Influence of bubble expansion and relative velocity on the performance and stability of an airlift pump

An airlift pump which raises liquid by means of compressed air introduced near the lower end of the eduction pipe is an example of a self-control system. It has been shown by Hjalmars (1973) that an occasionally observed breakdown in the self-control mechanism, which leads to instability, is due to the fact that the control mechanism is delayed, with the effect that a small, time-dependent perturbation of the stationary flow satisfies a differential equation with delayed argument. This investigation was carried out with the assumption of a single-phase flow of an ideal incompressible liquid. The aim of the present study is to consider the stability conditions of an airlift pump within the frame of a more general flow model, namely a separate two-phase flow of compressible gas and incompressible liquid, which takes into account the effects of the expasion of gas bubbles during their lift and of the relative velocity, i.e. the difference in the velocity of gas bubbles and the liquid.