝐸1 +1 − 𝜈2 2 𝐸2]−1 (7) with 𝜈𝑖and 𝐸𝑖the Poisson ratio and the Young’s modulus, respectively, of the solids (𝑖= 1,2) at contact, and 𝜆is a parameter depending on