Equations of spatial hydrodynamic interaction of weakly nonspherical gas bubbles in liquid in an acoustic field

7th Conference on Low temperature Plasma in the Processes of Functional Coating Preparation

Davletshin, A.I.^1 ; Khalitova, T.F.^1

Institute of Mechanics and Engineering, Kazan Science Center, Russian Academy of Sciences, 2/31 Lobachevsky str., Kazan

420111, Russia^1

关键词: Characteristic distance;    Dynamic boundary conditions;    Hydrodynamic interaction;    Position vector;    Small deformations;    Spherical functions;    Spherical harmonics;    System of ordinary differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/669/1/012008/pdf
DOI  :  10.1088/1742-6596/669/1/012008

来源: IOP

【 摘 要 】

A mathematical model of spatial hydrodynamic interaction of gas bubbles in liquid in an acoustic field taking into account small deformations of their surfaces is proposed. It is a system of ordinary differential equations of the second order in radii of the bubbles, the position vectors of their centers and the amplitudes of deviation of their shape from the spherical one in the form of spherical harmonics. The equations derived are of the first order of accuracy in A / R and of the fourth order in R / D, where R is the characteristic radius of the bubbles, A is the amplitude of characteristic deviation of their surface from the spherical one in the form of spherical harmonics, D is the characteristic distance between bubbles. The derivation of the equations is carried out by the method of spherical functions with the use of the Bernoulli integral, the kinematic and dynamic boundary conditions on the surface of the bubbles. The effects of viscosity and compressibility of the liquid are considered approximately, the gas in the bubbles is assumed homobaric.