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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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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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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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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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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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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)
1400:. Upper Saddle River, New Jersey: Prentice Hall. pp.
698:{\displaystyle {\frac {dP_{A}}{dx}}=-{\frac {dP_{B}}{dx}}}
65:. 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
1424:(20). Royal Society of Chemistry (RSC): 4740–4742.
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537:{\displaystyle N_{A}=-D_{AB}{\frac {dC_{A}}{dx}}}
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315:
311:
307:
303:
299:
295:
292:
291:
290:
283:
275:
268:
266:
264:
260:
256:
253:
249:
245:
241:
237:
235:
231:
227:
223:
215:
213:
211:
202:
195:
190:
186:
183:
180:
177:
174:
171:
168:
165:
162:
158:
154:
151:
150:
149:
143:
141:
139:
134:
132:
120:
116:
104:
100:
96:
83:
81:
77:
72:
68:
64:
63:absolute zero
60:
56:
52:
45:
41:
37:
33:
28:
22:
1464:
1460:
1454:
1421:
1417:
1410:
1395:
1387:
1250:
1092:
936:
842:
784:
783:is equal to
777:
773:
772:in a volume
769:
763:
708:
616:
570:
554:
547:
453:/dx, where C
447:
420:
408:
402:
396:Contrary to
395:
386:
385:
372:
368:
360:
339:
336:equilibrium.
332:
297:
293:
288:
238:
222:cell biology
219:
207:
196:Significance
147:
144:Applications
135:
93:at the same
84:
59:temperatures
54:
50:
49:
43:
39:
35:
1371:Rigid rotor
363:equilibrium
244:respiration
226:amino acids
95:temperature
1563:Categories
1379:References
1342:Permeation
791:therefore
467:Fick's Law
424:increases.
240:Metabolism
1574:Diffusion
1499:1063-651X
1446:1463-9076
1365:Viscosity
1330:Mass flux
1262:Diffusion
1223:−
1192:−
1155:−
965:−
867:−
666:−
592:−
559:/dx or dC
492:−
413:diffusion
326:spin echo
252:mammalian
153:Sintering
99:particles
67:viscosity
55:diffusion
21:Diffusion
1507:11304296
1255:See also
173:Catalyst
161:ceramics
1479:Bibcode
1426:Bibcode
1336:Osmosis
1097:/dx=-dP
937:where D
764:where n
391:solvent
375:entropy
248:alveoli
234:osmosis
216:Biology
131:entropy
44:Bottom:
40:Middle:
1505:
1497:
1444:
320:(PFG)
259:oxygen
185:Doping
169:design
119:energy
113:(μ is
61:above
32:solute
1469:arXiv
1402:66–67
1120:and x
255:lungs
179:Steel
117:) an
109:>μ
89:and S
80:phase
1503:PMID
1495:ISSN
1442:ISSN
1124:is P
1113:is P
340:The
296:and
242:and
125:to S
71:flux
36:Top:
1487:doi
1434:doi
789:/ V
322:NMR
250:of
220:In
1565::
1501:.
1493:.
1485:.
1477:.
1465:63
1463:.
1440:.
1432:.
1420:.
1107:BA
1105:=D
1103:AB
939:AB
614:.
439:).
393:.
236:.
140:.
133:.
1509:.
1489::
1481::
1471::
1448:.
1436::
1428::
1422:2
1404:.
1231:1
1227:x
1218:2
1214:x
1208:)
1203:1
1200:A
1196:P
1187:2
1184:A
1180:P
1176:(
1167:T
1164:R
1160:D
1152:=
1147:A
1143:N
1128:2
1126:A
1122:2
1117:1
1115:A
1111:1
1099:B
1095:A
1075:x
1072:d
1065:A
1061:P
1057:d
1048:T
1045:R
1041:1
1034:B
1031:A
1027:D
1023:=
1017:x
1014:d
1007:B
1003:P
999:d
990:T
987:R
983:1
976:A
973:B
969:D
962:=
957:B
953:N
919:x
916:d
909:A
905:P
901:d
892:T
889:R
885:1
878:B
875:A
871:D
864:=
859:A
855:N
828:T
825:R
820:A
816:C
812:=
807:A
803:P
787:A
785:n
780:A
778:C
774:V
770:A
766:A
749:T
746:R
741:A
737:n
733:=
730:V
725:A
721:P
705:.
690:x
687:d
680:B
676:P
672:d
663:=
657:x
654:d
647:A
643:P
639:d
623:B
619:A
600:B
596:N
589:=
584:A
580:N
561:B
557:A
550:A
529:x
526:d
519:A
515:C
511:d
503:B
500:A
496:D
489:=
484:A
480:N
463:A
459:B
455:A
451:A
421:D
409:D
191:.
163:)
127:2
123:1
111:2
107:1
91:2
87:1
23:.
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