1. Multiparameter and Multiscale Problems with “Sharpening" in Cavitation
Robert I. Nigmatulin
RUSSIAN ACADEMY OF SCIENCES
P.P. Shirshov Institute of Oceanology
The 5-th International Conference
SOLITONS, COLLAPSES and TURBULENCE:
Achievments, Developments and Perspectives August, 2009

2. Shock Tube High pressure chamber Diaphragm Low pressure chamber
Pressure Transducers

3. Local Deformational Inertia of Bubbly LiquidspG
Classic Equation
of State
Local Deformational Inertia of Bubbly Liquids

4. Free volume oscillations of the spherical air bubble in water

5. Thermophysical parameters in bubbly liquid
a radius of the bubbles (monodispersed mixture)
n number concentration of the bubbles
- volume concentration of the bubbles (G < 0,1)
- density of the liquid
- density of the gas
- density of two phase mixture
i - thermal conductivity of the liquid (i = L) and gas (i = G)
сi - heat capacity of the liquid (i = L) and gas (i = G)
Сi -sound speed in the liquid (i = L) and gas (i = G)
G – adiabatic exponent of the gas
L – viscosity of the liquid
 - surface tension

6. After Transformations for potential flow:

9. AMPLIFICATION OF SHOCK WAVES WHEN REFLECTING FROM BUBBLY SHIELDS
No bubbles
With bubbles
0 = 1%

10. AMPLIFICATION OF SHOCK WAVES IN CLAY SUSPENSIONS (with bubbles)
WATER+MONTMORILLONITE 2m 5m 7m p0
HPC
DIAPHRAGM
(6%, a~10-1mm)
WATER+KAOLINITE
(25%, a~1+10-1mm)
200
REFLECTION FROM WALL
WATER+MONTMORILLONITE
(15%, a~10-1mm)

12. Multibubble & Single Bublle SONOLUMINESCENCE
MBSL
SBSL

13. Images of oscillating bubbles
0.0 65
13.3 95
19.4
150
30.6
180
36.7
20 m
Frame
Time: s
185
37.7
190
38.7
199
40.6
204
41.6
209
42.6
with
SONOLUMINESCENCE
190
38.7
195
39.8
210
42.8
220
44.8
230
46.9
245
49.9
Frame
Time: s 45
9.2
120
24.5
155
31.6
160
32.6
165
33.6
180
36.6
20 m
Nonspherical shapes and
NO SONOLUMINESCENCE

14. SPECIFIC FEATURES OF SINGLE BUBBLE SONOLUMINESCENCE
Two parts of the period:
SLOW expansion and initial stage of compression
EXTREMELY FAST collapse with the «sharpening»
Equilibrium bubble size
a0 ~ 3 – 5 mm
Adiabatic temperature of the compressed gas Tmax ~ 5000 K (?!)
Noble gas effect a tw
Radius of the bubble
Cold water effect
tw50s a0
amin
dtC ~ 10-8s t
Tmax ~ 5000 K (adiabatic compression
EXTREMELY SHORT light flashes !!! tF ~ 50 ps = (5 - 10) 10-11s
Light emission
→ t   s → 4 years
→ tFusion  0.2 ps → 0.7 s
dtF ~ s
t w ~ 30s days
dtC ~ 30 ns min
dtF ~ 50 ps ,7 s t

15. Micro-Hydrogen Thermonuclear Bomb with Deutorated Vapor Micro-Bubble?
SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATION Collapsed Bubble as Micro-Hydrogen Bomb
Initiation of a Spherical Shock Wave by the Convergent Interface
Selfsimilar Cumulation
of the Spherical Shock Wave from the Infinity
Guderley, 1942;
Nigmatulin, 1967
Micro-Hydrogen Thermonuclear Bomb
with Deutorated Vapor Micro-Bubble?
Focusing of the Spherical Shock Wave at the Center of the Bubble
The Spherical Shock Wave after the Reflection from the Center of the Bubble

16. SUPERCOMPRESSION BY CONVERGENT SPHERICAL SHOCK WAVE
W. Moss et al (Livermore National Laboratory, 1994)
Gasdynamic code for air bubble in water for single bubble sonoluminescence
(There are some principle errors in the code)
Radius of supercompressed and superhot plasma core:  109 m = 1 – 3 nm
Density:  10 g/cm3
Temperature:  106 K
Duration:  1011 s = 10 ps
FOR BUBBLE WITH DEUTERIUM (D2) or
FOR BUBBLE WITH DEUTORATED WATER VAPOR (D2O)
in heavy (deutorated liquid water D2O)
MAXIMUM TEMPERATURE is a few time less
(They say that they don’t know how to take into account the phase transitions)
No Thermonuclear Fusion

17. HOW TO AMPLIFY THE SUPERCOMPRESSION?
AMPLIFING THE ACOUSTIC WAVE (pI  bar)
GAS IN THE BUBBLE: CONDENSING VAPOR (VAPOR CAVITATION)
- Minimizing Effect of Gas Cushioning
- Higher Kinetic Energy of Convergent Liquid
COLD LIQUID
– More Intensive Condensation
LARGE MOLECULES (ORGANIC) LIQUID
- Low Sound Speed in Vapor ( ), where MG is molecular weight)
- High Condensation (Accommodation) Coefficient (   1, for water   0. 04)
- High Cavitation Strength
CLUSTER of the Bubbles: Two “sharpening”:
- in bubbly cluster
- in central bubbles

18. Tritium and Fast Neutron Production
R. Taleyarkhan, C. West, R. Lahey, R. Nigmatulin, R. Block, 14 12
Standart Deviation 10 8
T ~ 7105 s-1
C3D6O
Cavitation
0°C
22°C
No Cavitation
C3H6O 6 4
Change in count, min-1
T ~ 4105 s-1 2
Background -2 -4
NPNG ~ 106 s-1,
Nzone ~ 10 сs-1
Е = 14 MеV
fPNG = 200 sс-1 -6 2 4 6 8 10 12 14
Time (hours)

19. CLUSTER of Microbubbles: Formation and Evolution
Spherical Cluster
d  1 cm
1 cm
Loosing of Spherical Shape and Last Neutron emissions
Acetone,
T0 = 4C, p0 = 16.7 kPa
p = 17 bars,
Comet like streamers
Duration  50 ms
No strong Shocks on the Glass Wall
Y. Xu & A. Butt, Confirmatory experiments for nuclear emissions during acoustic cavitation, Nuclear Engineering and Design, 2005

20. The first approximations for the bubbles in the cluster
r - Lagrangian radial macro-coordinate for two-phase continua in the cluster
r – Eulerian radial micro-coordinate for the testing bubble
x(r, t) – Eulerian radial coordinate for two phase r r
 = L0(1 - G), 1  4.5 G R
R. Nigmatulin, “Dynamics of Multiphase Flow”, Hemisphere, 1991
R. Nigmatulin, et al. The Theory of Supercompression of Vapor Bubbles and Nano-Scale Thermonuclear Fusion, Physics of Fluids, Vol. 17, , 1-31, 2005.

21. Amplification of the Compression Wave in Cluster
Объемное содержание
пузырьков
Number of bubbles N = 50
Maximum microbubble radius
Radius of the cluster a, m
0.05 R
a = a = 400 mм
max
R = 4 мм
r = 0
r = 2 mm
r = 4 mm
t, s m
p, bar
p,bar
t = 32 s m
t, s m
r, mm
Nigmatulin, et al. The Theory of Supercompres-sion of Vapor Bubbles and Nano-Scale Thermonuclear Fusion, Physics of Fluids, Vol. 17, , 1-31, 2005.
R. Nigmatulin “Dynamics of Multiphase Flow”, Hemisphere, 1991

22. Low Mach Number Stage (microseconds)1 2 3 4
t, s
a, m/s
40
80
200
400
600
800
a, m .
0.12 a 1 2 4 5 6 7 9 3 8 8 20
0.08 6 a r a
pG, bar 4 b , 3 p I
0.04 p 1 2 pG I
15-26 t° t°
-20 1 2 3 4
t, s
330
mG, ng
G , kg/m3
0.2
0.3 T G
TG , K
290
310
200  m
100 G G
0.1
270
t, s
t, s 1 2 3 4 1 2 3 4
Low Mach Number Stage (microseconds)

23. Interface (nanosecond stage)2 - 4
a , m
a, km/s 2 1 14 15 16
18-26 17 2 1 n s t -
La , kg/m3
2000 a
Shock wave
1000 a 1 - 1 - - t o , 6 2 - , n t
1000
2000
TLa, K 2 - 1 5 3 4
t  - t° = ns
pLa, bar t - 1 - 1 1 t
Interface (nanosecond stage) - t o , n s o s

24. Shock jump and critical point (submicrosecond stage)1 3 1 4 11
Critical point 13 14
Critical point 14 1 3 1 3 12 1 2 3 12 m 1 2 r / a g b k , , p 1 r 1 1 1 11 1 1 1 - 1
r, m
Shock jump 4 8 1 2 1 6 2 4 8 1 2 1 6
r, m
t11 = t s,
t12 = t s,
t13 = t s,
t14 = t s,
t  s - minimum bubble radius
- interface 4 8 1 2 1 6 2 . 1 6 1 4 - . 4 11 1 2 12 -
w, km/s . 8 13 K 1 3 8 ,
Critical point 1 2 - 1 . 2 T 14 11 4 - 1 . 6 - 2 .
r, m 4 8 1 2 1 6
Shock jump and critical point (submicrosecond stage)

25. , kg/m3
max
104
103
(4)
Sh Sh
102
101
ad
t - t*, 106 ps
- 10
- 40
- 20
100
- 30 0
- 0.5
0.5
t - t*, ps
min
p, bar
pmax
BLOW UP “Sharpening”
109 Sh
106
Evolution of density, pressure and temperature for r = r*, where maximum neutron production takes place
103
100
- 40
- 30
- 20
- 10
t - t*, 106 ps
10-1
pmin
T , K
Tmax
108 Sh
106
104
- 40
- 30
- 20
- 10
t - t*, 106 ps -1
-0.5
0.5
t - t*, ps

26. THERMO-NUCLEAR CORE T, K , kg/m3 Convolution: ( × 0) 1010 Tmax 108
0.12
1010
Tmax
T, K
108
0.08
TSh
Nr , nm-1
106
max
, kg/m3
0.04 .
104
(4)
Sh r *
102
ad 20 40 60 80
min
100 0 r*
r, nm 1 10
100
1000
r, nm
r* = 27 nm – Radius of the maximum
neutron production
rF ≈ 60 nm – Radius of the Fusion Core
Convolution: ( × 0)

27. Production of the Fast Neutrons and Tritium nucleus
RESULTS OF ANALYSIS
Bubble Fusion (Ufa Branch of RAS
+ORNL+RPI)
Sonoluminescence
(Livermore)
Density: g/cm3
Temperature: 108 K = 10 KeV
Pressure: 1011 bar = 102 Gbar
Velocity: 1000 km/s
Density: 10 g/cm3
Temperature: 106 K
Pressure: 3108 bar
Velocity: 10 km/s
t   s → 1 year
t(M 1)  300 ns → 2 days
t(Dis, Ion)  2 ns → 20 min
tFusion  0.2 ps → 0.1 s
Duration: 1013 – s = 10 1 – 1 ps
Radius of the Thermonuclear Core: 100 nm
Number of Ions in the Thermonuclear
Core: 2  109
Duration: 10 ps
Radius of the Т = 106 К core: 1- 3 nm
Number of Ions in the Core:
2  105
Production of the Fast Neutrons and Tritium nucleus
s-1

28. LIQUID VISCOSITY (acetone) during collapse:
DISTURBANCES OF SPHERICAL SHAPE DURING INTENSIVE COLLAPSE of VAPOR BUBBLE
- - amplitude of disturbance (Legedre polynomial power i)
Absolute
instability
i = 2 3 5 4 
104
Disturbances
103
102 10 3 40 i
Relative amplitude growth depending on i
LIQUID VISCOSITY (acetone) during collapse:
does not influence for growth of long wave disturbances for ;
kills short wave disturbances ( , i > 40);
helps to save almost spherical shape of the bubble.

29. Bubbly Liquids are the most Paradoxical Fluids
PARADOX is a real phenomenon that contradicts ordinary insights, intuition and prejudices
The PARADOXES are MILESTONES in the space of SCIENCE
Bubbly Liquids are the most Paradoxical Fluids

30. LONG LIVE VLADIMIR ZAKHAROV