Natural frequencies of a bubble near a solid sphere

This paper presents an analytical and computational method to describe natural frequencies of a spherical bubble residing near solid sphere arbitrary size in otherwise unbounded fluid. Under low capillary Reynolds number limits, the relevant hydrodynamic fields are converted into time-invariant but frequency-dependent quantities by temporal Fourier transform. Then, spatial variations velocity pressure can be expressed terms two sets harmonic basis functions involving coordinates centered around particle bubble. A subsequent derivation transformation coefficients between aforementioned allows matrix equation relating unknown amplitudes boundary conditions at all interfaces. Finally, corresponding different modes pulsation obtained from eigenvalues constructed matrix. The results show fast convergence computed with increasing functions. These values change significantly distance even decay zero for some when their surface-to-surface separation vanishes. Furthermore, oscillation plate is also discussed radius increased infinitely large dimension. Thus, this article renders comprehensive study naturally pulsating submerged bubbles presence nearby surface various kinds.