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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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411:, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent (ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles and the interactions between solvent molecules; in this case, the particles do not interact when inside the solvent).
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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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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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In the case of an attractive interaction between particles, particles exhibit a tendency to coalesce and form clusters if their
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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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1094:{\displaystyle N_{B}=-D_{BA}{\frac {1}{RT}}{\frac {dP_{B}}{dx}}=D_{AB}{\frac {1}{RT}}{\frac {dP_{A}}{dx}}}
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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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Because chemical diffusion is a net transport process, the system in which it takes place is not an
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A basic introduction to the classical theory of volume diffusion (with figures and animations)
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For an ideal gas the partial pressure is related to the molar concentration by the relation
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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
Fickian) diffusion of sodium chloride in water
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rely in part upon diffusion in addition to bulk or active processes. For example, in the
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suggests, this process is a not a true equilibrium since the system is still evolving.
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Short movie on brownian motion (includes calculation of the diffusion coefficient)
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Diffusion from a microscopic and macroscopic point of view. Initially, there are
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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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Thermal motion of liquid or gas particles at temperatures above absolute zero
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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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over the distance dx. Similarly, the partial pressure of B changes dP
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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)
1411:. Upper Saddle River, New Jersey: Prentice Hall. pp.
709:{\displaystyle {\frac {dP_{A}}{dx}}=-{\frac {dP_{B}}{dx}}}
76:. The rate of this movement is a function of temperature,
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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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Pages displaying wikidata descriptions as a fallback
1435:(20). Royal Society of Chemistry (RSC): 4740–4742.
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548:{\displaystyle N_{A}=-D_{AB}{\frac {dC_{A}}{dx}}}
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1535:Some pictures that display diffusion and osmosis
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1478:(1). American Physical Society (APS): 012105.
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1384: – Model of rotating physical systems
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844:{\displaystyle P_{A}=C_{A}RT}
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410:
405:
403:
399:
390:
387:
382:
378:
375:
366:
357:
354:
345:
342:
338:
334:
330:
326:
322:
318:
314:
310:
306:
303:
302:
301:
294:
286:
277:
275:
271:
267:
264:
260:
256:
252:
248:
246:
242:
238:
234:
224:
222:
213:
201:
197:
194:
191:
188:
185:
182:
179:
176:
173:
169:
165:
162:
161:
160:
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:
1475:
1471:
1465:
1432:
1428:
1421:
1406:
1398:
1261:
1103:
947:
853:
795:
794:is equal to
788:
784:
783:in a volume
780:
774:
719:
627:
581:
565:
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:
1382:Rigid rotor
374:equilibrium
255:respiration
237:amino acids
106:temperature
1574:Categories
1390:References
1353:Permeation
802:therefore
478:Fick's Law
435:increases.
251:Metabolism
1585:Diffusion
1510:1063-651X
1457:1463-9076
1376:Viscosity
1341:Mass flux
1273:Diffusion
1234:−
1203:−
1166:−
976:−
878:−
677:−
603:−
570:/dx or dC
503:−
424:diffusion
337:spin echo
263:mammalian
164:Sintering
110:particles
78:viscosity
66:diffusion
32:Diffusion
1518:11304296
1266:See also
184:Catalyst
172:ceramics
1490:Bibcode
1437:Bibcode
1347:Osmosis
1108:/dx=-dP
948:where D
775:where n
402:solvent
386:entropy
259:alveoli
245:osmosis
227:Biology
142:entropy
55:Bottom:
51:Middle:
1516:
1508:
1455:
331:(PFG)
270:oxygen
196:Doping
180:design
130:energy
124:(μ is
72:above
43:solute
1480:arXiv
1413:66–67
1131:and x
266:lungs
190:Steel
128:) an
120:>μ
100:and S
91:phase
1514:PMID
1506:ISSN
1453:ISSN
1135:is P
1124:is P
351:The
307:and
253:and
136:to S
82:flux
47:Top:
1498:doi
1445:doi
800:/ V
333:NMR
261:of
231:In
1576::
1512:.
1504:.
1496:.
1488:.
1476:63
1474:.
1451:.
1443:.
1431:.
1118:BA
1116:=D
1114:AB
950:AB
625:.
450:).
404:.
247:.
151:.
144:.
1520:.
1500::
1492::
1482::
1459:.
1447::
1439::
1433:2
1415:.
1242:1
1238:x
1229:2
1225:x
1219:)
1214:1
1211:A
1207:P
1198:2
1195:A
1191:P
1187:(
1178:T
1175:R
1171:D
1163:=
1158:A
1154:N
1139:2
1137:A
1133:2
1128:1
1126:A
1122:1
1110:B
1106:A
1086:x
1083:d
1076:A
1072:P
1068:d
1059:T
1056:R
1052:1
1045:B
1042:A
1038:D
1034:=
1028:x
1025:d
1018:B
1014:P
1010:d
1001:T
998:R
994:1
987:A
984:B
980:D
973:=
968:B
964:N
930:x
927:d
920:A
916:P
912:d
903:T
900:R
896:1
889:B
886:A
882:D
875:=
870:A
866:N
839:T
836:R
831:A
827:C
823:=
818:A
814:P
798:A
796:n
791:A
789:C
785:V
781:A
777:A
760:T
757:R
752:A
748:n
744:=
741:V
736:A
732:P
716:.
701:x
698:d
691:B
687:P
683:d
674:=
668:x
665:d
658:A
654:P
650:d
634:B
630:A
611:B
607:N
600:=
595:A
591:N
572:B
568: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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