39:
20:
1917:
2761:
101:
836:, the particles will move from big concentrations, corresponding to areas surrounding small particles, to small concentrations, corresponding to areas surrounding large nanoparticles. Thus, the small particles will tend to shrink while the big particles will grow. As a result, the average size of the nanoparticles in the solution will grow, and the dispersion of sizes will decrease. Therefore, if a solution is left for a long time, in the extreme case of
42:
41:
46:
45:
40:
47:
657:
44:
1683:(i.e. individual molecules or atoms) from smaller droplets to larger droplets due to greater solubility of the single monomer molecules in the larger monomer droplets. The rate of this diffusion process is linked to the solubility of the monomer in the continuous (water) phase of the emulsion. This can lead to the destabilization of emulsions (for example, by creaming and sedimentation).
1701:
1513:
446:
109:
example, more atoms are bonded to 6 neighbors and fewer atoms are at the unfavorable surface. As the system tries to lower its overall energy, molecules on the surface of a small particle (energetically unfavorable, with only 3 or 4 or 5 bonded neighbors) will tend to detach from the particle and diffuse into the solution.
1691:
Inhibition of sulfathiazole crystal growth by polyvinylpyrrolidone. The polymer forms a noncondensed netlike film over the sulfathiazole crystal, allowing the crystal to grow out only through the openings of the net. The growth is thus controlled by the pore size of the polymer network at the crystal
870:
of material is the slowest process. They began by stating how a single particle grows in a solution. This equation describes where the boundary is between small, shrinking particles and large, growing particles. They finally conclude that the average radius of the particles âšRâ©, grows as follows:
1526:
was slow and also where attachment and detachment at the particle surface was slow. Although his calculations and approach were different, Wagner came to the same conclusions as
Lifshitz and Slyozov for slow-diffusion systems. This duplicate derivation went unnoticed for years because the two
1667:
of length per time. Since the average radius is usually something that can be measured in experiments, it is fairly easy to tell if a system is obeying the slow-diffusion equation or the slow-attachment equation. If the experimental data obeys neither equation, then it is likely that another
108:
Consider a cubic crystal of atoms: all the atoms inside are bonded to 6 neighbours and are quite stable, but atoms on the surface are only bonded to 5 neighbors or fewer, which makes these surface atoms less stable. Large particles are more energetically favorable since, continuing with this
1335:
43:
652:{\displaystyle k_{\mathrm {B} }T\log \left({\frac {C_{\mathrm {eq} }}{C_{\infty }}}\right)={\frac {2\sigma \nu _{\mathrm {at} }}{r}}\rightarrow C_{\mathrm {eq} }(r)=C_{\mathrm {eq} }(\infty )\mathrm {e} ^{\frac {2\sigma \nu _{\mathrm {at} }}{rk_{\mathrm {B} }T}}}
988:
97:-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles. This stems from the fact that molecules on the surface of a particle are energetically less stable than the ones in the interior.
1647:
2461:
McClements, David Julian; Henson, Lulu; Popplewell, L. Michael; Decker, Eric Andrew; Choi, Seung Jun (2012). "Inhibition of
Ostwald Ripening in Model Beverage Emulsions by Addition of Poorly Water Soluble Triglyceride Oils".
865:
The history of research progress in quantitatively modeling
Ostwald ripening is long, with many derivations. In 1958, Lifshitz and Slyozov performed a mathematical investigation of Ostwald ripening in the case where
172:
1531:
in 1961. It was not until 1975 that
Kahlweit addressed the fact that the theories were identical and combined them into the Lifshitz-Slyozov-Wagner or LSW theory of Ostwald ripening. Many experiments and
347:
1508:{\displaystyle f(R,t)={\frac {4}{9}}\rho ^{2}\left({\frac {3}{3+\rho }}\right)^{\frac {7}{3}}\left({\frac {1.5}{1.5-\rho }}\right)^{\frac {11}{3}}\exp \left(-{\frac {1.5}{1.5-\rho }}\right),\rho <1.5}
761:
1768:
ageing, the term refers to the growth of larger crystals from those of smaller size which have a higher solubility than the larger ones. In the process, many small crystals formed initially (
281:
to the radius of the particle. The chemical potential of an ideal solution can also be expressed as a function of the soluteâs concentration if liquid and solid phases are in equilibrium.
1671:
Although LSW theory and
Ostwald ripening were intended for solids ripening in a fluid, Ostwald ripening is also observed in liquid-liquid systems, for example, in an oil-in-water
877:
860:
255:
66:
that involves the change of an inhomogeneous structure over time, in that small crystals or sol particles first dissolve and then redeposit onto larger crystals or sol particles.
1022:
435:
379:
1088:
69:
Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described by
1048:
219:
830:
690:
1182:
1776:). The smaller crystals act as fuel for the growth of bigger crystals. Limiting Ostwald ripening is fundamental in modern technology for the solution synthesis of
195:
2379:"Using Quantitative Textural Analysis to Understand the Emplacement of Shallow-Level Rhyolitic Laccolithsâa Case Study from the Halle Volcanic Complex, Germany"
1239:
1210:
1146:
1117:
804:
784:
403:
279:
1716:
which gives old ice cream a gritty, crunchy texture. Larger ice crystals grow at the expense of smaller ones within the ice cream, creating a coarser texture.
1553:
2119:
Baldan, A. (2002). "Review
Progress in Ostwald ripening theories and their applications to nickel-base superalloys Part I: Ostwald ripening theories".
1986:
2577:
2299:
2060:
2030:
2930:
121:
1781:
287:
698:
862:, its particles would evolve until they would finally form a single huge spherical particle to minimize the total surface area.
115:
describes the relationship between the radius of curvature and the chemical potential between the surface and the inner volume:
1286:
is irrelevant, an approach that respects the meanings of all terms is to take the time derivative of the equation to eliminate
2507:"How important is the spectral ripening effect in stratiform boundary layer clouds? Studies using simple trajectory analysis"
2361:
2309:
2103:
2070:
34:
at 6 (a), 24 (b), 48 (c) and 72 hours (d). The small palladium particles are being consumed as the larger ones grow bigger.
1930:
Huang, Zhandong; Su, Meng; Yang, Qiang; Li, Zheng; Chen, Shuoran; Li, Yifan; Zhou, Xue; Li, Fengyu; Song, Yanlin (2017).
1692:
surface. The smaller the pore size, the higher is the supersaturation of the solution required for the crystals to grow.
2570:
1547:
Wagner derived that when attachment and detachment of molecules is slower than diffusion, then the growth rate becomes
2940:
2418:
Vengrenovich, R.D.; Gudyma, Yu. V.; Yarema, S. V. (December 2001). "Ostwald ripening of quantum-dot nanostructures".
2351:
1325:
of particles. For convenience, the radius of particles is divided by the average radius to form a new variable, Ï =
1849:
2263:
Vladimirova, N.; Malagoli, A.; Mauri, R. (1998). "Diffusion-driven phase separation of deeply quenched mixtures".
2735:
1319:
2531:
2506:
2745:
2725:
2563:
983:{\displaystyle \langle R\rangle ^{3}-\langle R\rangle _{0}^{3}={\frac {8\gamma c_{\infty }v^{2}D}{9R_{g}T}}t}
2935:
2700:
2162:
Lifshitz, I.M.; Slyozov, V.V. (1961). "The
Kinetics of Precipitation from Supersaturated Solid Solutions".
1257:, and only the former one can be used to calculate average volume, and that the statement that âšRâ© goes as
2760:
839:
228:
2925:
2775:
1795:
systems, with molecules diffusing from small droplets to large ones through the continuous phase. When a
833:
2093:
2795:
2198:
1001:
408:
437:
to the solute concentration in a solution in which the solid and the liquid phase are in equilibrium.
355:
2835:
2720:
1765:
1214:
1916:
2878:
2605:
2645:
2201:[Theory of the aging of precipitates by dissolution-reprecipitation (Ostwald ripening)].
1824:
1672:
1066:
1876:"Redox reaction induced Ostwald ripening for size- and shape-focusing of palladium nanocrystals"
2945:
2740:
2670:
1660:
1537:
1522:
performed his own mathematical investigation of
Ostwald ripening, examining both systems where
1874:
Zhang, Zhaorui; Wang, Zhenni; He, Shengnan; Wang, Chaoqi; Jin, Mingshang; Yin, Yadong (2015).
19:
2860:
2855:
2660:
2620:
1932:"A general patterning approach by manipulating the evolution of two-dimensional liquid foams"
1829:
1810:
in the atmosphere at the expense of smaller drops is also characterized as
Ostwald ripening.
1772:) slowly disappear, except for a few that grow larger, at the expense of the small crystals (
1033:
204:
809:
665:
2810:
2695:
2640:
2518:
2427:
2390:
2272:
2171:
2128:
1943:
1819:
1785:
1664:
1160:
180:
8:
2630:
1844:
1735:
1642:{\displaystyle \langle R\rangle ^{2}={\frac {64\gamma c_{\infty }v^{2}k_{s}}{81R_{g}T}}t}
1518:
Three years after that
Lifshitz and Slyozov published their findings (in Russian, 1958),
2522:
2431:
2394:
2276:
2175:
2132:
1947:
2690:
2586:
2443:
2218:
2144:
1964:
1931:
1900:
1875:
1224:
1195:
1131:
1102:
789:
769:
388:
382:
264:
198:
16:
Process by which small crystals dissolve in solution for the benefit of larger crystals
1279:
outside the bounds of validity of the equation. In contexts where the actual value of
2830:
2705:
2665:
2487:
2479:
2475:
2357:
2305:
2249:
2222:
2183:
2099:
2066:
1969:
1905:
1839:
2447:
2148:
1996:
2526:
2471:
2435:
2398:
2280:
2245:
2210:
2179:
2136:
2000:
1991:
1959:
1951:
1895:
1887:
1761:
1150:
1318:
Also contained in the Lifshitz and Slyozov derivation is an equation for the size
2888:
2825:
2750:
2730:
2710:
2685:
2625:
2403:
2378:
1854:
1834:
1754:
1536:
have shown LSW theory to be robust and accurate. Even some systems that undergo
1053:
222:
112:
70:
2904:
2615:
1746:
1541:
1057:
94:
59:
2326:
2140:
1788:. The digested precipitate is generally purer, and easier to wash and filter.
2919:
2845:
2820:
2483:
2284:
2214:
1995:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
63:
2004:
2805:
2790:
2680:
2650:
2491:
1973:
1909:
1796:
1723:, where the droplets in the cloudy microemulsion grow by Ostwald ripening.
1528:
1186:
1121:
258:
100:
82:
31:
27:
1712:
One example of Ostwald ripening is the re-crystallization of water within
2780:
2635:
2549:
2199:"Theorie der Alterung von NiederschlÀgen durch Umlösen (Ostwald-Reifung)"
1800:
1777:
1731:
1720:
1533:
1519:
1955:
692:, is lower around bigger particles than it is around smaller particles.
2800:
2785:
2675:
2610:
2555:
1891:
1750:
1739:
1269:
1092:
2439:
2033:[Studies on the formation and transformation of solid bodies]
2883:
1742:
1713:
1676:
1523:
867:
167:{\displaystyle \Delta \mu ={\frac {2\sigma \nu _{\mathrm {at} }}{r}}}
24:
2262:
2840:
2815:
2600:
1792:
1738:
temperature. It is often ascribed as a process in the formation of
78:
2715:
1727:
1680:
1668:
mechanism is taking place and Ostwald ripening is not occurring.
74:
2460:
2655:
1705:
440:
Combining both expressions the following equation is obtained:
2095:
Growth and Coarsening: Ostwald Ripening in Material Processing
2850:
1807:
342:{\displaystyle \mu =k_{\mathrm {B} }T\log(C_{\mathrm {eq} })}
756:{\displaystyle C_{\mathrm {eq} }(r)>C_{\mathrm {eq} }(R)}
2532:
10.1175/1520-0469(2002)059<2681:HIITSR>2.0.CO;2
2161:
1803:
compound is added to stop this process from taking place.
1700:
1527:
scientific papers were published on opposite sides of the
2236:
Kahlweit, M. (1975). "Ostwald Ripening of Precipitates".
2417:
1745:, as an alternative to the physical processes governing
77:
systems, Ostwald ripening is also found in water-in-oil
51:
Growth of bubbles in a liquid foam via Ostwald ripening.
2091:
2031:"Studien ĂŒber die Bildung und Umwandlung fester Körper"
1556:
1338:
1227:
1198:
1163:
1134:
1105:
1069:
1036:
1004:
880:
842:
812:
792:
772:
701:
668:
449:
411:
391:
358:
290:
267:
231:
207:
183:
124:
1730:, it is the textural coarsening, aging or growth of
2054:
2052:
1806:Diffusional growth of larger drops in liquid water
1850:Solubility equilibrium § Particle size effect
1780:. Ostwald ripening is also the key process in the
1641:
1507:
1233:
1204:
1176:
1140:
1111:
1082:
1042:
1016:
982:
854:
824:
798:
778:
755:
684:
651:
429:
397:
373:
341:
273:
249:
213:
189:
166:
2917:
2049:
1784:and aging of precipitates, an important step in
1544:obey LSW theory after initial stages of growth.
1272:is a separate process from growth, this places
1873:
2504:
2356:. Royal Society of Chemistry. pp. 78â79.
1734:and crystals in solid rock which is below the
1686:
2571:
2324:
1929:
2235:
1675:. In this case, Ostwald ripening causes the
1564:
1557:
1011:
1005:
907:
900:
888:
881:
2062:Encyclopedia of Surface and Colloid Science
2028:
2578:
2564:
2505:Wood, R.; Irons, S.; Jonas, P. R. (2002).
2196:
2164:Journal of Physics and Chemistry of Solids
2118:
2092:Ratke, Lorenz; Voorhees, Peter W. (2002).
1708:mixed with water grow by Ostwald ripening.
2530:
2402:
2238:Advances in Colloid and Interface Science
1963:
1899:
1297:. Another such approach is to change the
104:Cubic crystal structure (sodium chloride)
2585:
1699:
99:
37:
18:
2058:
2918:
2297:
2559:
2349:
1719:Another gastronomical example is the
662:Thus, the equilibrium concentration,
2376:
2085:
2039:Zeitschrift fĂŒr Physikalische Chemie
1695:
1026:average radius of all the particles
855:{\displaystyle t\rightarrow \infty }
250:{\displaystyle \nu _{\mathrm {at} }}
85:is found in oil-in-water emulsions.
2931:Chemical engineering thermodynamics
2552:a 3D Kinetic Monte Carlo simulation
2511:Journal of the Atmospheric Sciences
2019:, vol. 2, part 1. Leipzig, Germany.
1791:Ostwald ripening can also occur in
13:
1992:Compendium of Chemical Terminology
1590:
1075:
938:
849:
738:
735:
711:
708:
636:
619:
616:
597:
589:
580:
577:
553:
550:
529:
526:
497:
486:
483:
456:
421:
418:
365:
330:
327:
303:
241:
238:
152:
149:
125:
14:
2957:
2543:
1017:{\displaystyle \langle R\rangle }
430:{\displaystyle C_{\mathrm {eq} }}
2759:
2476:10.1111/j.1750-3841.2011.02484.x
1915:
374:{\displaystyle k_{\mathrm {B} }}
2498:
2454:
2411:
2370:
2343:
2318:
2291:
2256:
2229:
2190:
2017:Lehrbuch der Allgemeinen Chemie
2155:
2112:
2098:. Springer. pp. 117â118.
2022:
2009:
1980:
1923:
1867:
1354:
1342:
846:
806:are the particles radius, and
750:
744:
723:
717:
592:
586:
565:
559:
541:
336:
318:
1:
2298:Branen, Alfred Larry (2002).
2203:Zeitschrift fĂŒr Elektrochemie
1860:
834:Fickâs first law of diffusion
2325:Pharmatech-rx (2024-08-10).
2250:10.1016/0001-8686(75)85001-9
2184:10.1016/0022-3697(61)90054-3
2121:Journal of Materials Science
88:
58:is a phenomenon observed in
7:
2065:. CRC Press. p. 4230.
2059:Hubbard, Arthur T. (2004).
1813:
1687:Controlled Ostwald Ripening
1221:
1192:
1157:
1128:
1099:
1083:{\displaystyle c_{\infty }}
1063:
1030:
998:
10:
2962:
2796:Electrostatic precipitator
2404:10.1093/petrology/44.5.833
2304:. CRC Press. p. 724.
2897:
2869:
2836:Rotary vacuum-drum filter
2768:
2757:
2593:
1799:is desired, an extremely
1315:having a positive value.
1153:of the particle material
1124:of the particle material
1095:of the particle material
2941:Crystallographic defects
2879:Aqueous two-phase system
2701:Liquidâliquid extraction
2353:The Science of Ice Cream
2285:10.1103/PhysRevE.58.7691
2215:10.1002/bbpc.19610650704
1268:being zero; but because
2776:API oilâwater separator
2646:Dissolved air flotation
2464:Journal of Food Science
2141:10.1023/A:1015388912729
2005:10.1351/goldbook.O04348
1825:Coalescence (chemistry)
1673:emulsion polymerization
1249:Note that the quantity
1043:{\displaystyle \gamma }
405:to the temperature and
214:{\displaystyle \sigma }
2741:Solid-phase extraction
1709:
1661:reaction rate constant
1643:
1538:spinodal decomposition
1509:
1311:with the initial time
1235:
1206:
1178:
1142:
1113:
1084:
1044:
1018:
984:
856:
826:
825:{\displaystyle r<R}
800:
780:
757:
686:
685:{\displaystyle C_{eq}}
653:
431:
399:
375:
343:
275:
251:
215:
191:
168:
105:
52:
35:
2861:Vacuum ceramic filter
2856:Sublimation apparatus
2661:Electrochromatography
2621:Cross-flow filtration
2350:Clark, Chris (2004).
1936:Nature Communications
1830:Coalescence (physics)
1703:
1644:
1510:
1320:distribution function
1236:
1207:
1179:
1177:{\displaystyle R_{g}}
1151:diffusion coefficient
1143:
1114:
1085:
1045:
1019:
985:
857:
827:
801:
781:
758:
687:
654:
432:
400:
376:
344:
276:
252:
216:
192:
169:
103:
50:
22:
2811:Fractionating column
2606:Acidâbase extraction
2587:Separation processes
2383:Journal of Petrology
2029:Ostwald, W. (1897).
2015:Ostwald, W. (1896).
1786:gravimetric analysis
1554:
1336:
1225:
1215:absolute temperature
1196:
1161:
1132:
1103:
1067:
1034:
1002:
878:
840:
810:
790:
770:
699:
666:
447:
409:
389:
356:
288:
265:
229:
205:
190:{\displaystyle \mu }
181:
122:
23:Ostwald ripening in
2936:Colloidal chemistry
2631:Cyclonic separation
2523:2002JAtS...59.2681W
2432:2001Semic..35.1378V
2395:2003JPet...44..833M
2277:1998PhRvE..58.7691V
2197:Wagner, C. (1961).
2176:1961JPCS...19...35L
2133:2002JMatS..37.2171B
1956:10.1038/ncomms14110
1948:2017NatCo...814110H
1845:Rock microstructure
1663:of attachment with
1540:have been shown to
920:
381:corresponds to the
197:corresponds to the
2926:Physical chemistry
2691:Gravity separation
2327:"Ostwald Ripening"
1892:10.1039/C5SC01787D
1710:
1639:
1505:
1253:is different from
1231:
1202:
1187:ideal gas constant
1174:
1138:
1109:
1080:
1040:
1014:
980:
906:
852:
822:
796:
776:
753:
682:
649:
427:
395:
383:Boltzmann constant
371:
339:
271:
247:
211:
199:chemical potential
187:
164:
106:
53:
36:
2913:
2912:
2831:Rapid sand filter
2726:Recrystallization
2706:Electroextraction
2666:Electrofiltration
2517:(18): 2681â2693.
2440:10.1134/1.1427975
2426:(12): 1378â1382.
2377:Mock, A. (2003).
2363:978-0-85404-629-4
2311:978-0-8247-9343-2
2265:Physical Review E
2127:(11): 2171â2202.
2105:978-3-540-42563-2
2072:978-0-8247-0759-0
1840:Kirkendall effect
1696:Specific examples
1634:
1486:
1453:
1439:
1415:
1401:
1368:
1247:
1246:
1234:{\displaystyle t}
1205:{\displaystyle T}
1141:{\displaystyle D}
1112:{\displaystyle v}
975:
832:. Inferring from
799:{\displaystyle R}
779:{\displaystyle r}
646:
539:
502:
398:{\displaystyle T}
274:{\displaystyle r}
162:
113:Kelvin's equation
95:thermodynamically
48:
2953:
2763:
2580:
2573:
2566:
2557:
2556:
2550:Ostwald Ripening
2537:
2536:
2534:
2502:
2496:
2495:
2458:
2452:
2451:
2415:
2409:
2408:
2406:
2374:
2368:
2367:
2347:
2341:
2340:
2338:
2337:
2322:
2316:
2315:
2295:
2289:
2288:
2271:(6): 7691â7699.
2260:
2254:
2253:
2233:
2227:
2226:
2194:
2188:
2187:
2159:
2153:
2152:
2116:
2110:
2109:
2089:
2083:
2082:
2080:
2079:
2056:
2047:
2046:
2036:
2026:
2020:
2013:
2007:
1997:Ostwald ripening
1984:
1978:
1977:
1967:
1927:
1921:
1920:
1919:
1913:
1903:
1886:(9): 5197â5203.
1871:
1762:aqueous solution
1753:and growth rate
1704:Oil droplets in
1658:
1648:
1646:
1645:
1640:
1635:
1633:
1629:
1628:
1615:
1614:
1613:
1604:
1603:
1594:
1593:
1577:
1572:
1571:
1514:
1512:
1511:
1506:
1492:
1488:
1487:
1485:
1471:
1455:
1454:
1446:
1444:
1440:
1438:
1424:
1417:
1416:
1408:
1406:
1402:
1400:
1386:
1379:
1378:
1369:
1361:
1328:
1324:
1314:
1310:
1303:
1296:
1292:
1285:
1278:
1267:
1260:
1256:
1252:
1240:
1238:
1237:
1232:
1211:
1209:
1208:
1203:
1183:
1181:
1180:
1175:
1173:
1172:
1147:
1145:
1144:
1139:
1118:
1116:
1115:
1110:
1089:
1087:
1086:
1081:
1079:
1078:
1049:
1047:
1046:
1041:
1023:
1021:
1020:
1015:
996:
995:
989:
987:
986:
981:
976:
974:
970:
969:
956:
952:
951:
942:
941:
925:
919:
914:
896:
895:
861:
859:
858:
853:
831:
829:
828:
823:
805:
803:
802:
797:
785:
783:
782:
777:
762:
760:
759:
754:
743:
742:
741:
716:
715:
714:
691:
689:
688:
683:
681:
680:
658:
656:
655:
650:
648:
647:
645:
641:
640:
639:
625:
624:
623:
622:
602:
600:
585:
584:
583:
558:
557:
556:
540:
535:
534:
533:
532:
512:
507:
503:
501:
500:
491:
490:
489:
476:
461:
460:
459:
436:
434:
433:
428:
426:
425:
424:
404:
402:
401:
396:
380:
378:
377:
372:
370:
369:
368:
348:
346:
345:
340:
335:
334:
333:
308:
307:
306:
280:
278:
277:
272:
256:
254:
253:
248:
246:
245:
244:
220:
218:
217:
212:
196:
194:
193:
188:
173:
171:
170:
165:
163:
158:
157:
156:
155:
135:
56:Ostwald ripening
49:
2961:
2960:
2956:
2955:
2954:
2952:
2951:
2950:
2916:
2915:
2914:
2909:
2893:
2871:
2865:
2826:Protein skimmer
2764:
2755:
2751:Ultrafiltration
2731:Reverse osmosis
2711:Microfiltration
2686:Froth flotation
2626:Crystallization
2589:
2584:
2546:
2541:
2540:
2503:
2499:
2459:
2455:
2416:
2412:
2375:
2371:
2364:
2348:
2344:
2335:
2333:
2323:
2319:
2312:
2296:
2292:
2261:
2257:
2234:
2230:
2195:
2191:
2160:
2156:
2117:
2113:
2106:
2090:
2086:
2077:
2075:
2073:
2057:
2050:
2034:
2027:
2023:
2014:
2010:
1985:
1981:
1928:
1924:
1914:
1872:
1868:
1863:
1855:Viedma ripening
1835:Critical radius
1816:
1698:
1689:
1657:
1653:
1624:
1620:
1616:
1609:
1605:
1599:
1595:
1589:
1585:
1578:
1576:
1567:
1563:
1555:
1552:
1551:
1475:
1470:
1466:
1462:
1445:
1428:
1423:
1419:
1418:
1407:
1390:
1385:
1381:
1380:
1374:
1370:
1360:
1337:
1334:
1333:
1326:
1322:
1312:
1309:
1305:
1302:
1298:
1294:
1291:
1287:
1284:
1280:
1277:
1273:
1266:
1262:
1258:
1254:
1250:
1226:
1223:
1222:
1197:
1194:
1193:
1168:
1164:
1162:
1159:
1158:
1133:
1130:
1129:
1104:
1101:
1100:
1074:
1070:
1068:
1065:
1064:
1054:surface tension
1035:
1032:
1031:
1003:
1000:
999:
965:
961:
957:
947:
943:
937:
933:
926:
924:
915:
910:
891:
887:
879:
876:
875:
841:
838:
837:
811:
808:
807:
791:
788:
787:
771:
768:
767:
734:
733:
729:
707:
706:
702:
700:
697:
696:
673:
669:
667:
664:
663:
635:
634:
630:
626:
615:
614:
610:
603:
601:
596:
595:
576:
575:
571:
549:
548:
544:
525:
524:
520:
513:
511:
496:
492:
482:
481:
477:
475:
471:
455:
454:
450:
448:
445:
444:
417:
416:
412:
410:
407:
406:
390:
387:
386:
364:
363:
359:
357:
354:
353:
326:
325:
321:
302:
301:
297:
289:
286:
285:
266:
263:
262:
237:
236:
232:
230:
227:
226:
223:surface tension
206:
203:
202:
182:
179:
178:
148:
147:
143:
136:
134:
123:
120:
119:
91:
71:Wilhelm Ostwald
60:solid solutions
38:
17:
12:
11:
5:
2959:
2949:
2948:
2943:
2938:
2933:
2928:
2911:
2910:
2908:
2907:
2905:Unit operation
2901:
2899:
2895:
2894:
2892:
2891:
2886:
2881:
2875:
2873:
2867:
2866:
2864:
2863:
2858:
2853:
2848:
2843:
2838:
2833:
2828:
2823:
2818:
2813:
2808:
2803:
2798:
2793:
2788:
2783:
2778:
2772:
2770:
2766:
2765:
2758:
2756:
2754:
2753:
2748:
2743:
2738:
2733:
2728:
2723:
2718:
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2673:
2668:
2663:
2658:
2653:
2648:
2643:
2638:
2633:
2628:
2623:
2618:
2616:Chromatography
2613:
2608:
2603:
2597:
2595:
2591:
2590:
2583:
2582:
2575:
2568:
2560:
2554:
2553:
2545:
2544:External links
2542:
2539:
2538:
2497:
2470:(1): C33âC38.
2453:
2420:Semiconductors
2410:
2389:(5): 833â849.
2369:
2362:
2342:
2317:
2310:
2301:Food Additives
2290:
2255:
2228:
2209:(7): 581â591.
2189:
2170:(1â2): 35â50.
2154:
2111:
2104:
2084:
2071:
2048:
2021:
2008:
1979:
1922:
1865:
1864:
1862:
1859:
1858:
1857:
1852:
1847:
1842:
1837:
1832:
1827:
1822:
1815:
1812:
1774:crystal growth
1764:chemistry and
1755:thermochemical
1747:crystal growth
1697:
1694:
1688:
1685:
1655:
1650:
1649:
1638:
1632:
1627:
1623:
1619:
1612:
1608:
1602:
1598:
1592:
1588:
1584:
1581:
1575:
1570:
1566:
1562:
1559:
1542:quantitatively
1516:
1515:
1504:
1501:
1498:
1495:
1491:
1484:
1481:
1478:
1474:
1469:
1465:
1461:
1458:
1452:
1449:
1443:
1437:
1434:
1431:
1427:
1422:
1414:
1411:
1405:
1399:
1396:
1393:
1389:
1384:
1377:
1373:
1367:
1364:
1359:
1356:
1353:
1350:
1347:
1344:
1341:
1307:
1300:
1289:
1282:
1275:
1264:
1245:
1244:
1241:
1230:
1219:
1218:
1212:
1201:
1190:
1189:
1184:
1171:
1167:
1155:
1154:
1148:
1137:
1126:
1125:
1119:
1108:
1097:
1096:
1090:
1077:
1073:
1061:
1060:
1058:surface energy
1050:
1039:
1028:
1027:
1024:
1013:
1010:
1007:
991:
990:
979:
973:
968:
964:
960:
955:
950:
946:
940:
936:
932:
929:
923:
918:
913:
909:
905:
902:
899:
894:
890:
886:
883:
851:
848:
845:
821:
818:
815:
795:
775:
764:
763:
752:
749:
746:
740:
737:
732:
728:
725:
722:
719:
713:
710:
705:
679:
676:
672:
660:
659:
644:
638:
633:
629:
621:
618:
613:
609:
606:
599:
594:
591:
588:
582:
579:
574:
570:
567:
564:
561:
555:
552:
547:
543:
538:
531:
528:
523:
519:
516:
510:
506:
499:
495:
488:
485:
480:
474:
470:
467:
464:
458:
453:
423:
420:
415:
394:
367:
362:
350:
349:
338:
332:
329:
324:
320:
317:
314:
311:
305:
300:
296:
293:
270:
243:
240:
235:
210:
186:
175:
174:
161:
154:
151:
146:
142:
139:
133:
130:
127:
90:
87:
15:
9:
6:
4:
3:
2:
2958:
2947:
2946:Precipitation
2944:
2942:
2939:
2937:
2934:
2932:
2929:
2927:
2924:
2923:
2921:
2906:
2903:
2902:
2900:
2896:
2890:
2887:
2885:
2882:
2880:
2877:
2876:
2874:
2868:
2862:
2859:
2857:
2854:
2852:
2849:
2847:
2846:Spinning cone
2844:
2842:
2839:
2837:
2834:
2832:
2829:
2827:
2824:
2822:
2821:Mixer-settler
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2773:
2771:
2767:
2762:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2736:Sedimentation
2734:
2732:
2729:
2727:
2724:
2722:
2721:Precipitation
2719:
2717:
2714:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2602:
2599:
2598:
2596:
2592:
2588:
2581:
2576:
2574:
2569:
2567:
2562:
2561:
2558:
2551:
2548:
2547:
2533:
2528:
2524:
2520:
2516:
2512:
2508:
2501:
2493:
2489:
2485:
2481:
2477:
2473:
2469:
2465:
2457:
2449:
2445:
2441:
2437:
2433:
2429:
2425:
2421:
2414:
2405:
2400:
2396:
2392:
2388:
2384:
2380:
2373:
2365:
2359:
2355:
2354:
2346:
2332:
2328:
2321:
2313:
2307:
2303:
2302:
2294:
2286:
2282:
2278:
2274:
2270:
2266:
2259:
2251:
2247:
2243:
2239:
2232:
2224:
2220:
2216:
2212:
2208:
2204:
2200:
2193:
2185:
2181:
2177:
2173:
2169:
2165:
2158:
2150:
2146:
2142:
2138:
2134:
2130:
2126:
2122:
2115:
2107:
2101:
2097:
2096:
2088:
2074:
2068:
2064:
2063:
2055:
2053:
2044:
2040:
2032:
2025:
2018:
2012:
2006:
2002:
1998:
1994:
1993:
1988:
1983:
1975:
1971:
1966:
1961:
1957:
1953:
1949:
1945:
1941:
1937:
1933:
1926:
1918:
1911:
1907:
1902:
1897:
1893:
1889:
1885:
1881:
1877:
1870:
1866:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1823:
1821:
1818:
1817:
1811:
1809:
1804:
1802:
1798:
1794:
1789:
1787:
1783:
1779:
1775:
1771:
1767:
1763:
1758:
1757:limitations.
1756:
1752:
1748:
1744:
1741:
1737:
1733:
1729:
1724:
1722:
1717:
1715:
1707:
1702:
1693:
1684:
1682:
1678:
1674:
1669:
1666:
1662:
1636:
1630:
1625:
1621:
1617:
1610:
1606:
1600:
1596:
1586:
1582:
1579:
1573:
1568:
1560:
1550:
1549:
1548:
1545:
1543:
1539:
1535:
1530:
1525:
1521:
1502:
1499:
1496:
1493:
1489:
1482:
1479:
1476:
1472:
1467:
1463:
1459:
1456:
1450:
1447:
1441:
1435:
1432:
1429:
1425:
1420:
1412:
1409:
1403:
1397:
1394:
1391:
1387:
1382:
1375:
1371:
1365:
1362:
1357:
1351:
1348:
1345:
1339:
1332:
1331:
1330:
1321:
1316:
1271:
1242:
1228:
1220:
1216:
1213:
1199:
1191:
1188:
1185:
1169:
1165:
1156:
1152:
1149:
1135:
1127:
1123:
1120:
1106:
1098:
1094:
1091:
1071:
1062:
1059:
1055:
1051:
1037:
1029:
1025:
1008:
997:
994:
977:
971:
966:
962:
958:
953:
948:
944:
934:
930:
927:
921:
916:
911:
903:
897:
892:
884:
874:
873:
872:
869:
863:
843:
835:
819:
816:
813:
793:
773:
747:
730:
726:
720:
703:
695:
694:
693:
677:
674:
670:
642:
631:
627:
611:
607:
604:
572:
568:
562:
545:
536:
521:
517:
514:
508:
504:
493:
478:
472:
468:
465:
462:
451:
443:
442:
441:
438:
413:
392:
384:
360:
322:
315:
312:
309:
298:
294:
291:
284:
283:
282:
268:
260:
259:atomic volume
233:
224:
208:
200:
184:
159:
144:
140:
137:
131:
128:
118:
117:
116:
114:
110:
102:
98:
96:
86:
84:
80:
76:
73:in 1896. For
72:
67:
65:
61:
57:
33:
30:dissolved in
29:
28:nanoparticles
26:
21:
2806:Filter press
2791:Depth filter
2681:Flocculation
2651:Distillation
2514:
2510:
2500:
2467:
2463:
2456:
2423:
2419:
2413:
2386:
2382:
2372:
2352:
2345:
2334:. Retrieved
2330:
2320:
2300:
2293:
2268:
2264:
2258:
2241:
2237:
2231:
2206:
2202:
2192:
2167:
2163:
2157:
2124:
2120:
2114:
2094:
2087:
2076:. Retrieved
2061:
2042:
2038:
2024:
2016:
2011:
1990:
1982:
1939:
1935:
1925:
1883:
1879:
1869:
1805:
1797:miniemulsion
1790:
1778:quantum dots
1773:
1769:
1766:precipitates
1759:
1725:
1718:
1711:
1690:
1670:
1651:
1546:
1529:Iron Curtain
1517:
1317:
1248:
1122:molar volume
992:
864:
765:
661:
439:
351:
176:
111:
107:
92:
83:flocculation
68:
55:
54:
32:formaldehyde
2781:Belt filter
2746:Sublimation
2636:Decantation
2244:(1): 1â35.
1820:Aggregation
1801:hydrophobic
1732:phenocrysts
1721:ouzo effect
1534:simulations
1520:Carl Wagner
64:liquid sols
2920:Categories
2870:Multiphase
2801:Evaporator
2786:Centrifuge
2676:Filtration
2671:Extraction
2611:Adsorption
2601:Absorption
2336:2024-09-20
2331:Pharmatech
2078:2007-11-13
2045:: 289â330.
1861:References
1751:nucleation
1743:megacrysts
1740:orthoclase
1270:nucleation
1261:relies on
1093:solubility
2884:Azeotrope
2594:Processes
2484:1750-3841
2223:178975941
1942:: 14110.
1880:Chem. Sci
1782:digestion
1714:ice cream
1677:diffusion
1591:∞
1583:γ
1565:⟩
1558:⟨
1524:diffusion
1497:ρ
1483:ρ
1480:−
1468:−
1460:
1436:ρ
1433:−
1398:ρ
1372:ρ
1076:∞
1052:particle
1038:γ
1012:⟩
1006:⟨
939:∞
931:γ
908:⟩
901:⟨
898:−
889:⟩
882:⟨
868:diffusion
850:∞
847:→
612:ν
608:σ
590:∞
542:→
522:ν
518:σ
498:∞
469:
316:
292:μ
234:ν
209:σ
185:μ
145:ν
141:σ
129:μ
126:Δ
89:Mechanism
79:emulsions
75:colloidal
25:palladium
2898:Concepts
2889:Eutectic
2841:Scrubber
2816:Leachate
2696:Leaching
2641:Dialysis
2492:22133014
2448:93899315
2149:12733546
1974:28134337
1910:29449925
1814:See also
1793:emulsion
1681:monomers
81:, while
2872:systems
2769:Devices
2716:Osmosis
2519:Bibcode
2428:Bibcode
2391:Bibcode
2273:Bibcode
2172:Bibcode
2129:Bibcode
1965:5290267
1944:Bibcode
1901:5669216
1736:solidus
1728:geology
1659:is the
1323:f(R, t)
257:to the
221:to the
2656:Drying
2490:
2482:
2446:
2360:
2308:
2221:
2147:
2102:
2069:
1972:
1962:
1908:
1898:
1808:clouds
1770:nuclei
1706:pastis
1652:where
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