An analytical and numerical study of liquid dynamics in a one-dimensional capillary under entrapped gas action

Capillary dynamics has been and is yet an important field of research, because of its very relevant role played as the core mechanism at the base of many applications. In this context, we are particularly interested in the liquid penetration inspection technique. Due to the obviously needed level of reliability involved with such a non-destructive test, this paper is devoted to study how the presence of an entrapped gas in a close-end capillary may affect the inspection outcome. This study is carried out through a 1D ordinary differential model that despite its simplicity is able to point out quite well the capillary dynamics under the effect of an entrapped gas. The paper is divided into two main parts; the first starts from an introductory historical review of capillary flows modeling, goes on presenting the 1D second order ordinary differential model, taking into account the presence of an entrapped gas and therefore ends by showing some numerical simulation results. The second part is devoted to the analytical study of the model by separating the initial transitory behavior from the stationary one. Besides, these solutions are compared with the numerical ones and finally an expression is deduced for the threshold radius switching from a fully damped transitory to an oscillatory one.