Multiparameter and Multiscale Problems with “Sharpening" in Cavitation Robert I. Nigmatulin RUSSIAN ACADEMY OF SCIENCES P.P. Shirshov Institute of Oceanology nigmar@ocean.ru The 5-th International Conference SOLITONS, COLLAPSES and TURBULENCE: Achievments, Developments and Perspectives 2 - 7 August, 2009

Shock Tube High pressure chamber Diaphragm Low pressure chamber Pressure Transducers

Local Deformational Inertia of Bubbly Liquids pG Classic Equation of State Local Deformational Inertia of Bubbly Liquids

Free volume oscillations of the spherical air bubble in water

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

After Transformations for potential flow:

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

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)

Multibubble & Single Bublle SONOLUMINESCENCE MBSL SBSL

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

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   30 s → 4 years → tFusion  0.2 ps → 0.7 s dtF ~ 10-11- 10-10 s t w ~ 30s 6 days dtC ~ 30 ns 7 min dtF ~ 50 ps 0,7 s t

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

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

HOW TO AMPLIFY THE SUPERCOMPRESSION? AMPLIFING THE ACOUSTIC WAVE (pI  15-20 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

Tritium and Fast Neutron Production R. Taleyarkhan, C. West, R. Lahey, R. Nigmatulin, R. Block, 2002- 2008. 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)

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

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, 107106, 1-31, 2005.

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 0 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, 107106, 1-31, 2005. R. Nigmatulin “Dynamics of Multiphase Flow”, Hemisphere, 1991

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)

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° = - 0.78 ns pLa, bar t - 1 - 1 1 t Interface (nanosecond stage) - t o , n s o s

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 - 0.25 s, t12 = t - 0.07 s, t13 = t - 0.04 s, t14 = t - 0.015 s, t  41.9932 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)

, 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

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)

Production of the Fast Neutrons and Tritium nucleus RESULTS OF ANALYSIS Bubble Fusion (Ufa Branch of RAS +ORNL+RPI) Sonoluminescence (Livermore) Density: 10-20 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   50 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 – 10-12 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 105 - 106 s-1

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 2 10 102 103 104 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.

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

LONG LIVE VLADIMIR ZAKHAROV