Collapse and rebound of a gas bubble

In this paper, we study the collapse and rebound of a gas bubble. Our goals are twofold: (1) we want to stress that different mathematical models may lead to extremely different results and (2) we introduce a new class of simplified reliable models. We accomplish our first goal by showing that the results obtained from two of the simplest and most widely used models (the isothermal and adiabatic approximations) are very different while the bubble is highly compressed. This period of time is short but it is of crucial importance in most phenomena where bubble collapses are relevant. To accomplish our second goal, we identify a nondimensional parameter that is a quantification of the strength of the bubble collapse and we show how to use this large parameter to obtain new simplified models through the use of standard asymptotic techniques. Illustrative examples and discussions on the wide range of applicability of the approach introduced in this work are given.