Cation exchange capacity (CEC) is one of the most important properties of soils. The NH<sub>4</sub>OAc (pH = 7.0) exchange method is usually recommended to determine CEC (CEC<sub>1</sub>) of al...Cation exchange capacity (CEC) is one of the most important properties of soils. The NH<sub>4</sub>OAc (pH = 7.0) exchange method is usually recommended to determine CEC (CEC<sub>1</sub>) of all soils with different pH values, particularly for studies on soil taxonomy. But comparatively the BaCl<sub>2</sub>-MgSO<sub>4</sub> forced-exchange method is more authentic in determining CEC (CEC<sub>2</sub>) of tropical and subtropical highly-weathered acid soils. But so far little is known about the difference between CEC<sub>1</sub> and CEC<sub>2</sub>. In this study, the physiochemical data of 114 acid B horizon soils from 112 soil series of tropical and subtropical China were used, CEC<sub>1</sub> and CEC<sub>2</sub> were determined and compared, the influencing factors were analyzed for the difference between CEC<sub>1</sub> and CEC<sub>2</sub>, and then a regression model was established between CEC<sub>1</sub> and CEC<sub>2</sub>. The results showed that CEC<sub>2</sub> was significantly lower than CEC<sub>1</sub> (p < 0.01), CEC<sub>2</sub> was 14.76% - 63.31% with a mean of 36.32% of CEC<sub>1</sub>. In view of the contribution to CEC from other properties, CEC<sub>2</sub> was mainly determined by pH (45.92%), followed by silt (21.05%), free Fe<sub>2</sub>O<sub>3</sub> (17.35%) and clay contents (12.76%), CEC<sub>1</sub> was mainly decided by free Fe<sub>2</sub>O<sub>3</sub> content (40.38%), followed by pH (28.39%) and silt content (27.29%;and the difference between CEC<sub>1</sub> and CEC<sub>2</sub> was mainly affected by free Fe<sub>2</sub>O<sub>3</sub> (50.92%), followed by silt content (26.46%) and pH (21.80%). The acceptable optimal regression model between CEC<sub>2</sub> and CEC<sub>1</sub> was established as CEC<sub>2</sub> = 2.3114 × CEC<sub>1</sub><sup>1.1496</sup> (R<sup>2</sup> = 0.410, P < 0.001, RMSE = 0.15). For the studies on soil taxonomy, the BaCl<sub>2</sub>-MgSO<sub>4</sub> forced-exchange method is recommended in determining CEC of the highly-weathered acid soils in the tropical and subtropical regions.展开更多
The alkylation mechanism catalyzed by an ionic liquid (as a Lewis acid) may be different from the traditional alkylation mechanism catalyzed by Br nsted acid,especially as their initiation steps are still not clear....The alkylation mechanism catalyzed by an ionic liquid (as a Lewis acid) may be different from the traditional alkylation mechanism catalyzed by Br nsted acid,especially as their initiation steps are still not clear.In this paper,an isotope exchange method is used to investigate the catalytic mechanism of AlCl 3 /butyl-methyl-imidazolium chloride ionic liquid in the alkylation of benzene with 1-dodecene.The proposed catalytic mechanism was confirmed by analysis of ionic liquid before and after reaction and of the alkylation products of deuterated benzene (C 6 D 6) with 1-dodecene.The proposed mechanism consists of the equilibrium reaction between [Al 2 Cl 7 ] +H + and [AlHCl 3 ] + +[AlCl 4 ],in which the Br nsted acid [AlHCl 3 ] + is supplied by the reaction of 2-H on the imidazolium ring and [Al 2 Cl 7 ].The alkylation reaction is initiated by the Br nsted acid [AlHCl 3 ] + which reacts with 1-dodecene to form a carbonium ion,then the carbonium ion reacts with benzene to form an unstable σ complex,leading to the formation of 2-phenyldodecane.展开更多
Ag/AgCl/TiO^(2)nanocomposite was synthesized through the combination of sol-gel process and hydrothermal(HT)method followed by ion exchange method in the paper.Transmission electron microscope,UVevis absorption proper...Ag/AgCl/TiO^(2)nanocomposite was synthesized through the combination of sol-gel process and hydrothermal(HT)method followed by ion exchange method in the paper.Transmission electron microscope,UVevis absorption property and X-ray diffraction were utilized to characterize the morphology,optical absorption property and phase structure of the as-prepared photocatalysts.The morphological and performance studies of Ag/AgCl/TiO^(2)revealed that a well-interconnected mixed phase heterojunction photocatalyst was achieved through as-prepared TiO^(2)and the subsequent ion exchange method.By the degradation of Rhodamine B under xenon lamp,Ag/AgCl/TiO^(2)exhibited a significant enhancement in photocatalytic activity compared with TiO^(2)and Ag/TiO^(2).The band gap of Ag/AgCl/TiO^(2)can reach to 2.53eV compared with 3.22eV of the prepared TiO^(2).Furthermore,the synthesis process and photoreaction mechanisms of TiO^(2),Ag/TiO^(2)and Ag/AgCl/TiO^(2)photocatalysts were proposed.It demonstrated that the enhancement of photocatalytic was mainly due to the reducing of electron-hole recombination in Ag/AgCl/TiO^(2).展开更多
In this paper the self-regeneration process of the mixed resins consisting of cationand anion ion exchangers in the electrolialyser of the packed bed is analyzed and anelectric regeneration method is put forward to su...In this paper the self-regeneration process of the mixed resins consisting of cationand anion ion exchangers in the electrolialyser of the packed bed is analyzed and anelectric regeneration method is put forward to supply the desalinated water by mixedbed The electric regeneration technology is a new one used for regeneration of theexhausted ion exchangers in the mixed bed instead of the traditional regeneratingprocess by using acid and abc liquor Electric energy is consumed to regenerat theion exchangers loaded by salts from water treatment without any chemicals- acid alkali. The advantage of the electric regeneration process edibited convenientoperation, no discharge any waste, and therefore no Polluted to the recehang waterbode and the environmental ground展开更多
Rockfalls in reservoirs are prone to induce surges, posing a severe threat to passing vessels and facilities. A scheme combined Single-phase freesurface method(SPF), momentum exchange method(MEM), and Lattice Boltzman...Rockfalls in reservoirs are prone to induce surges, posing a severe threat to passing vessels and facilities. A scheme combined Single-phase freesurface method(SPF), momentum exchange method(MEM), and Lattice Boltzmann method(LBM) is proposed to predict the impact of rockfall-induced surges. First, the LBM-SPF model is used to simulate the motion of the free surface, and the MEM model is used to calculate the hydrodynamic force acting on rock mass. To address the incompatibility issue arising from the coupling of LBM-SPF model and MEM model, a correction scheme inside the solid is induced. The simulation results of the single particle and double particle sedimentation in cavity show the feasibility and accuracy of the method designed in this paper. Moreover, the validation experiments of Scott Russel’s wave generator show that the proposed scheme can simulate wave profile stably. The simulation results emphasize that the waves induced by rockfalls have a significant impact on the safe operation of the Laxiwa dam and the passing vessels in the reservoir.展开更多
Photocatalytic ammonia generation via nitrogen reduction reaction(NRR)is a green and prospective nitrogen fixation technique.However,NRR is often hampered by the high N_(2) adsorption/activation energies and is accomp...Photocatalytic ammonia generation via nitrogen reduction reaction(NRR)is a green and prospective nitrogen fixation technique.However,NRR is often hampered by the high N_(2) adsorption/activation energies and is accompanied by a slow kinetics oxygen evolution reaction(OER).Herein,a robust Bi_(2)S_(3)/OVBi_(2)MoO_(6)S-scheme heterojunction is constructed using a simple in-situ anion exchange process,which enables oxygen vacancy(OVs)abundant Bi_(2)Mo O_(6) microspheres with surface deposited Bi_(2)S_(3).The asfabricated Bi_(2)S_(3)/OVBi_(2)MoO_(6) functioned as an effective photocatalyst to convert N_(2)-to-NH_(3) under mild conditions.The photocatalytic NH_(3)/NH_(4)^(+) production rate reached 126μmol g_(cat)^(-1)under visible light for2.5 h with 2%of Bi_(2)S_(3)/OVBi_(2)MoO_(6)photocatalyst,which was 8-fold higher than pristine Bi_(2)MoO_(6).Furthermore,the as-fabricated Bi_(2)S_(3)/Bi_(2)MoO_(6)heterojunction exhibited good selectivity,high stability and reproducibility.The excellent photocatalytic NRR performance was ascribed to the Bi_(2)S_(3)/Bi_(2)MoO_(6)heterojunction formed subsequent to the strong interaction between Bi_(2)S_(3)and Bi_(2)MoO_(6).The OVs facilitated the chemical adsorption process allowing activation of N_(2)molecule on the Bi_(2)S_(3)/Bi_(2)MoO_(6).Simultaneously,the S-scheme heterojunction prolonged the lifetime of photogenerated carriers,accelerated the electrons/holes spatial separation and accumulation on the Bi_(2)S_(3)(reduction)and Bi_(2)MoO_(6)side(oxidation),respectively,thus strengthening both OER and NRR half-reactions.This simple in-situ anion exchange method offers a novel technique for strengthening OER and NRR half-reactions in Bi-based photocatalysts for effective photocatalytic ammonia generation.展开更多
This paper presents the study of the flow structure and heat transfer,and also their correlations on the four walls of a radial cooling passage model of a gas turbine blade.The investigations focus on heat transfer an...This paper presents the study of the flow structure and heat transfer,and also their correlations on the four walls of a radial cooling passage model of a gas turbine blade.The investigations focus on heat transfer and aerodynamic measurements in the channel,which is an accurate representation of the configuration used in aeroengines.Correlations for the heat transfer coefficient and the pressure drop used in the design of radial cooling passages are often developed from simplified models.It is important to note that real engine passages do not have perfect rectangular cross sections,but include coiner fillet,ribs with fillet radii and special orientation.Therefore,this work provides detailed fluid flow and heat transfer data for a model of radial cooling geometry which possesses very realistic features.展开更多
Gas chromatography equipped with an electron capture detector (GC-ECD) has been widely used for measuring atmospheric N2O,but nonlinear response and the influence of atmospheric CO2 have been recognized as defects f...Gas chromatography equipped with an electron capture detector (GC-ECD) has been widely used for measuring atmospheric N2O,but nonlinear response and the influence of atmospheric CO2 have been recognized as defects for quantification.An original GCECD method using N 2 as carrier gas was improved by introducing a small flow rate of CO2 makeup gas into the ECD,which could well remedy the above defects.The N2O signal of the improved method was 4-fold higher than that of the original method and the relative standard deviation was reduced from 〉 1% to 0.31%.N2O concentrations with different CO2 concentrations (172.2×10-6-1722×10-6mol/mol) measured by the improved GC-ECD method were in line with the actual N2O concentrations.However,the N2O concentrations detected by the original method were largely biased with a variation range of-4.5%~7%.The N2O fluxes between an agricultural field and the atmosphere measured by the original method were greatly overestimated in comparison with those measured by the improved method.Good linear correlation (R2=0.9996) between the response of the improved ECD and N2O concentrations (93×10-9-1966×10-9mol/mol) indicated that atmospheric N2O could be accurately quantified via a single standard gas.Atmospheric N2O concentrations comparatively measured by the improved method and a high precision GC-ECD method were in good agreement.展开更多
A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximat...A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.展开更多
The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed (DL-FB). Power spectrum density (PSD) analysis was applied to obtai...The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed (DL-FB). Power spectrum density (PSD) analysis was applied to obtain the dominant frequency (F) of the simulated differential particle number (APLR) between the two half beds. Effects of fluidization velocity (u) and bed material inventory (H) on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.展开更多
文摘Cation exchange capacity (CEC) is one of the most important properties of soils. The NH<sub>4</sub>OAc (pH = 7.0) exchange method is usually recommended to determine CEC (CEC<sub>1</sub>) of all soils with different pH values, particularly for studies on soil taxonomy. But comparatively the BaCl<sub>2</sub>-MgSO<sub>4</sub> forced-exchange method is more authentic in determining CEC (CEC<sub>2</sub>) of tropical and subtropical highly-weathered acid soils. But so far little is known about the difference between CEC<sub>1</sub> and CEC<sub>2</sub>. In this study, the physiochemical data of 114 acid B horizon soils from 112 soil series of tropical and subtropical China were used, CEC<sub>1</sub> and CEC<sub>2</sub> were determined and compared, the influencing factors were analyzed for the difference between CEC<sub>1</sub> and CEC<sub>2</sub>, and then a regression model was established between CEC<sub>1</sub> and CEC<sub>2</sub>. The results showed that CEC<sub>2</sub> was significantly lower than CEC<sub>1</sub> (p < 0.01), CEC<sub>2</sub> was 14.76% - 63.31% with a mean of 36.32% of CEC<sub>1</sub>. In view of the contribution to CEC from other properties, CEC<sub>2</sub> was mainly determined by pH (45.92%), followed by silt (21.05%), free Fe<sub>2</sub>O<sub>3</sub> (17.35%) and clay contents (12.76%), CEC<sub>1</sub> was mainly decided by free Fe<sub>2</sub>O<sub>3</sub> content (40.38%), followed by pH (28.39%) and silt content (27.29%;and the difference between CEC<sub>1</sub> and CEC<sub>2</sub> was mainly affected by free Fe<sub>2</sub>O<sub>3</sub> (50.92%), followed by silt content (26.46%) and pH (21.80%). The acceptable optimal regression model between CEC<sub>2</sub> and CEC<sub>1</sub> was established as CEC<sub>2</sub> = 2.3114 × CEC<sub>1</sub><sup>1.1496</sup> (R<sup>2</sup> = 0.410, P < 0.001, RMSE = 0.15). For the studies on soil taxonomy, the BaCl<sub>2</sub>-MgSO<sub>4</sub> forced-exchange method is recommended in determining CEC of the highly-weathered acid soils in the tropical and subtropical regions.
基金financial support from the National Natural Science Foundation of China (NSFC,2052010)
文摘The alkylation mechanism catalyzed by an ionic liquid (as a Lewis acid) may be different from the traditional alkylation mechanism catalyzed by Br nsted acid,especially as their initiation steps are still not clear.In this paper,an isotope exchange method is used to investigate the catalytic mechanism of AlCl 3 /butyl-methyl-imidazolium chloride ionic liquid in the alkylation of benzene with 1-dodecene.The proposed catalytic mechanism was confirmed by analysis of ionic liquid before and after reaction and of the alkylation products of deuterated benzene (C 6 D 6) with 1-dodecene.The proposed mechanism consists of the equilibrium reaction between [Al 2 Cl 7 ] +H + and [AlHCl 3 ] + +[AlCl 4 ],in which the Br nsted acid [AlHCl 3 ] + is supplied by the reaction of 2-H on the imidazolium ring and [Al 2 Cl 7 ].The alkylation reaction is initiated by the Br nsted acid [AlHCl 3 ] + which reacts with 1-dodecene to form a carbonium ion,then the carbonium ion reacts with benzene to form an unstable σ complex,leading to the formation of 2-phenyldodecane.
基金the National Natural Science Foundation of China under Grant No.51762028 and No.11504146.
文摘Ag/AgCl/TiO^(2)nanocomposite was synthesized through the combination of sol-gel process and hydrothermal(HT)method followed by ion exchange method in the paper.Transmission electron microscope,UVevis absorption property and X-ray diffraction were utilized to characterize the morphology,optical absorption property and phase structure of the as-prepared photocatalysts.The morphological and performance studies of Ag/AgCl/TiO^(2)revealed that a well-interconnected mixed phase heterojunction photocatalyst was achieved through as-prepared TiO^(2)and the subsequent ion exchange method.By the degradation of Rhodamine B under xenon lamp,Ag/AgCl/TiO^(2)exhibited a significant enhancement in photocatalytic activity compared with TiO^(2)and Ag/TiO^(2).The band gap of Ag/AgCl/TiO^(2)can reach to 2.53eV compared with 3.22eV of the prepared TiO^(2).Furthermore,the synthesis process and photoreaction mechanisms of TiO^(2),Ag/TiO^(2)and Ag/AgCl/TiO^(2)photocatalysts were proposed.It demonstrated that the enhancement of photocatalytic was mainly due to the reducing of electron-hole recombination in Ag/AgCl/TiO^(2).
文摘In this paper the self-regeneration process of the mixed resins consisting of cationand anion ion exchangers in the electrolialyser of the packed bed is analyzed and anelectric regeneration method is put forward to supply the desalinated water by mixedbed The electric regeneration technology is a new one used for regeneration of theexhausted ion exchangers in the mixed bed instead of the traditional regeneratingprocess by using acid and abc liquor Electric energy is consumed to regenerat theion exchangers loaded by salts from water treatment without any chemicals- acid alkali. The advantage of the electric regeneration process edibited convenientoperation, no discharge any waste, and therefore no Polluted to the recehang waterbode and the environmental ground
基金supported by the National Natural Science Foundation of China (Nos.41902290,42007276,41972297)Program of Hundred Promising Innovative Talents in Hebei provincial education office (No.SLRC2019027)Natural Science Foundation of Hebei Province (Nos.D2020202002,D2021202001)。
文摘Rockfalls in reservoirs are prone to induce surges, posing a severe threat to passing vessels and facilities. A scheme combined Single-phase freesurface method(SPF), momentum exchange method(MEM), and Lattice Boltzmann method(LBM) is proposed to predict the impact of rockfall-induced surges. First, the LBM-SPF model is used to simulate the motion of the free surface, and the MEM model is used to calculate the hydrodynamic force acting on rock mass. To address the incompatibility issue arising from the coupling of LBM-SPF model and MEM model, a correction scheme inside the solid is induced. The simulation results of the single particle and double particle sedimentation in cavity show the feasibility and accuracy of the method designed in this paper. Moreover, the validation experiments of Scott Russel’s wave generator show that the proposed scheme can simulate wave profile stably. The simulation results emphasize that the waves induced by rockfalls have a significant impact on the safe operation of the Laxiwa dam and the passing vessels in the reservoir.
基金financially supported by the National Natural Science Foundation of China(Nos.22168040,21666039,21663030)the Open Project of State Key Laboratory of Organic-Inorganic Composites Beijing Key Laboratory,Beijing University of Chemical Technology Beijing(No.oic-201901009)+3 种基金the Project of Science&Technology Office of Shaanxi Province(Nos.2018TSCXL-NY-02–01,2020JQ-791)the Project of Yan’an Science and Technology Bureau(No.2018KG-04)the Graduate Innovation Project of Yan’an University(No.YCX2020005)the Open Project of Chongqing Key Laboratory of Inorganic Special Functional Materials,Yangtze Normal University(No.KFKT202001)。
文摘Photocatalytic ammonia generation via nitrogen reduction reaction(NRR)is a green and prospective nitrogen fixation technique.However,NRR is often hampered by the high N_(2) adsorption/activation energies and is accompanied by a slow kinetics oxygen evolution reaction(OER).Herein,a robust Bi_(2)S_(3)/OVBi_(2)MoO_(6)S-scheme heterojunction is constructed using a simple in-situ anion exchange process,which enables oxygen vacancy(OVs)abundant Bi_(2)Mo O_(6) microspheres with surface deposited Bi_(2)S_(3).The asfabricated Bi_(2)S_(3)/OVBi_(2)MoO_(6) functioned as an effective photocatalyst to convert N_(2)-to-NH_(3) under mild conditions.The photocatalytic NH_(3)/NH_(4)^(+) production rate reached 126μmol g_(cat)^(-1)under visible light for2.5 h with 2%of Bi_(2)S_(3)/OVBi_(2)MoO_(6)photocatalyst,which was 8-fold higher than pristine Bi_(2)MoO_(6).Furthermore,the as-fabricated Bi_(2)S_(3)/Bi_(2)MoO_(6)heterojunction exhibited good selectivity,high stability and reproducibility.The excellent photocatalytic NRR performance was ascribed to the Bi_(2)S_(3)/Bi_(2)MoO_(6)heterojunction formed subsequent to the strong interaction between Bi_(2)S_(3)and Bi_(2)MoO_(6).The OVs facilitated the chemical adsorption process allowing activation of N_(2)molecule on the Bi_(2)S_(3)/Bi_(2)MoO_(6).Simultaneously,the S-scheme heterojunction prolonged the lifetime of photogenerated carriers,accelerated the electrons/holes spatial separation and accumulation on the Bi_(2)S_(3)(reduction)and Bi_(2)MoO_(6)side(oxidation),respectively,thus strengthening both OER and NRR half-reactions.This simple in-situ anion exchange method offers a novel technique for strengthening OER and NRR half-reactions in Bi-based photocatalysts for effective photocatalytic ammonia generation.
基金funding from the European Union Seventh Framework Programme(FP7/2007-2013) under Grant Agreement No. 233799(ERICKA)
文摘This paper presents the study of the flow structure and heat transfer,and also their correlations on the four walls of a radial cooling passage model of a gas turbine blade.The investigations focus on heat transfer and aerodynamic measurements in the channel,which is an accurate representation of the configuration used in aeroengines.Correlations for the heat transfer coefficient and the pressure drop used in the design of radial cooling passages are often developed from simplified models.It is important to note that real engine passages do not have perfect rectangular cross sections,but include coiner fillet,ribs with fillet radii and special orientation.Therefore,this work provides detailed fluid flow and heat transfer data for a model of radial cooling geometry which possesses very realistic features.
基金supported by the Special Fund for Environmental Research in the Public Interest(No.201009001)the National Natural Science Foundation of China(No.41075094,21177140 and 40830101)the National Basic Research and the Development Program(973)of China(No.2010CB732304)
文摘Gas chromatography equipped with an electron capture detector (GC-ECD) has been widely used for measuring atmospheric N2O,but nonlinear response and the influence of atmospheric CO2 have been recognized as defects for quantification.An original GCECD method using N 2 as carrier gas was improved by introducing a small flow rate of CO2 makeup gas into the ECD,which could well remedy the above defects.The N2O signal of the improved method was 4-fold higher than that of the original method and the relative standard deviation was reduced from 〉 1% to 0.31%.N2O concentrations with different CO2 concentrations (172.2×10-6-1722×10-6mol/mol) measured by the improved GC-ECD method were in line with the actual N2O concentrations.However,the N2O concentrations detected by the original method were largely biased with a variation range of-4.5%~7%.The N2O fluxes between an agricultural field and the atmosphere measured by the original method were greatly overestimated in comparison with those measured by the improved method.Good linear correlation (R2=0.9996) between the response of the improved ECD and N2O concentrations (93×10-9-1966×10-9mol/mol) indicated that atmospheric N2O could be accurately quantified via a single standard gas.Atmospheric N2O concentrations comparatively measured by the improved method and a high precision GC-ECD method were in good agreement.
基金supported by Hong Kong Research Grants Council General Research Fund (Grant Nos. 403513 and 14302515)
文摘A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.
基金the support provided by the National Science and Technology Support Program of China(No.2012BAA02B00)
文摘The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed (DL-FB). Power spectrum density (PSD) analysis was applied to obtain the dominant frequency (F) of the simulated differential particle number (APLR) between the two half beds. Effects of fluidization velocity (u) and bed material inventory (H) on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.