An energy model for artificially generated bubbles in liquids

Abstract

A mathematical analysis is carried out to model the series of processes following the occurrence of an electron avalanche in a liquid right through to the emission of a pressure transient and the formation of a bubble. The initial energy distribution is chosen to be Gaussian and it is assumed that the electrical energy injected into the system is transformed into thermal and mechanical components. From the mechanical point of view, an outgoing spherical pressure transient is formed at the edge of the plasma region, and at a later time a bubble is also formed. Theoretically, the pressure transient accounts for about 15% of the total injected energy, while it is necessary to revert to experimental results to fix the energy associated with the bubble (about 2%). A minimum such value can, however, be estimated. The maximum pressure amplitude is calculated. Concerning the thermal component of the energy, some is absorbed as internal energy by the liquid, while the remainder is stocked as latent heat of vaporization. The maximum temperature difference is derived as are the different energies as functions of the total injected energy. The advantage of this type of model is that the gas/vapour temperature in the bubble can continue to rise after the phase change takes place. The maximum bubble size following a given energy injection is calculated assuming an adiabatic expansion process. A mathematical expression for the liquid flow induced by the outgoing pressure transient is also found. Comparison between experimental and theoretical results is particularly good.