The Structure of Roots of the Characteristic Equation for Free Oscillations of a Gas Bubble in Liquid

摘要

We consider gas bubbles performing free radial oscillations in a liquid. The structure of the roots of the dispersion equation is investigated in detail in the presence of heat exchange between phases. It is shown that this equation has two complexconjugated roots and also an infinite number of real roots. In this case, all roots lie in the lefthand complex halfplane, which explains the damping of radial oscillations. We obtained approximate expressions for these roots.