Bubble excitation of surface waves and aerosol droplet production: A simple dynamical model

Abstract

A novel theoretical analysis is presented of the dynamics of bubble‐mediated jet droplet production. The aerosol particle is recognized in its “bound state” in a capillary surface wave which is generated by a bursting bubble. The spatial excitation profile—as known from photographic data—is discussed by means of an argument involving a separation of time scales. By taking account of the dispersion relation for surface waves, the ensuing temporal behavior (of the local amplitude, vertical velocity, acceleration, and radius of curvature) is calculated analytically. The droplet is ejected just prior to the instant of maximum local (vertical) deceleration. Energy balance considerations applied to the transition from its bound state to its “free state” allow the prediction of the droplet size (as a function of bubble radius) and of the ejection velocity (as a function of droplet size). Numerical calculations support the analysis. The agreement with experimental data is shown to be good.