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found remote from their original positions. If the partition is removed, some molecules of A move towards the region occupied by B, their number depends on the number of molecules at the region considered. Concurrently, molecules of B diffuse toward regimens formerly occupied by pure A. Finally, complete mixing occurs. Before this point in time, a gradual variation in the concentration of A occurs along an axis, designated x, which joins the original compartments. This variation, expressed mathematically as -dC
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in the particle diffusion equation becomes dependent of concentration. For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases. For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration
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system (i.e. it is not at rest yet). Many results in classical thermodynamics are not easily applied to non-equilibrium systems. However, there sometimes occur so-called quasi-steady states, where the diffusion process does not change in time, where classical results may locally apply. As the name
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Transport of material in stagnant fluid or across streamlines of a fluid in a laminar flow occurs by molecular diffusion. Two adjacent compartments separated by a partition, containing pure gases A or B may be envisaged. Random movement of all molecules occurs so that after a period molecules are
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experiment this technique uses the nuclear spin precession phase, allowing to distinguish chemically and physically completely identical species e.g. in the liquid phase, as for example water molecules within liquid water. The self-diffusion coefficient of water has been experimentally determined
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of a system, i.e. diffusion is a spontaneous and irreversible process. Particles can spread out by diffusion, but will not spontaneously re-order themselves (absent changes to the system, assuming no creation of new chemical bonds, and absent external forces acting on the particle).
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occurs in a presence of concentration (or chemical potential) gradient and it results in net transport of mass. This is the process described by the diffusion equation. This diffusion is always a non-equilibrium process, increases the system entropy, and brings the system closer to
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of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of
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is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, this indicates that the rate of force is directly proportional to the driving force, which is the concentration gradient.
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Non-equilibrium fluid systems can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale.
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for these two types of diffusion are generally different because the diffusion coefficient for chemical diffusion is binary and it includes the effects due to the correlation of the movement of the different diffusing species.
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with high accuracy and thus serves often as a reference value for measurements on other liquids. The self-diffusion coefficient of neat water is: 2.299·10 m·s at 25 °C and 1.261·10 m·s at 4 °C.
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Holz, Manfred; Heil, Stefan R.; Sacco, Antonio (2000). "Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMR PFG measurements".
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With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas, following Fick's laws.
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in the particle diffusion equation is independent of particle concentration. In other cases, resulting interactions between particles within the solvent will account for the following effects:
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is the concentration of A. The negative sign arises because the concentration of A decreases as the distance x increases. Similarly, the variation in the concentration of gas B is -dC
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where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases. The rate of diffusion N
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If no bulk flow occurs in an element of length dx, the rates of diffusion of two ideal gases (of similar molar volume) A and B must be equal and opposite, that is
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molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container.
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with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.
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This basic equation applies to a number of situations. Restricting discussion exclusively to steady state conditions, in which neither dC
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Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion:
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Brogioli, Doriano; Vailati, Alberto (2000-12-22). "Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited".
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chemical reaction (and if the considered diffusing particles are chemical molecules in solution, then it is a
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With more molecules, there is a clear trend where the solute fills the container more and more uniformly.
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Maton, Anthea; Jean
Hopkins; Susan Johnson; David LaHart; Maryanna Quon Warner; Jill D. Wright (1997).
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This article is about spontaneous dispersion of mass. For a more generic treatment of diffusion, see
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diffuses out. Lungs contain a large surface area to facilitate this gas exchange process.
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Example of chemical (classical, Fick's, or
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of the fluid and the size (mass) of the particles. Diffusion explains the net
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Self diffusion, exemplified with an isotopic tracer of radioactive isotope Na
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can be diffused (e.g., with carbon or nitrogen) to modify its properties
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A tutorial on the theory behind and solution of the
Diffusion Equation.
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A similar equation may be derived for the counterdiffusion of gas B.
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is the diffusion of a large number of particles, most often within a
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Schematic representation of mixing of two substances by diffusion
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Molecular diffusion is typically described mathematically using
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within cells. Diffusion of solvents, such as water, through a
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Illustration of low entropy (top) and high entropy (bottom)
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NetLogo
Simulation Model for Educational Use (Java Applet)
1415:. Upper Saddle River, New Jersey: Prentice Hall. pp.
710:{\displaystyle {\frac {dP_{A}}{dx}}=-{\frac {dP_{B}}{dx}}}
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Fundamentally, two types of diffusion are distinguished:
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Diffusion on the nanoscale (with figures and animations)
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lies above a certain threshold. This is equivalent to a
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548:{\displaystyle N_{A}=-D_{AB}{\frac {dC_{A}}{dx}}}
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1482:(1). American Physical Society (APS): 012105.
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392:
390:
387:
382:
378:
375:
366:
359:
357:
354:
345:
342:
338:
334:
330:
326:
322:
318:
314:
310:
306:
303:
302:
301:
294:
286:
279:
277:
275:
271:
267:
264:
260:
256:
252:
248:
246:
242:
238:
234:
226:
224:
222:
213:
206:
201:
197:
194:
191:
188:
185:
182:
179:
176:
173:
169:
165:
162:
161:
160:
154:
152:
150:
145:
143:
131:
127:
115:
111:
107:
94:
92:
88:
83:
79:
75:
74:absolute zero
71:
67:
63:
56:
52:
48:
44:
39:
33:
19:
1479:
1475:
1469:
1436:
1432:
1425:
1410:
1402:
1262:
1104:
948:
854:
796:
795:is equal to
789:
785:
784:in a volume
781:
775:
720:
628:
582:
566:
558:
464:/dx, where C
458:
431:
419:
413:
407:Contrary to
406:
397:
396:
383:
379:
371:
350:
347:equilibrium.
343:
308:
304:
299:
249:
233:cell biology
230:
218:
207:Significance
158:
155:Applications
146:
104:at the same
95:
70:temperatures
65:
61:
60:
54:
50:
46:
1386:Rigid rotor
374:equilibrium
255:respiration
237:amino acids
106:temperature
1578:Categories
1394:References
1357:Permeation
803:therefore
478:Fick's law
435:increases.
251:Metabolism
1589:Diffusion
1514:1063-651X
1461:1463-9076
1380:Viscosity
1345:Mass flux
1274:Diffusion
1235:−
1204:−
1167:−
977:−
879:−
678:−
604:−
571:/dx or dC
503:−
424:diffusion
337:spin echo
263:mammalian
164:Sintering
110:particles
78:viscosity
66:diffusion
32:Diffusion
1522:11304296
1267:See also
184:Catalyst
172:ceramics
18:Diffused
1494:Bibcode
1441:Bibcode
1351:Osmosis
1109:/dx=-dP
949:where D
776:where n
402:solvent
386:entropy
259:alveoli
245:osmosis
227:Biology
142:entropy
55:Bottom:
51:Middle:
1520:
1512:
1459:
331:(PFG)
270:oxygen
196:Doping
180:design
130:energy
124:(μ is
72:above
43:solute
1484:arXiv
1417:66–67
1132:and x
266:lungs
190:Steel
128:) an
120:>μ
100:and S
91:phase
1518:PMID
1510:ISSN
1457:ISSN
1136:is P
1125:is P
351:The
307:and
253:and
136:to S
82:flux
47:Top:
1502:doi
1449:doi
801:/ V
333:NMR
261:of
231:In
1580::
1516:.
1508:.
1500:.
1492:.
1480:63
1478:.
1455:.
1447:.
1435:.
1119:BA
1117:=D
1115:AB
951:AB
626:.
450:).
404:.
247:.
151:.
144:.
1524:.
1504::
1496::
1486::
1463:.
1451::
1443::
1437:2
1419:.
1243:1
1239:x
1230:2
1226:x
1220:)
1215:1
1212:A
1208:P
1199:2
1196:A
1192:P
1188:(
1179:T
1176:R
1172:D
1164:=
1159:A
1155:N
1140:2
1138:A
1134:2
1129:1
1127:A
1123:1
1111:B
1107:A
1087:x
1084:d
1077:A
1073:P
1069:d
1060:T
1057:R
1053:1
1046:B
1043:A
1039:D
1035:=
1029:x
1026:d
1019:B
1015:P
1011:d
1002:T
999:R
995:1
988:A
985:B
981:D
974:=
969:B
965:N
931:x
928:d
921:A
917:P
913:d
904:T
901:R
897:1
890:B
887:A
883:D
876:=
871:A
867:N
840:T
837:R
832:A
828:C
824:=
819:A
815:P
799:A
797:n
792:A
790:C
786:V
782:A
778:A
761:T
758:R
753:A
749:n
745:=
742:V
737:A
733:P
717:.
702:x
699:d
692:B
688:P
684:d
675:=
669:x
666:d
659:A
655:P
651:d
635:B
631:A
612:B
608:N
601:=
596:A
592:N
573:B
569:A
561:A
540:x
537:d
530:A
526:C
522:d
514:B
511:A
507:D
500:=
495:A
491:N
474:A
470:B
466:A
462:A
432:D
420:D
202:.
174:)
138:2
134:1
122:2
118:1
102:2
98:1
34:.
20:)
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