913:
732:
404:
2240:
22:
1724:, and fast squeeze flow demonstrated that polymers may exhibit better lubrication than current constitutive models will predict. The current empirical model for power law fluids is relatively accurate for modeling inelastic flows, but certain kinematic flow assumptions and incomplete understanding of polymeric lubrication properties tend to provide inaccurate modeling of power law fluids.
1909:
2271:
final products to determine weld strength. Fiber strand length and size show significant effects on material strength, and squeeze flow causes fibers to orient along the load direction while being perpendicular to the joining direction to achieve the same final properties as thermosetting composites.
2270:
may become an analog to permit increased manufacturing of these stronger materials through their melting abilities and relatively inexpensive raw materials. Characterization and testing of thermoplastic composites experiencing squeeze flow allow for study of fiber orientations within the melt and
2252:
During conventional hot plate welding, a successful joining phase depends on proper maintenance of squeeze flow to ensure that pressure and temperature create an ideal weld. Excessive pressure causes squeeze out of valuable material and weakens the bond due to fiber realignment in the melt layer,
1735:
exhibit uncommon characteristics during squeeze flow. While undergoing compression, Bingham fluids should fail to move and act as a solid until achieving a yield stress; however, as the parallel plates move closer together, the fluid shows some radial movement. One study proposes a “biviscosity”
1379:
1741:
881:
558:
1051:
400:, or surface protrusion, allows for measurement of a very specific cross-section of a droplet. To measure macroscopic squeeze flow effects, models exist for two the most common surfaces: circular and rectangular plate squeeze flows.
2261:
Prevalent in the aerospace and automotive industries, composites serve as expensive, yet mechanically strong, materials in the construction of several types of aircraft and vehicles. While aircraft parts are typically composed of
1112:
2207:
Squeeze flow application is prevalent in several science and engineering fields. Modeling and experimentation assist with understanding the complexities of squeeze flow during processes such as rheological testing,
226:
78:(also called squeezing flow, squeezing film flow, or squeeze flow theory) is a type of flow in which a material is pressed out or deformed between two parallel plates or objects. First explored in 1874 by
1534:
2243:
Hot plate welding; (a) Heating Phase, (b) Change-over Phase, (c) Joining Phase. Polymer materials (gray), heating element (red), melt layers (orange), squeeze out regions (orange, hash mark borders).
2141:
2061:
2476:
Picher-Martel, G., Levy, A., & Hubert, P. (2015). Compression molding of Carbon/Polyether ether ketone composites: Squeeze flow behavior of unidirectional and randomly oriented strands.
2232:
provide useful results for squeeze flow measurements, testing conditions such as applied rotation rates, material composition, and fluid flow behaviors under shear may require the use of
82:, squeeze flow describes the outward movement of a droplet of material, its area of contact with the plate surfaces, and the effects of internal and external factors such as temperature,
728:
Based on conservation of mass calculations, the droplet width is inversely proportional to droplet height; as the width increases, the height decreases in response to squeezing forces.
2197:
1904:{\displaystyle \tau ={\begin{cases}\eta _{2}*{du \over dy}+\tau _{1},&{\text{if }}\tau \geq \tau _{1}\\\eta _{1}*{du \over dy},&{\text{if }}\tau <\tau _{1}\end{cases}}}
1736:
model where the
Bingham fluid retains some unyielded regions that maintain solid-like properties, while other regions yield and allow for some compression and outward movement.
1680:
During experimentation to determine the accuracy of the power law fluid model, observations showed that modeling slow squeeze flow generated inaccurate power law constants (
749:
421:
377:
371:
2171:
2090:
2000:
1969:
1938:
925:
723:
590:
1618:
1585:
673:
291:
613:
334:
271:
1718:
1698:
1670:
1644:
1556:
1445:
1421:
1401:
902:
693:
653:
633:
311:
248:
1374:{\displaystyle {\frac {h_{0}}{h}}=\left(1+t*({\frac {2n+3}{4n+2}})({\frac {(4*h_{0}*L_{0})^{n+1}*F*(n+2)}{(2*L_{0})^{2n+3}*W*m}})^{1/n}\right)^{n/2n+3}}
735:
Circular plate squeeze flow diagram at initial and follow-on conditions; circular plates (gray), droplet (hash marked ellipse between both plates).
94:
undergoing squeeze flow under various geometries and conditions. Numerous applications across scientific and engineering disciplines including
2228:
provide analysis for high viscosity materials such as rubber and glass, cure times for epoxy resins, and fiber-filled suspension flows. While
2225:
407:
Single asperity squeeze flow diagram at initial and follow-on conditions; plates (assumed to be semi-infinite, in gray), droplet (green).
125:
provide the foundations for calculating and modeling squeeze flow. Boundary conditions for such calculations include assumptions of an
141:
1456:
2460:
Fiebig, I., & Schoeppner, V. (2018). Factors influencing the fiber orientation in welding of fiber-reinforced thermoplastics.
2099:
2253:
while failure to allow cooling to room temperature creates weak, brittle welds that crack or break completely during use.
916:
Rectangular plate squeeze flow diagram at initial and follow-on conditions; rectangular plates (gray), droplet (green).
373:
is the change in droplet height over time. To simplify most calculations, the applied force is assumed to be constant.
2287:
Ullah, Hakeem; Khan, Muhammad Arif; Fiza, Mehreen; Ullah, Kashif; Ayaz, Muhammad; Al-Mekhlafi, Seham M. (2022-03-31).
2011:
2327:
Engmann, J., Servais, C., & Burbidge, A. S. (2005). Squeeze flow theory and applications to rheometry: A review.
62:
2289:"Analytical and Numerical Analysis of the Squeezed Unsteady MHD Nanofluid Flow in the Presence of Thermal Radiation"
2224:
allows for evaluation of polymers under wide ranges of temperatures, shear rates, and flow indexes. Parallel plate
2176:
397:
1055:
These calculations assume a melt layer that has a length much larger than the sample width and thickness.
1674:
118:
2513:
2508:
876:{\displaystyle {\frac {h_{0}}{h}}=\left(1+{\frac {16*F*t*h_{0}^{2}}{3*\pi *\eta *R^{4}}}\right)^{1/2}}
553:{\displaystyle {\frac {h_{0}}{h}}=\left(1+{\frac {5*F*t*h_{0}^{2}}{4*\eta *W*L_{0}^{3}}}\right)^{1/5}}
1076:
1756:
339:
40:
2150:
1084:
2068:
1978:
1947:
1916:
1046:{\displaystyle {\frac {h_{0}}{h}}=\left(1+{\frac {F*t*h_{0}^{2}}{2*\mu *W*L^{3}}}\right)^{1/2}}
2263:
698:
565:
2409:
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110:
8:
1068:
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32:
2413:
595:
316:
253:
1703:
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1541:
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1406:
1386:
1067:
allows for basic analysis of squeeze flow, but many polymers can exhibit properties of
887:
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638:
618:
296:
233:
2503:
2425:
2310:
2209:
1622:
99:
44:
2498:
2417:
2300:
1088:
86:, and heterogeneity of the material. Several squeeze flow models exist to describe
1732:
1104:
1092:
1072:
1064:
912:
390:
122:
87:
83:
1095:
model provides calculations based on variations in yield stress calculations.
731:
2492:
2429:
2314:
2267:
1080:
403:
37:. In particular, not written clearly for those unfamiliar with the subject..
2305:
2288:
1648:
79:
2421:
1079:. The power law fluid model is sufficient to describe behaviors above the
380:
Visualization of surface-to-surface contact; asperity highlighted in red.
2239:
2229:
1721:
130:
2233:
2221:
95:
2400:
Grimm, Roger J. (1978). "Squeezing flows of polymeric liquids".
221:{\displaystyle F=-{\frac {4*L^{3}*\eta *W}{h^{3}}}{dh \over dt}}
1529:{\displaystyle m=m_{0}*exp\left({\frac {-E_{a}}{R*T}}\right)}
1897:
376:
2378:
Wilson, S. (1993). Squeezing flow of a
Bingham material.
2136:{\displaystyle \epsilon ={\frac {\eta _{2}}{\eta _{1}}}}
2179:
2153:
2102:
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2014:
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319:
299:
279:
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236:
144:
2444:
Rheology: Principles, measurements, and applications
695:is the width of the assumed rectangular plate, and
102:provide examples of squeeze flow in practical use.
2286:
2191:
2165:
2135:
2084:
2055:
1994:
1963:
1932:
1903:
1712:
1692:
1664:
1638:
1612:
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1550:
1528:
1439:
1415:
1395:
1373:
1045:
896:
875:
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647:
627:
607:
584:
552:
393:droplet sizes under different initial conditions.
365:
328:
305:
285:
265:
242:
220:
2358:Grewell, D., Benatar, A., & Park, J. (2013).
2490:
2056:{\displaystyle \tau _{0}=\tau _{1}(1-\epsilon )}
2236:or other novel setups to obtain accurate data.
313:is the width of the assumed rectangular plate,
136:Relating applied force to material thickness:
2256:
2467:(5), 997-1012. doi:10.1007/s40194-018-0628-0
2442:Macosko, C. W., & Larson, R. G. (1994).
2334:(1-3), 1-27. doi:10.1016/j.jnnfm.2005.08.007
2173:, the fluid exhibits Newtonian behavior; as
43:. There might be a discussion about this on
2385:, 211-219. doi:10.1016/0377-0257(93)80051-c
129:, a two-dimensional system, neglecting of
2380:Journal of Non-Newtonian Fluid Mechanics,
2329:Journal of Non-Newtonian Fluid Mechanics,
2304:
63:Learn how and when to remove this message
2360:Plastics and composites welding handbook
2238:
911:
730:
402:
375:
336:is the final height of the droplet, and
1058:
2491:
2215:
2192:{\displaystyle \epsilon \rightarrow 0}
1091:for amorphous thermoplastics, and the
725:is the initial length of the droplet.
592:is the initial height of the droplet,
273:is the initial length of the droplet,
121:for conservation of momentum, and the
2399:
904:is the radius of the circular plate.
133:, and neglecting of inertial forces.
2483:(9), 1828-1837. doi:10.1002/pc.23753
2456:
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920:For rectangular plate squeeze flow:
907:
615:is the final height of the droplet,
105:
15:
389:Several equations accurately model
384:
13:
2212:, and composite material joining.
1098:
416:For single asperity squeeze flow:
411:
14:
2525:
2449:
2388:
2365:
2337:
744:For circular plate squeeze flow:
739:
2006:. To determine this new stress:
1727:
635:is the applied squeezing force,
250:is the applied squeezing force,
20:
2202:
2470:
2436:
2321:
2280:
2183:
2050:
2038:
1590:initial flow consistency index
1326:
1292:
1272:
1267:
1255:
1231:
1198:
1192:
1189:
1154:
1085:semicrystalline thermoplastics
1:
2274:
2199:, the Bingham model applies.
1975:of the solid-like state, and
1063:Simplifying calculations for
366:{\displaystyle {dh \over dt}}
1089:glass transition temperature
7:
2166:{\displaystyle \epsilon =1}
98:, welding engineering, and
10:
2530:
2257:Composite material joining
396:Consideration of a single
2085:{\displaystyle \tau _{0}}
2004:biviscosity region stress
1995:{\displaystyle \tau _{1}}
1964:{\displaystyle \eta _{1}}
1933:{\displaystyle \eta _{2}}
2293:Journal of Nanomaterials
1560:flow consistency index,
675:is the fluid viscosity,
293:is the fluid viscosity,
1973:"paradoxical" viscosity
1075:characteristics, under
655:is the squeezing time,
119:Navier-Stokes equations
2264:thermosetting polymers
2244:
2193:
2167:
2137:
2086:
2057:
1996:
1965:
1944:of the Bingham fluid,
1934:
1905:
1714:
1694:
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1614:
1581:
1552:
1530:
1441:
1425:flow consistency index
1417:
1397:
1375:
1103:For squeeze flow in a
1047:
917:
898:
877:
736:
719:
718:{\displaystyle 2L_{0}}
689:
669:
649:
629:
609:
586:
585:{\displaystyle 2h_{0}}
554:
408:
381:
367:
330:
307:
287:
267:
244:
222:
2462:Welding in the World,
2422:10.1002/aic.690240307
2242:
2194:
2168:
2143:is the dimensionless
2138:
2087:
2058:
1997:
1966:
1935:
1906:
1715:
1695:
1667:
1641:
1615:
1613:{\displaystyle E_{a}}
1582:
1580:{\displaystyle m_{0}}
1553:
1531:
1447:is the dimensionless
1442:
1418:
1398:
1376:
1048:
915:
899:
878:
734:
720:
690:
670:
668:{\displaystyle \eta }
650:
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406:
379:
368:
331:
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288:
286:{\displaystyle \eta }
268:
245:
223:
2306:10.1155/2022/1668206
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2151:
2100:
2069:
2012:
1979:
1948:
1917:
1742:
1704:
1684:
1675:absolute temperature
1656:
1630:
1597:
1564:
1542:
1457:
1431:
1407:
1387:
1113:
1069:non-Newtonian fluids
1059:Non-Newtonian fluids
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127:incompressible fluid
111:Conservation of mass
92:non-Newtonian fluids
33:confusing or unclear
2478:Polymer Composites,
2414:1978AIChE..24..427G
2362:. New York: Hanser.
2216:Rheological testing
1720:) using a standard
1449:flow behavior index
1081:melting temperature
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115:continuity equation
41:clarify the article
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608:{\displaystyle 2h}
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329:{\displaystyle 2h}
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266:{\displaystyle 2L}
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2514:Molding processes
2509:Materials science
2248:Hot plate welding
2210:hot plate welding
2131:
1876:
1866:
1813:
1790:
1713:{\displaystyle n}
1693:{\displaystyle m}
1665:{\displaystyle T}
1647:is the universal
1639:{\displaystyle R}
1623:activation energy
1551:{\displaystyle m}
1520:
1440:{\displaystyle n}
1416:{\displaystyle K}
1396:{\displaystyle m}
1323:
1187:
1131:
1022:
944:
908:Rectangular plate
897:{\displaystyle R}
852:
768:
688:{\displaystyle W}
648:{\displaystyle t}
628:{\displaystyle F}
529:
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361:
306:{\displaystyle W}
243:{\displaystyle F}
216:
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106:Basic Assumptions
100:materials science
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1065:Newtonian fluids
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113:(expressed as a
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2299:(1): e1668206.
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2145:viscosity ratio
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1105:power law fluid
1101:
1099:Power law fluid
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517:
494:
487:
482:
459:
457:
450:
446:
445:
431:
427:
425:
423:
420:
419:
414:
412:Single asperity
387:
353:
345:
343:
341:
338:
337:
318:
315:
314:
298:
295:
294:
278:
275:
274:
255:
252:
251:
235:
232:
231:
208:
200:
198:
190:
186:
167:
163:
156:
154:
143:
140:
139:
123:Reynolds number
108:
84:viscoelasticity
69:
58:
52:
49:
38:
25:
21:
12:
11:
5:
2527:
2517:
2516:
2511:
2506:
2501:
2486:
2485:
2469:
2448:
2435:
2408:(3): 427–439.
2387:
2364:
2336:
2320:
2278:
2276:
2273:
2268:thermoplastics
2258:
2255:
2249:
2246:
2217:
2214:
2204:
2201:
2188:
2185:
2182:
2162:
2159:
2156:
2128:
2124:
2118:
2114:
2108:
2105:
2079:
2075:
2052:
2049:
2046:
2043:
2040:
2035:
2031:
2027:
2022:
2018:
1989:
1985:
1958:
1954:
1927:
1923:
1898:
1891:
1887:
1883:
1880:
1872:
1870:
1864:
1861:
1856:
1853:
1847:
1842:
1838:
1834:
1833:
1828:
1824:
1820:
1817:
1809:
1807:
1802:
1798:
1794:
1788:
1785:
1780:
1777:
1771:
1766:
1762:
1758:
1757:
1755:
1750:
1747:
1733:Bingham fluids
1729:
1726:
1709:
1689:
1661:
1635:
1607:
1603:
1574:
1570:
1547:
1524:
1518:
1515:
1512:
1505:
1501:
1497:
1491:
1487:
1484:
1481:
1478:
1473:
1469:
1465:
1462:
1436:
1412:
1392:
1368:
1365:
1362:
1359:
1355:
1351:
1346:
1340:
1336:
1332:
1328:
1321:
1318:
1315:
1312:
1307:
1304:
1301:
1298:
1294:
1288:
1284:
1280:
1277:
1274:
1269:
1266:
1263:
1260:
1257:
1254:
1251:
1248:
1243:
1240:
1237:
1233:
1227:
1223:
1219:
1214:
1210:
1206:
1203:
1200:
1194:
1191:
1185:
1182:
1179:
1176:
1171:
1168:
1165:
1162:
1156:
1153:
1150:
1147:
1144:
1140:
1135:
1130:
1125:
1121:
1100:
1097:
1060:
1057:
1040:
1036:
1032:
1027:
1018:
1014:
1010:
1007:
1004:
1001:
998:
995:
988:
983:
979:
975:
972:
969:
966:
960:
957:
953:
948:
943:
938:
934:
909:
906:
893:
870:
866:
862:
857:
848:
844:
840:
837:
834:
831:
828:
825:
818:
813:
809:
805:
802:
799:
796:
793:
790:
784:
781:
777:
772:
767:
762:
758:
741:
740:Circular plate
738:
712:
708:
704:
684:
664:
644:
624:
604:
601:
579:
575:
571:
547:
543:
539:
534:
525:
520:
516:
512:
509:
506:
503:
500:
497:
490:
485:
481:
477:
474:
471:
468:
465:
462:
456:
453:
449:
444:
439:
434:
430:
413:
410:
386:
383:
359:
356:
351:
348:
325:
322:
302:
282:
262:
259:
239:
214:
211:
206:
203:
193:
189:
184:
181:
178:
175:
170:
166:
162:
159:
153:
150:
147:
107:
104:
71:
70:
28:
26:
19:
9:
6:
4:
3:
2:
2526:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2496:
2494:
2482:
2479:
2473:
2466:
2463:
2457:
2455:
2453:
2445:
2439:
2431:
2427:
2423:
2419:
2415:
2411:
2407:
2403:
2402:AIChE Journal
2396:
2394:
2392:
2384:
2381:
2375:
2373:
2371:
2369:
2361:
2355:
2353:
2351:
2349:
2347:
2345:
2343:
2341:
2333:
2330:
2324:
2316:
2312:
2307:
2302:
2298:
2294:
2290:
2283:
2279:
2272:
2269:
2265:
2254:
2241:
2237:
2235:
2231:
2227:
2223:
2220:Squeeze flow
2213:
2211:
2200:
2186:
2180:
2160:
2157:
2154:
2146:
2126:
2122:
2116:
2112:
2106:
2103:
2095:
2077:
2073:
2063:
2047:
2044:
2041:
2033:
2029:
2025:
2020:
2016:
2007:
2005:
1987:
1983:
1974:
1956:
1952:
1943:
1925:
1921:
1911:
1889:
1885:
1881:
1878:
1868:
1862:
1859:
1854:
1851:
1845:
1840:
1836:
1826:
1822:
1818:
1815:
1805:
1800:
1796:
1792:
1786:
1783:
1778:
1775:
1769:
1764:
1760:
1753:
1748:
1745:
1737:
1734:
1728:Bingham fluid
1725:
1723:
1707:
1687:
1678:
1676:
1672:
1659:
1650:
1646:
1633:
1624:
1620:
1605:
1601:
1591:
1587:
1572:
1568:
1545:
1536:
1522:
1516:
1513:
1510:
1503:
1499:
1495:
1489:
1485:
1482:
1479:
1476:
1471:
1467:
1463:
1460:
1452:
1450:
1434:
1426:
1410:
1390:
1381:
1366:
1363:
1360:
1357:
1353:
1349:
1344:
1338:
1334:
1330:
1319:
1316:
1313:
1310:
1305:
1302:
1299:
1296:
1286:
1282:
1278:
1275:
1264:
1261:
1258:
1252:
1249:
1246:
1241:
1238:
1235:
1225:
1221:
1217:
1212:
1208:
1204:
1201:
1183:
1180:
1177:
1174:
1169:
1166:
1163:
1160:
1151:
1148:
1145:
1142:
1138:
1133:
1128:
1123:
1119:
1108:
1106:
1096:
1094:
1093:Bingham fluid
1090:
1086:
1082:
1078:
1074:
1070:
1066:
1056:
1053:
1038:
1034:
1030:
1025:
1016:
1012:
1008:
1005:
1002:
999:
996:
993:
986:
981:
977:
973:
970:
967:
964:
958:
955:
951:
946:
941:
936:
932:
921:
914:
905:
891:
883:
868:
864:
860:
855:
846:
842:
838:
835:
832:
829:
826:
823:
816:
811:
807:
803:
800:
797:
794:
791:
788:
782:
779:
775:
770:
765:
760:
756:
745:
733:
729:
726:
710:
706:
702:
682:
662:
642:
622:
602:
599:
577:
573:
569:
560:
545:
541:
537:
532:
523:
518:
514:
510:
507:
504:
501:
498:
495:
488:
483:
479:
475:
472:
469:
466:
463:
460:
454:
451:
447:
442:
437:
432:
428:
417:
405:
401:
399:
394:
392:
378:
374:
357:
354:
349:
346:
323:
320:
300:
280:
260:
257:
237:
228:
212:
209:
204:
201:
191:
187:
182:
179:
176:
173:
168:
164:
160:
157:
151:
148:
145:
137:
134:
132:
128:
124:
120:
116:
112:
103:
101:
97:
93:
89:
85:
81:
77:
67:
64:
56:
46:
45:the talk page
42:
36:
34:
29:This article
27:
18:
17:
2480:
2477:
2472:
2464:
2461:
2443:
2438:
2405:
2401:
2382:
2379:
2359:
2331:
2328:
2323:
2296:
2292:
2282:
2260:
2251:
2226:plastometers
2219:
2206:
2203:Applications
2144:
2094:yield stress
2093:
2064:
2008:
2003:
1972:
1941:
1912:
1738:
1731:
1679:
1652:
1649:gas constant
1626:
1593:
1589:
1559:
1537:
1453:
1448:
1424:
1382:
1109:
1102:
1073:viscoelastic
1062:
1054:
922:
919:
884:
746:
743:
727:
561:
418:
415:
395:
388:
229:
138:
135:
109:
80:Josef Stefan
76:Squeeze flow
75:
74:
59:
50:
39:Please help
30:
2230:viscometers
1077:deformation
131:body forces
2493:Categories
2275:References
2234:rheometers
1722:viscometer
1071:, such as
53:April 2019
35:to readers
2430:1547-5905
2315:1687-4110
2222:rheometry
2184:→
2181:ϵ
2155:ϵ
2123:η
2113:η
2104:ϵ
2074:τ
2048:ϵ
2045:−
2030:τ
2017:τ
1984:τ
1953:η
1922:η
1886:τ
1879:τ
1846:∗
1837:η
1823:τ
1819:≥
1816:τ
1797:τ
1770:∗
1761:η
1746:τ
1514:∗
1496:−
1477:∗
1423:) is the
1317:∗
1311:∗
1279:∗
1253:∗
1247:∗
1218:∗
1205:∗
1152:∗
1009:∗
1003:∗
1000:μ
997:∗
974:∗
968:∗
839:∗
836:η
833:∗
830:π
827:∗
804:∗
798:∗
792:∗
663:η
511:∗
505:∗
502:η
499:∗
476:∗
470:∗
464:∗
391:Newtonian
281:η
180:∗
177:η
174:∗
161:∗
152:−
96:rheometry
88:Newtonian
2504:Plastics
1875:if
1812:if
398:asperity
2499:Welding
2410:Bibcode
2092:is the
2002:is the
1971:is the
1940:is the
1673:is the
1621:is the
1588:is the
1558:is the
1087:or the
117:), the
31:may be
2428:
2313:
2065:Where
1913:Where
1651:, and
1538:Where
1383:Where
562:Where
230:Where
2147:. If
2426:ISSN
2311:ISSN
2297:2022
2096:and
1882:<
1700:and
1427:and
1403:(or
1083:for
90:and
2418:doi
2332:132
2301:doi
2495::
2481:38
2465:62
2451:^
2424:.
2416:.
2406:24
2404:.
2390:^
2383:47
2367:^
2339:^
2309:.
2295:.
2291:.
2266:,
1677:.
1625:,
1592:,
1451:.
1107::
789:16
2432:.
2420::
2412::
2317:.
2303::
2187:0
2161:1
2158:=
2127:1
2117:2
2107:=
2078:0
2051:)
2042:1
2039:(
2034:1
2026:=
2021:0
1988:1
1957:1
1926:2
1890:1
1869:,
1863:y
1860:d
1855:u
1852:d
1841:1
1827:1
1806:,
1801:1
1793:+
1787:y
1784:d
1779:u
1776:d
1765:2
1754:{
1749:=
1708:n
1688:m
1660:T
1634:R
1606:a
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1517:T
1511:R
1504:a
1500:E
1490:(
1486:p
1483:x
1480:e
1472:0
1468:m
1464:=
1461:m
1435:n
1411:K
1391:m
1367:3
1364:+
1361:n
1358:2
1354:/
1350:n
1345:)
1339:n
1335:/
1331:1
1327:)
1320:m
1314:W
1306:3
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1300:n
1297:2
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1287:0
1283:L
1276:2
1273:(
1268:)
1265:2
1262:+
1259:n
1256:(
1250:F
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1236:n
1232:)
1226:0
1222:L
1213:0
1209:h
1202:4
1199:(
1193:(
1190:)
1184:2
1181:+
1178:n
1175:4
1170:3
1167:+
1164:n
1161:2
1155:(
1149:t
1146:+
1143:1
1139:(
1134:=
1129:h
1124:0
1120:h
1039:2
1035:/
1031:1
1026:)
1017:3
1013:L
1006:W
994:2
987:2
982:0
978:h
971:t
965:F
959:+
956:1
952:(
947:=
942:h
937:0
933:h
892:R
869:2
865:/
861:1
856:)
847:4
843:R
824:3
817:2
812:0
808:h
801:t
795:F
783:+
780:1
776:(
771:=
766:h
761:0
757:h
711:0
707:L
703:2
683:W
643:t
623:F
603:h
600:2
578:0
574:h
570:2
546:5
542:/
538:1
533:)
524:3
519:0
515:L
508:W
496:4
489:2
484:0
480:h
473:t
467:F
461:5
455:+
452:1
448:(
443:=
438:h
433:0
429:h
358:t
355:d
350:h
347:d
324:h
321:2
301:W
261:L
258:2
238:F
213:t
210:d
205:h
202:d
192:3
188:h
183:W
169:3
165:L
158:4
149:=
146:F
66:)
60:(
55:)
51:(
47:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
