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Two spherical bubbles with changing radii are considered to be moving inideal fluid along their center-line. The exact expression for the fluid kineticenergy is obtained. The Stokes stream function is expanded in Gegenbauerpolynomials in bispherical coordinates. This expansion is used to obtain theexact series for the fluid kinetic energy quadratic form coefficients. The newseries are confirmed to be correct by comparison with the known ones. The mainadvantage of the new kinetic energy form is the possibility to obtainasymptotic expansions at small separation distance between the bubbles. Theseexpansions are obtained and their convergence is analyzed. The results of thiswork can be used to describe the bubbles approach before the contact and theircoalescence in acoustic field.

Fluid kinetic energy asymptotic expansion for two variable radii moving spherical bubbles at small separation distance