literature Cited Operating Conditions for BrF6 Fluorination Step 300 Fluid bed temp., ’ C. 0.29 (BrFb in Nz) Initial BrF5 concentration, atm. 0.89 Superficial gas velocity, ft./sec. 4.4 U O Zcharge, kg. -100 or 48 to 100 Alumina particle size, mesh Fission products Present or absent
operating conditions which are not necessarily considered optimum. For this fluid-bed fluoride volatility process to reach production scale, further engineering-scale experiments o n fuels containing plutonium and radioactive fission products would have to be conducted. The results of this current study are considered highly acceptable for actual process application.
Anastasia, L. J., Alfredson, P. G., Redding, G. W., Haas, M., “Fluorination of U02-Pu02-Fission Product Pellets in a 2-Inch Diameter Reactor,” Chemical Engineering Division, U. S. Atomic Energy Commission, Rept. ANL-7325 (July-December 1966). Anderson, J. S., Bull. SOC.Chim. France 20, 781 (1953). Chilenskas, A. A., Gunderson, G. E., “Corrosion of Nickel in Process Environments,” U . S. Atomic Energy Commission, Rept. ANL-6979 (1966). Davies, 0. L., “Design and Analysis of Industrial Experiments,” Hafner, New York, 1954. Gabor, J. D., Ramaswami, D., “Exploratory Tests on Fluorination of Uranium Oxide with BrF, in a Bench-Scale Fluid Bed Reactor System,” U. S. Atomic Energy Commission, Rept. ANL-7362 (1967). Holmes, J. T., Koppel, L. B., Saratchandran, N., Strand, J., Ramaswami, D., “Pilot Plant Studies on Fluorinating Uranium Oxide with Bromine Pentafluoride.” U. S. Atomic Enerrrv -. Commission, Rept. ANL-7370 (1968j. Jarry, R. L., Steindler, M. J., J . Inorg. Nucl. Chem. 30, 127 (1968). RECEIVED for review February 14, 1968 ACCEPTEDApril 29, 1968
Acknowledgment
T h e authors thank J. B. Strand, C. B. Schoffstoll, and N. Saratchandran for their expert aid in operating the equipment.
Work performed under the auspices of the U. S. Atomic Energy Commission.
SECONDARY CELLS WITH LITHIUM ANODES AND IMMOBILIZED FUSED-SALT ELECTROLYTES H l R O S H l S H I M O T A K E , GEORGE L. ROGERS, AND ELTON J. Argonne National Laboratory, 9700 South Cass Ave., Argonne, Ill. 60439
CAIRNS
Secondary cells with a liquid-lithium anode, a fused LiF-LiCI-Lil eutectic electrolyte immobilized as a rigid paste, and a liquid bismuth or tellurium cathode have been investigated in both the discharge and charge modes of operation. The lithium/bismuth cell operating from 3 8 0 ” to 485’ C. yielded current densities up to 2.2 amperes per sq. cm., and a maximum power density of 0.57 watt per sq. cm. at 0.6 volt. The cell contained an amount of lithium equivalent to 0.25 amp.-hr.; the fully discharged cathode alloy composition was 41 atom % Li in Bi. The lithium/tellurium cell operating at 475” C. yielded a short-circuit density of 2.2 amperes per sq. cm., and a maximum power density of 1 watt per sq. cm. at 0.9 volt. This cell contained an amount of lithium equivalent to 6.36 amp.-hr.; the fully discharged cathode alloy composition was 71.6 atom 7 0 Li in Te. These performances suggest many applications, including special vehicle propulsion and energy storage.
ODAY’S rapidly advancing technology requires a wide specTtrum of power sources and energy-storage devices. I n many applications, the power sources must have a minimum size or weight per unit of power or energy. These requirements have motivated a great deal of the recent work on high-specificenergy (watt-hours per pound) and high-specific-power (watts per pound) secondary cells. T h e maximization of the specific energy requires that reactants of low equivalent weight and high free energy of reaction be used. For high-specific-energy (>50 watt-hours per pound) cells with aqueous electrolytes, zinc and cadmium have served as anode materials, while nickel oxide, silver oxide, and oxygen (or air) have served as cathode materials (Jasinski, 1967; Moos and Palmer, 1967;
Seiger et al., 1967). The elimination of water from the electrolyte permits more reactive metals such as calcium and the alkali metals to be considered as anode materials. The very low equivalent weight and low electronegativity of lithium make it particularly attractive as an anode material for highspecific-energy cells. A number of cathode materials have been used in combination with nonaqueous electrolytes and lithium anodes, depending on the operating temperature and the electrolyte. Lithium-anode cells designed for operation at room temperature use nonaqueous electrolytes composed of solutions of inorganic salts such as LiaPF4 or LiC104 dissolved in organic solvents such as propylene carbonate or dimethyl sulfoxide ; VOL. 8
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10'
Equivalent Weight,, p r lEguivolent
' '
@!
Figure 1. Relationship between theoretical specific energy a n d equivalent weight
Figure 3.
I t s -
-
-.
Figure 2.
Lithi
Enouoh cell oartr to make
(I
two -cell battery shown
the c athodes are usually metal h.alides such as NiF2, CuF2, . .. or &til (Jamski, 1 Y O I ; belger et al., 1967). Although these cells can supply over 100 watt-hour .~per pound at low discharge rates, their specific power is low (2 to 20 watts per .I 4"L?\ & I . : . LW,,, M I L L L I I ~ ~ LLXCLL pound) (Jasinski, 1967; Seiger et ab., range of applicability. The specific power for cells with organic-solvent electrolytes is low because of the low conohm-' cm.-'). ductivity of the electrolyte (The use of fused salts as electrolytes provides very hig-h conductivities (1 to 4 ohm" cm.?), allowing specific powers in excess of 100 watts per pound to be achieved (Cairns and Shimotake, 1967; Rightmire and Jones, 1967; Shimotake and Cairns, 1967b; Shimotake et el., 1967; Wilcox, 1967). Because of their relatively high melting points, fused-salt electrolytes require elevated operating temperatures (260' to 650° C , ) , A number of secondary cells with fused-salt electrolytes have been investigated, including sodium/bismuth (Shimotake and Cairns, 1967a), lithium/chlorine (Rightmire and Jones, 1967; Wilcox, 1967), lithium/tellurium (Cairns and Shimotake, 1967; Shimotake and Cairns, 1967b; Shimotake et al., 1967), and li~ium/selenium(Shimotake and Cairns, 1968), all using free liquid electrolytes. The theoretical maximum specific energies of some couples
-.,-
52
Lithium/tellurium cell
Upper. Assembled Lower. Parts
.^,_- .
l&EC PROCESS DESIGN A N D DEVELOPMENT
suitable for use with fused-salt electrolytes are given in Figure 1, where the specific energy (calculated from the equivalent weight of the cell products indicated and the average e.m.f. of the couple) is plotted against the equivalent weight of the active material. Usually, the higher specific energy materials are idle from a corrosion viewpoint. more to A great deal of d.esign flexibility and compactness can he gained by immobilii:ing the fused-salt electrolyte either in an absorbent matrix or in the farm of a rigid paste (Baker et al., 1965: Broers and Sr ~. - ~ h e n k e ,1963; Tantramet ol., 1965). This work deals with secondarv cells havinq liquid lithium anodes, liquid bismuth or tellurium cathodes, amd fused lithium halide :lectrolytes immobilized as a rigid pasti2, operating in the range 380' to 485' C. ~~
1
~~
~
~
Experimental Typical lithium/bismuth and lithium/tellurium cells are shown in Fig-ures 2 and 3. The cell housing in Figure 2 was made from Type 316 stainless steel; the electrode compartments were 3.2 mm. deep, and had four concentric fins which served as current collectors. The exposed electrolyte area was 1.98 sq. cm., and the paste electrolyte thickness was 0.34 cm. Prior to assembly, the anode compartment was loaded with 0.064 gram of lithium (Foote Mineral Co., 0.003'% Na, 0.003Y0 K, 0.003Y0 Cl, surface oxide removed), and heated to 530' C. to ensure good wetting of the current collector. The cathode compartment contained 2.764 grams of bismuth (United Mineral and Chemical Corp., 99.999% minimum purity). These amounts of reactants correspond to a cathode-alloy composition of 41
FILLER,HOT PRESS
I
CURRENT DENSITY, AMPS/CM~ Figure 4.
Voltage-current density curves for lithium/bisrnuth cell
atom yo Li in Bi a t complete discharge, and a cell capacity of 0.25 ampere-hour. The cell was prepared and assembled under a high-purity helium atmosphere (Johnson et al., 1967). KO gaskets were used ; the smooth-surfaced electrolyte disk provided a leak-tight seal against the cell housing. The lithium/tellurium cell, made of pure iron, had current collectors consisting of sheets of sintered porous stainless steel in the anode compartment, and a network of pure-iron wires in the cathode compartment in place of the meshes shown in Figure 3. The exposed electrolyte area was 3.25 sq. cm.; the electrolyte thickness was 0.32 cm. The cell compartments were loaded with 0.75 gram of lithium and 5.45 grams of tellurium (American Smelting and Refining Co., 99.99970 minimum purity) corresponding to 71.6 atom 7 0 Li in T e a t complete discharge. The electrolyte was the ternary eutectic composed of 11.7 LiCl, and 59.2 mole % LiI, which mole 70LiF, 29.1 mole melts at 340.9' C. and has a specific conductance of 2.3 ohm-' cm.-l a t 375' C. and 3.0 ohm-l cm.-' at 475' C. (Johnson, 1968). The eutectic was prepared from weighed amounts of the pure salts, LiF, LiC1, and LiI, all supplied by Anderson Physics Laboratories, Inc. After the components had melted together to form the eutectic, the electrolyte was solidified, pulverized to -300 mesh, and mixed (1 to 1 weight ratio) with an inert filler material. The electrolyte-filler powder mixture was then molded into disks. For the Li/Bi cell, disks 1.85 cm. in diameter were prepared by pressing the electrolyte-filler powder first a t room temperature to form "cold-pressed" disks, and then a t 400' C. for final densification. All operations except the hot-pressing were carried out in a pure helium atmosphere. For the Li/Te cell, disks 2.5 cm. in diameter were pressed at room temperature and sintered a t 400' C. without pressing; this eliminated all exposure to air. The paste electrolyte has a continuous phase of fusedlithium halide eutectic at the cell operating temperature. The relative amounts of finely divided inert filler and lithium halide are chosen such that the electrolyte fills the interstitial spaces among the very small filler particles, and holds the paste firmly by means of its high surface tension, low contact angle with the filler, and the small pore size of the paste. Similar paste electrolytes have been used with success in molten-
carbonate fuel cells (Baker et al., 1965; Broers and Schenke, 1963; Tantram et al., 1965). Cell performance was measured with the aid of a constantcurrent d.c. power supply, precision voltmeters and ammeters (0.25%), and a strip-chart recorder. The voltage-current density curves for the discharge mode of operation were measured starting with the cell in the fully charged condition; the curves for the charge mode of operation were usually measured from the fully discharged condition. All results are reported on a resistance-included basis. The cells were held a t operating temperature in an electrically heated tube furnace. Results and Discussion
The voltage-current density curves for the Li/Bi cell operating a t 380°, 453', and 485' C. are shown in Figure 4. As might be expected, the highest performance in both charge and discharge modes was obtained at the highest temperature. Current densities up to 2.2 amperes per sq. cm. were obtained, based on the effective electrode area of 1 sq. cm. (the electrode compartments were only about half-filled with active materials during these experiments). Since the cathode composition during the discharge experiments averaged about 5 atom % Li (Foster et al., 1964), these performances are typical of those obtainable near the beginning of the plateau of the corresponding voltage-time curves at constant-current discharge. The maximum power density at 485' C. was 0.57 watt per sq. cm. at 0.6 volt. The slopes of the charge and discharge curves in Figure 4 are different because of the difference in state of charge for the two modes of operation. The internal resistance of the cell is expected to be lower for the discharge curves because most of the original amount of lithium was still in the anode compartment when the discharge data were taken. During the charging experiments, however, almost no lithium was present in the lithium compartment, resulting in a relatively high internal resistance. When charge and discharge curves are taken under VOL.
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I
I
1
-
I
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Li/Li*/Li in Te (I) ANODE AREA 325 CM' CATHODE AREA 3.25 CM' INTERELECTROM DISTANCE 0 . 3 2 CM CAPACITY 2.91 AH TEMPERATURE 475.C PASTE ELECTROLYTE 50 .k FILLER COLD PRESS-
-
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-
-
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D ISCHARGE
CHARGE
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04-
3
.2--
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identical conditions, the curves have the same slope. The internal resistance of the cell at high current densities was 0.45 ohm at 485' C., compared to 0.23 ohm calculated from the specific conductance of the electrolyte and a paste-to-pure electrolyte resistivity ratio of 2 (Broers and Schenke, 1963; Tantrum et al., 1965). This discrepancy could be caused by the presence of some Liz0 resulting from hydrolysis of the lithium halides during hot-pressing or incomplete wetting of the paste by lithium. From the reasonably high current density capabilities of the Li/Bi cell of Figure 4, it is clear that the cell can be fully charged from complete discharge in about 15 minutes. The performance characteristics of the (larger) Li/Te cell operating at 475' C. are shown in Figure 5 . As expected on the basis of the e.m.f. measurements of Foster and Liu (1966) and earlier experience with Li/Te cells (Cairns and Shimotake, 1967; Shimotake and Cairns, 1967b; Shimotake et al., 1967), the open circuit voltage was 1.7 to 1.8 volts, and the voltagecurrent density curves were straight lines, indicating the absence of any significant concentration or activation overvoltages. The short-circuit current density was 2.2 amperes per sq. cm., and the maximum power density was 1 watt per sq. cm. a t 0.9 volt, a considerable improvement in power density over the Li/Bi cell. The internal resistance of the Li/Te cell during discharge was 0.24 ohm, compared to 0.065 ohm calculated from the electrolyte conductivity and a paste-to-pure electrolyte resistivity ratio of 2. The ratio of observed-to-calculated cell resistance is higher for the Li/Te cell than for the Li/Bi cell, possibly because the paste electrolyte disk for the Li/Te cell was not hot-pressed, and therefore probably contained voids which increased the resistivity of the paste. The Li/Te cell, with a capacity of 2.91 ampere-hours, could be fully charged from complete discharge in less than half an hour. This is a much higher charge rate than can be used with secondary cells having aqueous electrolytes or cells with nonaqueous organic solvent electrolytes. Extensive investigations of constant-current charge and dis54
I & E C PROCESS D E S I G N AND D E V E L O P M E N T
0
2
I
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3
Data for Battery Design Calculations Li/Bi Li/Te Open-circuit voltage, volts 0.8 1.75 Short-circuit current density, amp./sq. cm. For electrolyte thickness 1.8 2.2 0.3 cm. 6.1 7 .O 0.1 cm. Cathode alloy, fully discharged Composition, atm. yo Li 70 60 4.4 3.3 Density, g./cc. Anode metal density, g./cc. 0.53 0.53 100 100 Current efficiency, 0.1 0.1 Cell partition thickness, cm./cell Density of housing material, g./cc. 7.8 7.8 Density of paste electrolyte, g./cc. 3.0 3.0 Weight allowance for framing, terminals, etc., % ' (electrolyte partition weight) 50 50 Table 1.
+
charge characteristics, charge retention, and cycle life still remain to be done. The data presented above were interesting enough, however, to stimulate some preliminary design calculations based upon the voltage-current density curves of Figures 4 and 5. The principles, equations, and sample calculations involved in the design of secondary batteries have been discussed (Shimotake and Cairns, 1967b) ; therefore, no detailed explanations are given here. The most important parameter in many applications is battery weight; therefore, the energy and power values are expressed per unit weight as specific energy (watt-hours per pound) and specific power (watts per pound). The calculation of battery weight involves the selection of the ratio of reactant weights, and the calculation of the weights of reactants, electrolyte, cell housing, terminals, etc., required per unit of active cell area. The specific power available is calculated from the current density-voltage curve and the battery weight per unit active area. The specific energy is calculated from the average cell operating voltage, the amount of lithium per unit of active cell area, and the battery weight per unit of active area (Shimotake and Cairns, 1967b). The values used in these calculations are summarized in Table I.
I
1
1
1
1
I
1 1 1 1
1”. 0.32cm
I
/
I
I l 1 1 l
I
I
I
1
t“. 0.1cm
’
IOZ
ENERGY
I l l
TELLURIUM
IO
SPECIFIC
Figure 6.
I
I
LITHIUM
,
wall-hr/lb
Specific power-specific energy curves for some secondary batteries
The results of the design calculations for Li/Bi and Li/Te secondary batteries are shown in Figure 6. Because of the lower equivalent weight and higher electronegativity, the Li/Te cell has higher specific energy and specific power capabilities than the Li/Bi cell. As a n example, Figure 6 shows that for the 30-minute discharge rate, a Li/Bi cell having three cells per inch and a n electrolyte thickness of 0.32 cm. has a specific power of 43 watts per pound and a specific energy of 21 watt-hours per pound, whereas the Li/Te cell of similar dimensions can attain 110 watts per pound and 55 watt-hours per pound. The design analysis results presented in Figure 6 also indicate that if the electrolyte thickness is decreased to 0.1 cm., it is possible to achieve 90 watts per pound and 45 watthours per pound for the Li/Bi cell and 200 watts per pound and 110 watt-hours per pound for the Li/Te cell. The performances of some other types of secondary batteries including lead-acid, nickel-cadmium, and sodium/sulfur, are presented in Figure 6 for comparison. Possible applications for secondary cells with the characteristics of the Li/Te cell include space power sources, military communications power sources, military vehicle propulsion, and perhaps special commercial vehicle propulsion (Cairns and Shimotake, 1967). The areas which deserve further attention in the development of Li/Bi and Li/Te cells include the optimization of paste electrolyte properties (particularly the resistivity), current collection, corrosion, cycle life, and thermal cycling. Conclusions
I t is possible to form acceptable paste electrolytes from fused lithium halides and inert filler materials. The paste electrolytes now show two to three times the expected electrolytic resistivities. Lithium/bismuth and lithium/tellurium cells operating with
lithium halide paste electrolytes can operate at power densities of 0.57 and 1.0 watt per sq. cm., respectively, at about 480’ C. These cells can be charged at very high rates (less than 30 minutes), making them candidates for many applications where fast recharge is important. Design calculations indicate that the Li/Te cell with paste electrolyte can be expected to show a specific power in excess of 360 watts per pound and a specific energy of 80 watt-hours per pound, suggesting many applications, including special vehicle propulsion and energy storage. Acknowledgment
I t is a pleasure to thank Joseph Gerard for help with some of the experiments, and A. D. Tevebaugh, C. E. Johnson, and M. S. Foster for helpful discussions during the course of this work. literature Cifed
Baker, B. S., Marianowski, L. G., Zimmer, J., Price, G., in “Hydrocarbon Fuel Cell Technology,” B. S. Baker, ed., Academic Press, New York, 1965. Broers, G. H. J., Schenke, M., in “Fuel Cells,” Vol. 2, G. J. Young, ed., Reinhold, New York, 1963. Cairns, E. J., Shimotake, H., Division of Fuel Chemistry, 154th Meeting, ACS, Chicago, September 1967, Abstr. L-70; “Preprints of Papers Presented to the Division of Fuel Chemistry,” Vol. 11, No. 3, 321 (1967). Foster, M. S., Liu, C. C., J. Phys. Chem. 70, 950 (1966). Foster, M. S., Wood, S. E., Crouthamel, C. E., Znorg. Chem. 3, 1428 (1964). Jasinski, R., “High-Energy Batteries,” Plenum Press, New York, 1967. Johnson, C. E., Division of Inorganic Chemistry, 155th Meeting, ACS, San Francisco, April 1968, Abstr. M-128. Johnson, C. E., Foster, M. S., Kyle, M. L., Nuclear Appl. 3, 563 (1967). Moos, A. M., Palmer, N. I., in Proceedings of 21st Annual Power Sources Conference, PSC Publications Committee, Red Bank, N. J., 1967. VOL. 8
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Rightmire, R. A., Jones, A. L., in Proceedings of 21st Annual Power Sources Conference, PSC Publications Committee, Red Bank, N. J., 1967. Seiger, H. N., Charlip, S., Lyall, A. E., Shair, R. C., in Proceedings of 21st Annual Power Sources Conference, PSC Publications Committee, Red Bank, N. J., 1967. Shimotake, H., Cairns, E. J., CITCE Meeting, Detroit, Mich., September 1968. Shimotake, H., Cairns, E. J., Electrochemical Society Meeting, Dallas, May 1967, Abstr. 143; Extended Abstrs. Ind. Electrolytic Diu. 3,4 (1967a). Shimotake, H., Cairns, E. J., Intersociety Energy Conversion Engineering Conference, Miami Beach, Fla., August 1967 ; “Advances in Energy Conversion Engineering,” p. 951, American Society of Mechanical Engineers, New York, 1967b.
Shimotake, H., Rogers, G. L., Cairns, E. J., Electrochemical Society Meeting, Chicago, October 1967, Abstr. 18; Extended Abstrs. J - l Battery Diu. 12, 42 (1967). Tantram, A. D. S., Tseung, A. C. C., Harris, B. S., in “Hydrocarbon Fuel Cell Technology,” B. S. Baker, ed., Academic Press, New York, 1965. Wilcox, H. A., in Proceedings of 21st Annual Power Sources Conference, PSC Publications Committee, Red Bank, N. J., 1967. RECEIVED for review April 22, 1968 ACCEPTEDJuly 15, 1968 Division of Fuel Chemistry, 155th Meeting, ACS, San Francisco, Calif., April 1968. Work performed under the auspices of the U. S. Atomic Energy Commission.
A COALESCENCE MODEL FOR GRANULATION P. C. KAPUR AND D. W . FUERSTENAU
Department of Mineral Technology, Unioersity of California, Berkeley, Calif.
94720
In the nuclei and transition regions of granulation the pellets or granules grow in size by coalescence with one another. A random coalescence model has been proposed which characterizes the size distributions of pellets in these two regions. The interrelationships between the various parameters of the size distributions generated by the random coalescence model are in agreement with the experimental data for particulate systems of different surface areas and water contents.
far, granulation or wet pelletization kinetics and pellet Tsize . distributions have not been adequately treated. Such HUS
a description, apart from formalizing the postulated pellet growth mechanisms, is required for appropriate simulation and control models for industrial balling circuits. The first systematic investigation of the growth rates and size distributions of the pellets, made by agglomerating closely sized sands and sand-silt mixtures in a laboratory batch balling drum, was carried out by Newitt and Conway-Jones (1958). They postulated that the pellets grow by direct coalescence, but made no attempt to analyze the empirical size distributions in terms of this model. More recently, Capes and Danckwerts (1965a, b) studied the mechanism of pellet growth by a technique involving the granulation of two sands of contrasting colors. They concluded that, if sufficient water is present in the system, the small nuclei pellets grow in size by direct coalescence. This growth mode ceases when the pellets reach such a size that the torque tending to separate the “twin” formed at the instance of collision between the two pellets is too large to allow a permanent bond to be formed. Subsequent growth, according to Capes and Danckwerts, takes place by crushing of the smallest pellets in the rotating charge, the resulting fragments being distributed over the remaining pellets. Based on this preferential crushing and layering mechanism, they formulated a relationship for the size distributions of pellets, which is self-preserving in the sense that successive distributions become coincident when plotted in the specified dimensionless form. Capes and Danckwerts worked exclusively with comparatively coarse and closely sized sands and did not extend their analysis to comminuted poly-dispersed systems which are normally encountered in industrial pelletization operations. Using comminuted limestone as a model system, Kapur and Fuerstenau (1964) carried out detailed studies of pelletiza56
I&EC PROCESS DESIGN A N D DEVELOPMENT
tion kinetics and concluded that the growth mechanism depends on the size of the growing pellets. Initially three-phase air-water-solid nuclei are formed which grow by random coalescence of the rotating pellets. When the nuclei are compacted to such an extent that the over-all porosity of the pellet is approximately equal to its water content, the integrity of the two-phase pellet is barely maintained by surface tension of the surrounding liquid film (Rumpf, 1962) and its pronounced dilatant behavior (Newitt and Conway-Jones, 1958). I n this transition region, the pellets are readily deformable and possess a high degree of surface plasticity. As a result, the growth mechanism retains its coalescence character. Indeed, the coalescence rate may be appreciably accelerated, particularly if the system is comprised of relatively fine particles. This may be seen in Figure 1, which shows pictures of conglomerated pellets formed a t a very rapid coalescence rate in the transition region. Finally, in the two-phase water-solid ball growth region, where the comparatively large pellets are held together by negative capillary potential, the growth mechanism acquires a highly complex character based upon one or more of the following modes (Capes and Danckwerts, 1965a; Kapur and Fuerstenau, 1964; Newitt and Conway-Jones, 1958): random coalescence, preferential coalescence between balls of different sizes, surface abrasion and material transfer from one ball to another, and crushing and layering. Capes and Danckwerts found that, for 97-micron diameter sand, coalescence essentially ceases when the pellets grow to a size of the order of 6 mm. However, the size range over which the coalescence mechanism might prevail will depend, coupled with the dynamics of the balling device, on the strength, plasticity, and allied rheological properties of the pellet, which may vary with the degree of compaction of the particulate assembly as well as the thermodynamic potential (suction) of water in the pellet matrix.
