Turbulent mixing and beyond
ICTP, Trieste, GrigNANO Mare 2007
Rayleigh-Taylor Instability in
Micro and Nano Hydrodynamics
Eduard Son
©Moscow
Institute of
Physics and
Technology
Physical
Mechanics
Department
Talk outline
• Dispersive relations for finite Kn numbers
• Size effects in transport properties (viscosity, diffusion,
heat conductivity)
• Creating shock waves in a gas-piston system in MNFM
• Gas-Liquid interface and Surface tension in micro- and
nanofield modification of dispersive equations
• Features of rarefied flows and connection to turbulent
flows
• Boltzman Equation – NS equations
• Vortexes dynamics in 2D and 3D
• Thermal Induced vortexes (experiment and theory)
• Air dynamic flow control by creating vortexes
• Plasma (DBD) induced vortexes
• Micro- and Nano Rheology properties of liquids and
Viscous-Plastic Fluid Turbulence
Micro- and Nano Hydrodynamics
• One phase flows
– Internal Hydrodynamics – gas flows in micro- and
nanochannelsand pipes (including CNT – carbon
nanotubes)
– External Hydrodynamics – flows around microand nanoparticles
• Two phase flows
– Flows of solid micro- nano particles
• Gas flow around particles
• Gas flow around particles
– Micro- and nano bubble flows
• Multi Phase hydro- and electrodynamics
Applications of micro- and nano
hydrodynamics
(NT boundary = 100 nm = 0.1 µm)
–
–
–
–
–
–
–
–
–
HDD (Hard Disc Drives d=50 nm)
Micro- and nano electronic devices (MEMS)
Micro- and nano separators
Microchannels, micropumps, microvalves
Micronozzles, microgiroscopes, micro- and nanosatellites
Medicine (blood flow in the human body, etc.)
Flow Sensors
Auto- car Industry (ABS, fuel, etc.)
Electro hydrodynamics super sensitive sensors for micro- and
nano fields (MIPT)
– Micro- Nano hydrodynamics of porous media
– Oil – hydraulic fracture
– Rheology (micro- nano structure properties of liquid, viscousplastic and elastic non Newtonian media
Features micro- and nanoflows
(mesodynamics)
• Channel size compared with mean free path, interparticle
distance and even with particle size
• Density fluctuations are large
• Transport properties (viscosity, diffusion, heat
conductivity) could have size effects (like in turbulence)
• Nano flow - wall interaction may be main factor
• There are no exact boundary conditions
• Continuum flow approximation is not valid
• Some phenomena does not exist in microdynamics: flow
memory after penetrating the holes
• Some quantum effects are essential in nanoflows
• Laplace law for surface tension pressure is modified
GAS MICROFLOWS:
What happens at
microscale?
• Compressibility (density
variations)
• Rarefaction (low
pressure)
• Viscous heating (work
done by viscous forces)
• Thermal creep (gas
molecules go from cold to
hot)
• Non-continuum effects
(Kn>0.1-0.5)
LIQUID NANO FLOWS:
What happens at
micro/nanoscale?
• Hydrophobic vs.
hydrophilic surface
(wetting)
• Adsorption of species on
wall-induced roughness
• Electrokinetic effects
• Intrinsic surface
roughness
• Non Neutonian media
• Different rheology
Couette free molecular flow
Particle distribution functions
qx
qy
qy
qy
Stress
S1  U / h  h 
Heat flux
Fourier Law (q ~ - grad T)
Heat flux (q ~ ┴ grad T)
Does not exist in hydrodynamics,
But could exist in turbulent flow !!!
Boltzmann equation for instabilities
f  f 0 (1  aKn  bKn2 )
2D simulation, Infinite order scheme
Energy spectrum vs. time Re=infty, Re=40000
What are main features of kinetic
approach to HD instabilities
Why tau-approximation reasonable for HD instabilities
• Use opportunity compare with DNSC (SMILE)
• Nonlinear Euler equations are taken into account
• Exact viscosity is not essential
• Maxwellization is underestimated
1.
2.
3.
4.
5.
Nonlinear transport and finite correlation size are taken into account
Boundaries in rarefied gas become smoothed for MFP length –
No singularities in vorticity and other parameters
Effective viscosity appears
Analogy to turbulence (long correlations, size effects)
BE solution at arbitrary Kn number
Onuphriev A, Sapharov R., Son
K. Son E.
Semiempirical models of
turbulence,
Theory and Experiment, Russia
2003,
TBT: Begell House, 2007
Feature rarefied gas flows
•
•
•
•
•
Stress and heat flux are not depend on the distance between plates and velocity
and temperature profiles, but depend on differences of velocities and
tyemperature
Near walls creating Knudsen layers with jumps of temperature and velocities
Directions of heat fluxes and temperature gradients not coincide
Highly transport anysotropy: under action of transversal temperature difference
arise heat flux in the direction of homogeneous (along x) Possible arising
«negative thermal conductivity» (heat flux directed along the temperature
gradient), i.e. Fourie Law is invalid.
At decreasing mean free path (in the limit of Kn<<1) Stokes law and Fourier Law
follows, along x heat flux limits to zero, the nonzero x- q-flux appears in next
order of expansion on fields gradients
Micro Gas Dynamics
Pe 
Classical gas dynamics
UL

Pea 

  v  0
t
 v

   ( v ) v   p   
 t

al

,
 c p 2  p 
,a   

   S
 104
1 dS  0
k
c
p  
Адиабата :    , k  p
p0   0 
cv
Micro-nano gas dynamics

  v  0
t
 v

   ( v ) v   p   
 t

УРС : p   RT , T  const  Tw
Compression shock waves –
Follows fron 2nd Thermodynamics Law
No rarefying shock waves
1см / с *105 см
Pea  
 105
2

1см / c
Ul
1 T  const  Tw
Riemann problem
In Nano Gas Dynamics
2nd Thermodynamics Law invalid
Moments equations in rarefied gas –
expansion on Kn number
• Zero approximation in Kn – thermodynamic equilibrium
• First approximation on Kn – dense gas – Navier –
Stokes equations, Fourie, etc – linear relations between
thermodynamic forces and fluxes
• Second approximation on Kn – Barnett approximation,
nonlinear relations between forces and fluxes
• Higher approximations on Kn – complex problem
• Limit high Kn numbers – free molecular regime (FMR)
• Numerical simulation Boltzmann Equation (SMILE),
there are some exact solutions
• Lattice Boltzmann
• Molecular Dynamics for nonequilibrium
nonhomogeneous system (Supercomputing)
Vortex creation in Nuclear explosion in
atmosphere
v
1
 ( v ) v   p  g
t

 Ω
 1

 ( v )Ω     p
 t
 
Apply nabla to momentum eqn:
pressure illuminates
grad p acts as external force
like suppose volume force
independent on density
p
E
Fundamentals of Thermal
Actuator
1   
1  v 
1
  p  
  
    

  T  p
v  T  p
T
1
1
 Ω


 ( v )Ω    T  p
T
 t

Plasma DBD Actuators Flow Control
 v

   ( v ) v   p   c E
 t

DΩ
c
1
  2   E    c  E
Dt


Vorticity transport
by flow

 Ω

 ( v  ) Ω    c   E    c  E

 t

1
1
E  Eext  Eind ,  Eind   cind ,  Eext   cext

0
Vorticity source
from plasma
0
Important:
Vorticity creates only in sheets
of space charge gradient,
interacts with external and
induced
Electric fields
DBD Plasma actuator equations

 ( v )     v
t
compressibility

v


   ( v ) v   p   σ   c E
 t

n p
 ( v )n p  n p ( v )   ( n p U p )  nenki (Te )  nen*ki* (Te )  nen p k r( e ) (Te )  nenn k r( i ) (T )  Seext
t
nn
 ( v )nn  nn ( v )   ( nn U n )  ne nka (Te )  n p nn k ri (T )  nn n p kd( e ) (T ) 
t
n*
 ( v )n*  n* ( v )  ne nk* (Te )  ne n*ki* (T )  S*ext
t
 0  E   c  e ( n p  nn  n e )
Flow transport
ne
 ( v )ne   (neUe ) 
t
 nenki (Te )  nen*ki* (Te )  nnnkd (T )  nen pk r( e ) (Te )  nenk a (Te )  Seext
neUe  (ne De )  ne De(ln n)  ne eE
Electron
transport
Internal, Vibrational and Electron Temperature
equations
d
nm
(nU TR )  (nU TR  p ) v   qTR   
UV (TV )  UV (T )   ne TR (TV )kTe
dt
 VT
d
nm
nmUV (TV )  nmUV (TV )  v   qV  UV (TV )  UV (T )   neV (Te )kTe
dt
 VT
d 3
 3

n
kT

n
kT

p
e   v  je E   q e  ne u (Te )kTe
 e e  e e
dt  2
 2

External source Ionization could be photoionization
 
'
'
'
'


k
(
x
,
y
)
h
dx
dy

*
'
S ph
( x ', y ')     ph ne' ex i v v
2arctan  st  v v
kieff ( EA / N ) R
 2 '   '
 0
Problem: in strong E-fields equation for electron temperature not valid,
It is extra equation. Electron energy is controlled by external or
selfsustained E-field
Plasma-wall vortex formation
Numerical simulation (GDT – parallel code)
Plasma flow control streamer size
less 1 micron
Multiscale problems
• Turbulence: L/l=Re^3/4, T/t=Re^1/2, for
Re=10^4 L/l=1000, N=(L/l)^3*(T/t)=10^11
max Re=20000 for DNS (Livermore, Blue
Jin)
predictions (Spalmaret, Boeing) 2040 –
LES,
2080 - DNS
• In DBD L/l=10^5, T/t=10^6, Multiscale is
nesessary
Numerical simulation Boltzmann Equation
Метод прямого
статстического моделирования
В мире существует три основных
кода ПСМ:
• DS2V (скалярный код G. Bird)
• DAC (NASA, только для NASA)
• SMILE (ИТПМ СО РАН).
Результаты для трех кодов:
• давление
• напряжение трения
• тепловой поток
Surface tension depends on curvature
V.Byakov, S. Stepanov (ITEP)
Rayleigh-Taylor Instability in MNHD
RTI in a magnetic field
  vT
v T2





3
3 2(   w )  (1  Kn)
Hydrodynamics MEMS Technology (MIPT)
Molecular-electronic transducer
Instability in electronic~new device
1.
Ceramic or glass
channel;
Clamping rings;
Electrolyte;
Ceramic spacers;
Anodes;
Cathodes
As does a pentode,
an MET provides
extremely high power
gain (>108)
2.
3.
4.
5.
6.
7.
•
The relationship between the pressure drop
and external acceleration is the following:
across the cell
p    l  aext
where  - is electrolyte density, l – is the length of the cell,
is the external acceleration. So the input signal for MET is
acceleration.
-
Oil microhydrodynamics
p  v=0
v
Darci Law
Re 1:  p   2 =0
d
K
v   p, K  d 2 , 1D  1  m 2

•
Oil moves in pores 1 µm size. For hydraulic fracturing
nesessary to have media with oil density and viscosity –
microbubbles media with 1 µm bubble diameter
•
We developed experiments and theory for micro- nano bubble
media, methods of generation and applications for hydraulic fracturing
Stability and mixing in bubble flows
(AFM) Atomic – Force microscopy
Spectra and image microdisperse water gas
mixture (MDWGM)
Size spectra distribution
700
1
15
22
27
37
31
40
45
25
7
11
16
12 14
8
17
43
48
59
46
55
61
38
53
87
115
119
97
100
120
111
83
90
94
116
135
Число пузырьков в заданном
интервале диаметров
153
156
162
145
154
157
164
159
183
187
258
192193
204 200
265
298
290
310
322
328329
368379 373
391
408
394
436435
443
466 459
475 471
487
395
403
411
421
427
383
511
410
405
534531
543
546
554
Statistics 1560 bubbles.
505
490
497
529
620
624629
635
672
679
638 636
680681682
689
692
717
300
744
729
745
920
965 971
974
967
975
991
883
900
904
922923 926
953 950
990
892
889
884
905
924
947
960 964
1032
1055
1042
1069
1076
1079
11201125
11011105
1106
1102
951
979
1124
1142
1141
1165
1173
1126
1152
1166
1158
1177
1183
1187
1209 1211
1139
1134
1153
1161
1159
1180
1194 1195
1235 1230
1284
1286
1290
1296
0
1335
6
8
10
12
14
1372
1356
1369
1378
1379
13841377
Bubble Diameter, µm
1435
1441
1458
1485
1488
1489
1494 1493
14981500
1503
1495
1501
1504
1515 1518 1519
1530
1510
1551
1420
1425
1559
1423
1443
1448
1449
1418
1424
1433
13801381
1528 1523 1538 1531
1375
1383
1387
1391
1432
1454 1450
1453
1442
1455 1452
1464
14761471
1473
1516
1532
1560
1525
1535
1542
1557
1475
1484
1496
1497
1505
1502
1508
1546 1549
1472
1480
1490
1534
1382
1417
1436
1440
1451
1482 1483
1318
1326
1341
1410
1416
1429
1431
1461
1469 1468
1329
1355
1402
1413
1520
1524
1325
1337
1340
1386
1398
1393
1400 1403 1401
1412
1421
14301426 1427
1244
1271
1278
1313
1317
1327
1349
1407
1411
1509
15451548
1547
1396
1409
1444
1446
1457
1460 1463
1465
1474
1479
1481 1478
1487
14861492
1507
1316
1113
1138 1133
1151
1175
11821184
1370
1389
1397
1521
1527
1537
1543
1511
1365
1078
1109
1265
1266 12671260
1277
1276
1289
1297
1339
1348
1354 1360
1361
1237
1309
1310
1330
1343
1350
1050
1074
1205 1202
1218
1221
1228
1234
1243
1249
1252
1227
1251
1263
1280
1291
1294
1311
1026
1038
1118
12081210 1199
1220
1236
1242
1288
1292
1303 1305
1037
10711075
1188
1259
12681264
1374
1447
1459
1517
50 мкм
1428
1438
1437
1467
1477
1491
1357
1415
1419
1439
1466
1240
980
1007
1131 1132
11441145 1137
1154 1155
1164 1160
1169 1171 1167 1172
1174
1198
1207
1239
1300
1306
1368
1408
1422
1445
1456
1462
1470
1347
1363
1392
1399
1434
1275
1287
1295
13761373
14051406
1404
1414
1233
939
943
962
993
1019
1112
1217
1226
1232
1299
13041302
1307
1320
1192
1201
1254 1247
1262
1255
1346
1353
1366
1030
10531049 1054
1136
1149 1150
1331
1344
1364
1367
13901385
1388
1394
1212
1219
1274
1336
1345
1352
1358
1371
1200
1214
1216
1319
1323 1324
13321333
1338
1342
1351
1362
4
1204
1315
1321 1322
1328
1334
1281
1312
1130
1191
916
932
959
10671068
1100
1148
1156 1147
11891190
1245
1250
1269 1270
1279
1285
1293
1301
1314
1128
1135
1238
1246
1273
1272
1225 1223
1224
1229
1231
1241
1257
1261
1066
11761179 1170
1181
1196
1203
1213
1253
1122
1140
1168
1178
1186
1197
1206
1025
1048
1064
871
882
894
899
909911
931 925
956961
1073
10811082
1083
10921093
1117
838
849
863
984
989
997 998 1001 1002
1003
10091013
1104
831
837
896
987
1061
1063
1091
11081103
791
809
915 913
949
786
771
773
875
878
938
973970
1024
1044
1116
1129
937
946
10081006
10961097
1111
1146
1163
1162
972
1017
770
782
788
914
992
1005
1016
10231021
1095
1121
1127
1143
1185
1256
12821283
1094
1090
935
955
969
1000996
1036
1047
1060
1065
1070
1077
1056
1080
1086
1099
1222
1308
1022
1041
1062
1087
1115
942
988
866
746
756
903
912
928
927
948
958
934
966
1029
1085
898
918919
952
691
711705
737738
816
828
840
842
847
854 856
860861
867
851
865
908
968
628
716
768
821 825827
855
986
1040
1046
1059
1058
728
740
753 749
794
820
930
632 623
633
647
646
654
659 666
722
755
573
674
701
881
1004
1031
1033
1057 1052
1098
1110
941
957
977
976
983
653
661
671
688
687
808
917
1010
1084
1107
907
631
667
685
733727
886
885
936
945
999
994
1011 1012
1018 1015 1020
1028
1039
1043
630
649
658
596591
605
619
634
611
670
858
890
921
929
540
559
565
584
610
844
853
870
523
551
558 564
577
590
616
760
798
804
815
805
824
829
836
880
508
545
553
715 723
731 732
811
877
887
906 902
486 489
502
700
765
772 774
797
807
852
901
963
1114
800
835
876
398
469
528
752
785
792
796
498510
589
641
673
704
714
358
438
450 454
494
563
572
648
696
709
703
736
743
464
493488
556
566
576
586
599
617
622
644
312
341
367371
380
433
462 463
525
598
678
708
767
982
1045
1157
790
874
888
893
910
940
954
1089
748
830
859
595
607 604
657
676
690
707
781
841
978
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1027
1088
742
779
814
823
640
655
669
695
706
757
787
799
812 817 813
857
995
1034
1051
100
784
822
843
1072
1119 1123
780
803
872 873
730
751
741
764 758
763
597 593 594
627
637
665
721
507522
557
575
618
694
720
933
1014
1035
778
834
879
664
675 677
699
747
762
777
802
833
850
862 869
626
639
643 652
668
712 713
550
583
331
414
417
446
461
472
492
357350
390 393
397
407
420
431
434
453
330
338 339
362
538
580
585
601
615
724
750
795
895
897
200
735
579
588
625
660
710
725
761
826
839
848
846
864
609
683
806
810
818
845
621
651
663
719
776
783
789
793
801
656
600
608
697
698
739734
754
766
868
642
650
693
702
718
726
592
501
521
530
555
571
582
606 603
614
491 496 500
517
536
542
539
552
547
562
574
430
429
449
303
319
316
315
340 335
356353
370
378
382
482474
481
484 485
506
520
519
541
561
442
470
495
581
422
424 425
439441
452 456 457458
480
532
568
570
314
327
352
389
280
283
284 293
301
320
349
402
413
460
221
229
235
240
249
261253264 254
252
282
300
334
361
372
384
388
399
406
202
211
245
273
306
309 305
311
365
473
544
548 549
560
567
250251
289
313
355
437
448
467
602
662
419 412
418
423
432
587
613
400
401
416
426
451
188
190
199 197
228
345
375 377
387
409
445
483
503 504 499
516 527
535
569
381
386
206
242
333
363 364
376
122
132 128 134
172
234
241
292 296
304
337
343
114
137
276
291 294
302
317
308
109 102
182
268
272 275
325
477
514
524
513
578
287
131
260
263
72
96 106 103
155
176 178
186
179
205
274
288 279
342
374
385 392
415
468
479
533
262
105
141
231
239
42
58
64
68
81
213
233
248
6
21
30
39
52
54 56
67 71 63
91
167
175
244
344
354
428
440
444
455
515 509
518
336
396
404
447
476 478
286
321
332
347
359 351 360
369
348
127
151
161
201
256
271
278
295
20
24
85
113
185
189
196
3
51
77 76
89
99
108
117
170
210
266
267
70
88
140
152
163 160
224 220
232
299
307
318
323
324
346
191
195
212
270
281
126
129
144
147
177
227
259
277
285
297
169
237
255
269
500
194
207
214 216
223219 226
236
243
247
257
222
225
230
238
246
400
184
198
203 208 209
217218 215
166
168
181
104
118
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146 149
158
148
171
180
101
136
139
143
150
95
5
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66
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110 112
124
130 125
121 123
133
138
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10 4 13
50
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19
35
36
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29
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15551556
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1499
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15131514
1526
1540 1536
1550
1558
NANORHEOLOGY
Viscous – Plastic Media

   v  0
t
v
 (  v  v )   p    τ  g
t
τ  2S
1  vi
v k 2
v l

Sik  

  ik
2  x k x i 3
x l
p  p0  E
  0
0
 ik  2 0 S   0 S
1
n1
S
 0
ik
 0
Sik  0
Boundary conditions:



p   p    p,
x 0
x L
1
S  S:S
2
2
1
  τ:τ
2
2
ua
S
0
Bingham and Hershel-Bulkley flows
(3D pipe)
1.4E-01
V (m /sec)
1.2E-01
1.0E-01
8.0E-02
6.0E-02
Theory
11*11 cells
21*21 cells
4.0E-02
41*41 cells
2.0E-02
-6.0E-02
-4.0E-02
-2.0E-02
0.0E+00
0.0E+00
R (m )
2.0E-02
4.0E-02
6.0E-02
Micro- nano- structure VPF
Micro-Nano rheology analysis
(Stress-Deformation rate)
Thermal gradients render the magnetic force nonuniform through
the temperature-dependent magnetic susceptibility
Fluid control in microgravity
Edwards B. F. et al. Magnetothermal
convection
in
nonconducting
diamagnetic and paramagnetic fluids.
Proceedings of the 3-d International
Microgravity
Fluid
Physics
Conference, Cleveland, USA, 1996.
Odenbach
S.
Microgravity
experiments on thermomagnetic
convection in magnetic fluids.
J.
Magnetism
and
Magnetic
Materials, 149 (1995)
Diamagnetic control
DeLucas L.J. et al. Diamagnetic control of
convection during crystal growth. (Protein
experiments on DC-9 Reduced Gravity
Aircraft) Science ,1989, 246.
Yin D. C. et al. Formation of protein
crystals
in
quasi-microgravity
environment
obtained
by
superconducting magnet. J. Crystal
Growth, 2004, 270.
Ramachandran N., Leslie F. W. Using
magnetic fields to control convection
during protein crystallization – analysis and
validation studies. J. Crystal Growth,
2005, 274.
Control of oxygen content in the
air… on board ISS
2
Ageikin D.I. Definition of heat emission by
magnetothermal convection. Proceedings
Academy of Sciences the USSR, 1950, 74.
Magnetic field effects on the
morphology and orientation
of
lysozyme
crystals
crystallized with NiCl2.
Pictures were taken 2 days
after supersaturating the
solution with NiCl2:
under 0 T and under10 T
Formation of protein crystals (orthorhombic lysozyme) in quasi-microgravity
environment obtained by superconducting magnet.
D.C. Yina, N.I. Wakayamaa, K. Haratab, M. Fujiwarac, T. Kiyoshia,
H. Wadaa, N. Niimurad, S. Araid, W.D. Huange, Y. Tanimotoc
Tsukuba Magnet Laboratory, National Institute for Materials Science, Tsukuba, Japan; Biological Information
Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan;
Institute for Molecular Science, Okazaki, Japan; Neutron in Biology, Advanced Science Research Center,
Japan Atomic Energy Research Institute, Tokai, Japan; Stake Key Laboratory of Solidification Processing,
Northwestern Polytechnical University, Shaanxi, China
Fig. 2. The superconducting magnet which can provide
effective gravity ranging from mG to 1.8G simultaneously.
The crystals obtained inside the magnet (15 T) show better quality than obtained
outside.This result is in agreement with the previous results of orthorhombic
lysozyme crystals. The improvement of crystal quality was not clear at the
center of the magnet (10 T).
3
Journal of Crystal Growth 270 (2004)
Ferromagnetic nanoparticles
Single domain ferromagnetic particles
(~10 nm) are coated with long chained
molecules to prevent particle
agglomeration and suspended in an
appropriate carrier fluid;
kerosene-based magnetic fluid:
magnetic saturation MS = 48 kA/m,
 = 5.7, concentration 10 %, Pr =100
differential magnetic susceptibilities 
protein media
 -10-5
paramagnetic melts
 10-3
magnetic fluid
1
Lysozime crystals immersed
in paramagnetic solutions
MnCl2, CoCl2 etc.:
 is several orders greater
CONTROL PARAMETERS
 o (  m h) 2
Ram 
a(1   )
N.B.!
Ra g 
Ram  2
~
M
Rag
h
g
Th 3
a
h ~ 1mm
Т - temperature difference across fluid
h - layer thickness
g - acceleration due to gravity
 - thermal expansion coefficient
а – thermal diffusivity
 - kinematic viscosity
m - relative pyromagnetic coefficient
М – magnetization
 - differential susceptibility
 - density of magnetic fluid
o – permeability of free space
6
Finlayson B. A. Convective instability of
ferromagnetic fluids. J. Fluid Mech. 40 (1970)
The convection instability in spherical cavity heated from
below (above) in the presence of magnetic fields
(v v = Р  v  (GrТ2 еz – Grm Т2H2);
div v = 0;
0 =T1; Pr vT2 = T2;
rot Hi = 0; divBi = 0; B1 = H1; B2 = (H2 + M);
i=1,2: the parameters and functions relating to body
(fluid) are marked inferior index 1 (2).
The conditions at infinity and in the center of ball are:
r: Н1 =Н0 еz; Т1 = еz;
r = 0: all function are limited
r = 1: v = 0; Т1 =Т2;
Нn1 = {– Grm(T2/H2)}Нn2; H1 = H2
11
PLASMA CRYSTAL IN -GRAVITY
INTERNATIONAL MICROGRAVITY SPACE
EXPERIMENT PKE - NEFEDOV
PKE - NEFEDOV
ISS-1 PKE - NEFEDOV Yu. Gidzenko, S. Krikalev
Dusty plasma space experiments
Conclusion
Nanofluidistics
is very fast developments area which need basic research, both
theory and experiments and will be one of the main fields of
Nano National Initiatives
with different applications
• Science
• Technology
• Micromechanics
• Optics
• Space equipment
• Clothes
• Toys
•Art (ballet, painting, …)
•Household
• Others
•Oil Industry
•Plasma Technology