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

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.

Drop and Bubble in liquid

Navier – Stokes equation       4

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

IIEFM-2017, March 1-6, Elbrus

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

The solution of Plesset and Zwick   The solution of Plesset and Zwick    

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

Quadrupol and octupol nuclear deformations

Incompressibility and potentiality conditions of fluid motion

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

Boundary Conditions

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

Potential Energy

Energy Dissipation

Euler-Lagrange equations

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

The critical radius for the oscillations of a viscous drop

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.

Damping Rate

Charged Drop θ x y z a a0 R(θ) ε2 ε1

Relationships between radii used

Unperturbed electric potential

Poisson equation for electrostatic potential variation

Electrostatic potential variations

Boundary conditions

Boundary conditions

Electrostatic energy deviation for deformed nucleus

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

Electrostatic energy deviation for deformed nucleus

Charged drop immersed in viscous liquid

Estimations for water         for    

Lowson criterion  

Gamov factor    

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.

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