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Azamat Khokonov

Neutron flux estimation for collapsing bubble filled by hydrogen isotopes. Kabardino-Balkarian State University, Nalchik, Kabardino-Balkaria, Russia. Azamat Khokonov. Institute for Nuclear Research of the Russian Academy of Science. Contents.

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Azamat Khokonov

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  1. Neutron flux estimation for collapsing bubble filled by hydrogen isotopes Kabardino-Balkarian State University, Nalchik, Kabardino-Balkaria, Russia Azamat Khokonov Institute for Nuclear Research of the Russian Academy of Science

  2. Contents • The problem of small capillary oscillations of a liquid droplets. Rayleigh solutions. • Accounting for energy dissipation due to viscosity. • Capillary bubble oscillations, immersed in liquid. • Oscillations of a gas bubble, immersed in a viscous liquid under the assumption of constant volume. • Oscillations of charged droplet immersed in liquid.

  3. Drop and Bubble in liquid

  4. Navier – Stokes equation 4

  5. Boundary condition on the bubble surface The force per unit area 5

  6. IIEFM-2017, March 1-6, Elbrus

  7. The generalized Rayleigh-Plesset equation Pressure for bubble content vapor plus gas

  8. The solution of Plesset and Zwick

  9. Normal coordinates for capillary oscillations of a spherical droplet John William Strutt (Rayleigh). The theory of sound. London, Macmillan and co. 1877, vol. 2, 476 P. KhokonovA.Kh. Liquid drop model of spherical nuclei with account of viscosity. Nuclear Physics A 945 (2016) 58–66

  10. Quadrupol and octupol nuclear deformations

  11. Incompressibility and potentiality conditions of fluid motion

  12. Solution of the Laplace equation in the inner (r <a) and external (r> a) areas

  13. Boundary Conditions

  14. The kinetic energy of the drop and the liquid surrounding the bubble

  15. Potential Energy

  16. Energy Dissipation

  17. Euler-Lagrange equations

  18. Frequency of capillary oscillations of a viscous drop Khokonov A.Kh. Calculation of capillary oscillations of a drop with the energy dissipation due to viscosity. Physics and chemistry of the surface. Nalchik, KBSU, 1982, P.32-35. s

  19. The critical radius for the oscillations of a viscous drop

  20. Frequency of capillary oscillations of a bubble in a viscous fluid Khokonov A.Kh. Capillary oscillations of the drop and the bubble immersed in a liquid with taking into account the viscosity. Izvestiya RAN, 2012, Vol.76, № 13, pp.57-58.

  21. Damping Rate

  22. Charged Drop x ε2 R(θ) ε1 θ a0 a z y

  23. Relationships between radii used

  24. Unperturbed electric potential

  25. Poisson equation for electrostatic potential variation

  26. Electrostatic potential variations

  27. Boundary conditions

  28. Boundary conditions

  29. Electrostatic energy deviation for deformed nucleus

  30. Frequency of capillary oscillations of a charged drop immersed in a polariseable medium

  31. Electrostatic energy deviation for deformed nucleus

  32. Charged drop immersed in viscous liquid

  33. Estimations for water for

  34. Lowson criterion

  35. Gamov factor

  36. Conclusions 1. It has been shown that viscosity leads to critical radii for bubble and droplets capillary oscillations 2. The decrease of surface tension for small bubbles (radii less then 0.1 µm) cause to nonstability of bubbles spherical form. Therefore, fusion conditions in bubble for existence materials is impossible.

  37. Thank you for your attention

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