270:
1277:
1289:
31:
1301:
246:
Depending on the goal, these two techniques are frequently employed since they are complimentary. It is obvious that the microscopic description is required to comprehend surface phenomena like the adsorption of macromolecules from polymer solutions and the blocking of pores, whereas the macroscopic
288:
Numerous factors influence fluid flow in porous media, and its fundamental function is to expend energy and create fluid via the wellbore. In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes
238:
At the microscopic and macroscopic levels, porous media can be classified. At the microscopic scale, the structure is represented statistically by the distribution of pore sizes, the degree of pore interconnection and orientation, the proportion of dead pores, etc. The macroscopic technique makes
354:. The generalized Murray's law is based on optimizing mass transfer by minimizing transport resistance in pores with a given volume, and can be applicable for optimizing mass transfer involving mass variations and chemical reactions involving flow processes, molecule or ion diffusion.
97:) can sometimes be derived from the respective properties of its constituents (solid matrix and fluid) and the media porosity and pores structure, but such a derivation is usually complex. Even the concept of porosity is only straightforward for a poroelastic medium.
789:
Martinez M.J., McTigue D.F. (1996) Modeling in
Nuclear Waste Isolation: Approximate Solutions for Flow in Unsaturated Porous Media. In: Wheeler M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York,
301:
A representation of the void phase that exists inside porous materials using a set or network of pores. It serves as a structural foundation for the prediction of transport parameters and is employed in the context of pore structure characterisation.
277:
Fluid flow through porous media is a subject of common interest and has emerged a separate field of study. The study of more general behaviour of porous media involving deformation of the solid frame is called
462:
330:-like structure, having a pore surface area that seems to grow indefinitely when viewed with progressively increasing resolution. Mathematically, this is described by assigning the pore surface a
960:
972:
Peng, Sheng; Hu, Qinhong; Dultz, Stefan; Zhang, Ming (2012). "Using X-ray computed tomography in pore structure characterization for a Berea sandstone: Resolution effect".
833:
Mohammadizadeh, SeyedMehdi; Moghaddam, Mehdi
Azhdary; Talebbeydokhti, Naser (2021). "Analysis of Flow in Porous Media using Combined Pressurized-Free surface Network".
961:
M. K. Head, H. S. Wong, N. R. Buenfeld, "Characterisation of 'Hadley’ Grains by
Confocal Microscopy", Cement & Concrete Research (2006), 36 (8) 1483 -1489
100:
Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a
1127:
564:
Hierarchically
Structured Porous Materials: From Nanoscience to Catalysis, Separation, Optics, Energy, and Life Science - Wiley Online Library
740:
537:
597:"Tuning and transferring slow photons from TiO2 photonic crystals to BiVO4 nanoparticles for unprecedented visible light photocatalysis"
147:
can be considered as porous media. Many of their important properties can only be rationalized by considering them to be porous media.
378:
293:, particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media.
1164:
1122:
877:
817:
645:
54:(voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a
1005:"Porous Liner Coated Inlet Duct: A Novel Approach to Attenuate Automotive Turbocharger Inlet Flow-Induced Sound Propagation"
285:
The theory of porous flows has applications in inkjet printing and nuclear waste disposal technologies, among others.
723:
687:
579:
255:
are of highest concern. and the molecular dimensions are significantly smaller than pore size of the porous system.
1305:
1189:
264:
542:
1137:
17:
1157:
342:. Porous materials have found some applications in many engineering fields including automotive sectors.
780:
Stephen D. Hoath, "Fundamentals of Inkjet
Printing - The Science of Inkjet and Droplets", Wiley VCH 2016
305:
There are many idealized models of pore structures. They can be broadly divided into three categories:
1184:
934:
Crawford, J.W. (1994). "The relationship between structure and the hydraulic conductivity of soil".
595:
Madanu, Thomas L.; Mouchet, Sébastien R.; Deparis, Olivier; Liu, Jing; Li, Yu; Su, Bao-Lian (2023).
187:
1281:
90:
1150:
1327:
1293:
1207:
517:
269:
214:. Two important current fields of application for porous materials are energy conversion and
179:
1053:
977:
906:
82:
1132:
8:
1202:
507:
335:
331:
124:
1057:
981:
910:
1332:
1252:
1133:
Graphical depiction of different flow rates through materials of differing permeability
1082:
1041:
947:
763:
679:
512:
105:
334:
greater than 2. Experimental methods for the investigation of pore structures include
150:
The concept of porous media is used in many areas of applied science and engineering:
1288:
1087:
1069:
873:
869:
813:
767:
719:
683:
667:
641:
575:
470:
is the ratio of mass variation during mass transfer in the parent pore, the exponent
316:
199:
132:
39:
759:
1077:
1061:
1016:
985:
943:
914:
865:
857:
838:
805:
755:
711:
675:
633:
608:
567:
522:
339:
227:
211:
86:
989:
1247:
895:"Fractal pore structure of sedimentary rocks: Simulation by ballistic deposition"
842:
351:
136:
1037:
1021:
1004:
809:
612:
290:
215:
183:
171:
167:
112:
1321:
1173:
1073:
715:
596:
532:
279:
252:
240:
626:
Zhang, Tao; Asefa, Tewodros (2020). Gitis, Vitaly; Rothenberg, Gadi (eds.).
1257:
1242:
1091:
703:
195:
163:
571:
1262:
1237:
919:
894:
191:
175:
1065:
1227:
1222:
527:
502:
248:
207:
203:
151:
94:
1232:
832:
310:
223:
219:
159:
155:
1036:
Zheng, Xianfeng; Shen, Guofang; Wang, Chao; Li, Yu; Dunphy, Darren;
741:"Tortuosity of porous media: Image analysis and physical simulation"
497:
78:
51:
637:
218:, where porous materials are essential for superpacitors, (photo-)
1217:
1212:
327:
247:
approach is frequently quite sufficient for process design where
144:
128:
120:
1142:
627:
74:
are often also usefully analyzed using concept of porous media.
30:
457:{\displaystyle r_{o}^{a}={1 \over 1-X}\sum _{i=1}^{N}r_{i}^{a}}
140:
101:
59:
1042:"Bio-inspired Murray materials for mass transfer and activity"
243:
that have been averaged at scales far bigger than pore size.
67:
55:
739:
Fu, Jinlong; Thomas, Hywel R.; Li, Chenfeng (January 2021).
562:
Su, Bao-Lian; Sanchez, Clément; Yang, Xiao-Yu, eds. (2011).
476:
is dependent on the type of the transfer. For laminar flow
116:
71:
104:. However, there is also a concept of closed porosity and
63:
672:
Non-Newtonian Flow and
Applied Rheology (Second Edition)
708:
Modelling, Simulation and
Control of the Dyeing Process
594:
661:
659:
657:
381:
666:
Chhabra, R. P.; Richardson, J. F. (1 January 2008).
77:A porous medium is most often characterised by its
1040:; Brinker, C. Jeffrey; Su, Bao-Lian (2017-04-06).
654:
456:
258:
665:
1319:
971:
1035:
1128:Tailoring porous media to control permeability
710:. Woodhead Publishing: 54–81. 1 January 2014.
375:, the formula of generalized Murray's law is:
233:
1158:
561:
899:Journal of Geophysical Research: Solid Earth
357:For connecting a parent pipe with radius of
345:
1165:
1151:
1138:Fundamentals of Fluid Flow in Porous Media
738:
625:
108:, i.e. the pore space accessible to flow.
1081:
1020:
918:
1002:
933:
855:
601:Journal of Colloid and Interface Science
350:One of the Laws for porous materials is
296:
268:
29:
81:. Other properties of the medium (e.g.
14:
1320:
484:=7/3; for molecule or ionic diffusion
366:to many children pipes with radius of
66:). The skeletal material is usually a
27:Material containing fluid-filled voids
1146:
892:
1300:
704:"3 - Dye transport in fluid systems"
1110:Dynamics of Fluids in Porous Media.
24:
1102:
948:10.1111/j.1365-2389.1994.tb00535.x
680:10.1016/b978-0-7506-8532-0.00005-6
674:. Butterworth-Heinemann: 249–315.
139:), and man made materials such as
25:
1344:
1172:
1116:
668:"Chapter 5 - Particulate systems"
315:arrays of solid particles (e.g.,
1299:
1287:
1276:
1275:
936:European Journal of Soil Science
870:10.1007/978-3-642-40872-4_1055-2
111:Many natural substances such as
1029:
996:
965:
954:
927:
886:
849:
826:
760:10.1016/j.earscirev.2020.103439
632:. Singapore: WORLD SCIENTIFIC.
273:Fluid flow through porous media
265:Fluid flow through porous media
259:Fluid flow through porous media
793:
783:
774:
732:
696:
619:
588:
555:
326:Porous materials often have a
13:
1:
990:10.1016/j.jhydrol.2012.09.034
548:
1009:Engineering Research Express
843:10.1615/JPorMedia.2021025407
629:Handbook of Porous Materials
352:the generalized Murray's law
7:
1003:Ravanbod, Mohammad (2023).
491:
234:Microscopic and macroscopic
10:
1349:
856:Burganos, Vasilis (2015).
837:. Begel House Inc.: 1–15.
810:10.1142/9789811219535_0002
802:Fluid Flow in Porous Media
613:10.1016/j.jcis.2022.12.033
262:
1271:
1198:
1180:
862:Encyclopedia of Membranes
346:Laws for porous materials
50:is a material containing
1022:10.1088/2631-8695/acbfa4
804:: 47–67. November 2020.
716:10.1533/9780857097583.54
188:construction engineering
835:journal of Porous Media
480:=3; for turbulent flow
91:electrical conductivity
1123:Defining Permeability
893:Dutta, Tapati (2003).
458:
438:
274:
70:, but structures like
35:
1208:Environmental science
1046:Nature Communications
748:Earth-Science Reviews
572:10.1002/9783527639588
518:Percolation threshold
459:
418:
297:Pore structure models
272:
180:petroleum engineering
33:
1112:(Elsevier, New York)
976:. 472–473: 254–261.
974:Journal of Hydrology
920:10.1029/2001JB000523
503:Nanoporous materials
379:
125:petroleum reservoirs
1203:Atmospheric science
1066:10.1038/ncomms14921
1058:2017NatCo...814921Z
982:2012JHyd..472..254P
911:2003JGRB..108.2062D
508:NMR in porous media
453:
396:
336:confocal microscopy
332:Hausdorff dimension
289:this connection is
135:(e.g. bones, wood,
1253:Physical geography
538:Reactive transport
513:Percolation theory
454:
439:
382:
275:
133:biological tissues
106:effective porosity
36:
1315:
1314:
879:978-3-642-40872-4
864:. Springer: 1–2.
819:978-981-12-1952-8
647:978-981-12-2322-8
416:
317:random close pack
200:petroleum geology
40:materials science
34:Open-cell ceramic
16:(Redirected from
1340:
1303:
1302:
1291:
1279:
1278:
1167:
1160:
1153:
1144:
1143:
1096:
1095:
1085:
1033:
1027:
1026:
1024:
1000:
994:
993:
969:
963:
958:
952:
951:
931:
925:
924:
922:
890:
884:
883:
853:
847:
846:
830:
824:
823:
800:"Basic theory".
797:
791:
787:
781:
778:
772:
771:
745:
736:
730:
729:
700:
694:
693:
663:
652:
651:
623:
617:
616:
592:
586:
585:
559:
523:Reticulated foam
463:
461:
460:
455:
452:
447:
437:
432:
417:
415:
401:
395:
390:
340:x-ray tomography
212:material science
87:tensile strength
21:
1348:
1347:
1343:
1342:
1341:
1339:
1338:
1337:
1318:
1317:
1316:
1311:
1267:
1248:Paleogeoscience
1194:
1176:
1171:
1119:
1108:J. Bear; (1972)
1105:
1103:Further reading
1100:
1099:
1038:Hasan, Tawfique
1034:
1030:
1001:
997:
970:
966:
959:
955:
932:
928:
891:
887:
880:
854:
850:
831:
827:
820:
799:
798:
794:
788:
784:
779:
775:
743:
737:
733:
726:
702:
701:
697:
690:
664:
655:
648:
624:
620:
593:
589:
582:
560:
556:
551:
494:
448:
443:
433:
422:
405:
400:
391:
386:
380:
377:
376:
372:
363:
348:
299:
267:
261:
241:bulk properties
236:
206:), biology and
48:porous material
28:
23:
22:
15:
12:
11:
5:
1346:
1336:
1335:
1330:
1313:
1312:
1310:
1309:
1297:
1285:
1272:
1269:
1268:
1266:
1265:
1260:
1255:
1250:
1245:
1240:
1235:
1230:
1225:
1220:
1215:
1210:
1205:
1199:
1196:
1195:
1193:
1192:
1187:
1181:
1178:
1177:
1170:
1169:
1162:
1155:
1147:
1141:
1140:
1135:
1130:
1125:
1118:
1117:External links
1115:
1114:
1113:
1104:
1101:
1098:
1097:
1028:
995:
964:
953:
942:(4): 493–502.
926:
885:
878:
848:
825:
818:
792:
782:
773:
731:
724:
695:
688:
653:
646:
618:
587:
580:
553:
552:
550:
547:
546:
545:
540:
535:
530:
525:
520:
515:
510:
505:
500:
493:
490:
451:
446:
442:
436:
431:
428:
425:
421:
414:
411:
408:
404:
399:
394:
389:
385:
370:
361:
347:
344:
324:
323:
320:
313:
298:
295:
263:Main article:
260:
257:
235:
232:
216:energy storage
184:bioremediation
172:rock mechanics
168:soil mechanics
26:
9:
6:
4:
3:
2:
1345:
1334:
1331:
1329:
1326:
1325:
1323:
1308:
1307:
1298:
1296:
1295:
1290:
1286:
1284:
1283:
1274:
1273:
1270:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1246:
1244:
1241:
1239:
1236:
1234:
1231:
1229:
1226:
1224:
1221:
1219:
1216:
1214:
1211:
1209:
1206:
1204:
1201:
1200:
1197:
1191:
1188:
1186:
1183:
1182:
1179:
1175:
1174:Earth science
1168:
1163:
1161:
1156:
1154:
1149:
1148:
1145:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1120:
1111:
1107:
1106:
1093:
1089:
1084:
1079:
1075:
1071:
1067:
1063:
1059:
1055:
1051:
1047:
1043:
1039:
1032:
1023:
1018:
1015:(1): 015047.
1014:
1010:
1006:
999:
991:
987:
983:
979:
975:
968:
962:
957:
949:
945:
941:
937:
930:
921:
916:
912:
908:
904:
900:
896:
889:
881:
875:
871:
867:
863:
859:
852:
844:
840:
836:
829:
821:
815:
811:
807:
803:
796:
786:
777:
769:
765:
761:
757:
753:
749:
742:
735:
727:
725:9780857091338
721:
717:
713:
709:
705:
699:
691:
689:9780750685320
685:
681:
677:
673:
669:
662:
660:
658:
649:
643:
639:
638:10.1142/11909
635:
631:
630:
622:
614:
610:
606:
602:
598:
591:
583:
581:9783527639588
577:
573:
569:
565:
558:
554:
544:
541:
539:
536:
534:
533:Poromechanics
531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
495:
489:
487:
483:
479:
475:
474:
469:
468:
449:
444:
440:
434:
429:
426:
423:
419:
412:
409:
406:
402:
397:
392:
387:
383:
374:
373:
365:
364:
355:
353:
343:
341:
337:
333:
329:
321:
318:
314:
312:
308:
307:
306:
303:
294:
292:
286:
283:
281:
280:poromechanics
271:
266:
256:
254:
253:mass transfer
250:
244:
242:
231:
229:
225:
221:
217:
213:
209:
205:
201:
197:
193:
189:
185:
181:
177:
173:
169:
165:
161:
157:
153:
148:
146:
142:
138:
134:
130:
126:
122:
118:
114:
109:
107:
103:
98:
96:
92:
88:
84:
80:
75:
73:
69:
65:
61:
57:
53:
49:
45:
44:porous medium
41:
32:
19:
1328:Porous media
1304:
1292:
1280:
1258:Soil science
1243:Oceanography
1109:
1049:
1045:
1031:
1012:
1008:
998:
973:
967:
956:
939:
935:
929:
905:(B2): 2062.
902:
898:
888:
861:
858:"Pore Model"
851:
834:
828:
801:
795:
785:
776:
751:
747:
734:
707:
698:
671:
628:
621:
604:
600:
590:
563:
557:
543:Permeability
485:
481:
477:
472:
471:
466:
465:
464:, where the
368:
367:
359:
358:
356:
349:
325:
309:networks of
304:
300:
287:
284:
276:
251:, heat, and
245:
237:
196:hydrogeology
164:geomechanics
149:
110:
99:
83:permeability
76:
47:
43:
37:
18:Porous media
1263:Volcanology
1238:Meteorology
607:: 290–299.
319:of spheres)
311:capillaries
291:Darcy's law
192:geosciences
176:engineering
1322:Categories
1228:Glaciology
1223:Geophysics
754:: 103439.
549:References
528:Filtration
249:fluid flow
224:fuel cells
208:biophysics
204:geophysics
152:filtration
95:tortuosity
1333:Materials
1233:Hydrology
1074:2041-1723
1052:: 14921.
768:229386129
488:=2; etc.
420:∑
410:−
228:batteries
220:catalysis
160:acoustics
156:mechanics
1282:Category
1092:28382972
498:Cenocell
492:See also
322:trimodal
145:ceramics
129:zeolites
121:aquifers
79:porosity
1306:Commons
1218:Geology
1213:Geodesy
1185:Outline
1083:5384213
1054:Bibcode
978:Bibcode
907:Bibcode
328:fractal
239:use of
141:cements
1294:Portal
1090:
1080:
1072:
876:
816:
766:
722:
686:
644:
578:
226:, and
119:(e.g.
102:sponge
60:liquid
1190:Index
764:S2CID
744:(PDF)
113:rocks
72:foams
68:solid
56:fluid
52:pores
46:or a
1088:PMID
1070:ISSN
874:ISBN
814:ISBN
720:ISBN
684:ISBN
642:ISBN
576:ISBN
338:and
143:and
137:cork
117:soil
115:and
42:, a
1078:PMC
1062:doi
1017:doi
986:doi
944:doi
915:doi
903:108
866:doi
839:doi
806:doi
756:doi
752:212
712:doi
676:doi
634:doi
609:doi
605:634
568:doi
190:),
174:),
127:),
64:gas
62:or
38:In
1324::
1086:.
1076:.
1068:.
1060:.
1048:.
1044:.
1011:.
1007:.
984:.
940:45
938:.
913:.
901:.
897:.
872:.
860:.
812:.
790:NY
762:.
750:.
746:.
718:.
706:.
682:.
670:.
656:^
640:.
603:.
599:.
574:.
566:.
282:.
230:.
222:,
210:,
202:,
198:,
186:,
182:,
170:,
166:,
162:,
154:,
131:,
123:,
93:,
89:,
85:,
1166:e
1159:t
1152:v
1094:.
1064::
1056::
1050:8
1025:.
1019::
1013:5
992:.
988::
980::
950:.
946::
923:.
917::
909::
882:.
868::
845:.
841::
822:.
808::
770:.
758::
728:.
714::
692:.
678::
650:.
636::
615:.
611::
584:.
570::
486:α
482:α
478:α
473:α
467:X
450:a
445:i
441:r
435:N
430:1
427:=
424:i
413:X
407:1
403:1
398:=
393:a
388:o
384:r
371:i
369:r
362:0
360:r
194:(
178:(
158:(
58:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
