1. Institute for Nuclear Research of the Russian Academy of Science
Neutron flux estimation for collapsing bubble filled by hydrogen isotopes
Azamat Khokonov
Kabardino-Balkarian State University, Nalchik, Kabardino-Balkaria, Russia
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 equation4

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
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.
Khokonov A.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 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

21. Damping Rate

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

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