The modeling of flow phenomena in air-agitated pachuka tanks
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x2
0.0300 0.0996 0.2065 0.2069 0.3507 0.5020 0.7024 0.0294 0.0994 0.2000 0.3508 0.3526 0.5017 0.6980 0.0299 0.0301 0.0997 0.1995 0.3494 0.4995 0.6981
0.2425 0.2251 0.1984 0.1983 0.1623 0.1245 0.0744 0.4853 0.4503 0.4000 0.3246 0.3238 0.2492 0.1510 0.7275 0.7274 0.6752 0.6004 0.4880 0.3754 0.2264 S1,Eq. [2]
x3
Eq. [2]
Eq. [12]
Experimental[5]
0.7275 0.0122 0.0155 0.0155 0.6753 0.0484 0.0556 0.0564 0.5951 0.1239 0.1306 0.1287 0.5948 0.1242 0.1309 0.1314 0.4870 0.2572 0.2604 0.2648 0.3735 0.4245 0.4280 0.4278 0.2232 0.6650 0.6721 0.6665 0.4853 0.0198 0.0219 0.0217 0.4503 0.0718 0.0771 0.0752 0.4000 0.1571 0.1649 0.1624 0.3246 0.3029 0.3140 0.3186 0.3236 0.3048 0.3160 0.3197 0.2491 0.4630 0.4778 0.4767 0.1510 0.6394 0.6935 0.6905 0.2426 0.0312 0.0321 0.0324 0.2425 0.0314 0.0323 0.0328 0.2251 0.1033 0.1060 0.1066 0.2001 0.2051 0.2104 0.2121 0.1627 0.3558 0.3653 0.3614 0.1251 0.5048 0.5176 0.5154 0.0755 0.7007 0.7118 0.7070 5 50.0062 S1,Eq. [12] 5 50.0020
RT ln g 1 5
ΣΣa
j52 k50
jk
y 1j y 2k
[11]
where ajk is the coefficient to be determined by the ternary data, y1 5 1 2 x1, and y2 5 x3/(x2 1 x3). The experimental data of the activity of component AgCl in the AgClNaCl-RbCl melts at 1073 K may be fitted by a least-squares technique to an expansion of the explicit form of Eq. [11] as follows:[5] RT ln g 1 5 ( 26389 1 23,857 y2 2 14,581 y 22 )y 21 1( 214,092 1 2000 y 2 1 12,606 y 22)y 31 1( 10,954 2 12,627 y2 1 2469 y 22)y 41 J mole21 [12] The activities of component AgCl calculated from Eq. [12] are also listed in Table IV. It can be seen that although Eq. [12] is suitable for the ternary melts, it indeed involves some trouble ternary constants. The authors think that an original cause of the Wilson equation applied successfully to predicting thermodynamic properties of organic solutions,[3,10] liquid alloys,[11,12] and molten salts lies in its implied assumption that liquid molecules in a solution are somewhat in local orderly condition, which reflects just the nonideality of solutions. In fact, both stronger and weaker interactions exist among liquid molecules, which means that the probability of determining stronger pairs on intermolecular attraction is reasonably larger than that of weaker pairs in random condition. Thus, some differences between the local concentrations of components around a type of molecule and their average concentrations in bulk solutions exist. On the basis of this consideration, Wilson first proposed a concept concerning the local molecular fraction xji, which is defined as a ratio of the number of molecules of j around a center molecule METALLURGICAL AND MATERIALS TRANSACTIONS B
i to the sum of molecules of types j and i around a center molecule i (the number is only confined to the first coordination shell), and derived the well-known Eq. [1], which resulted in the establishment of more local composition equations later.[10] In conclusion, a significant advantage of the Wilson equation lies in its ability to predict the thermodynamic properties of ternary molten salts using only
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