Oscillatory instability of the gas-liquid meniscus in a capillary under the imposed temperature difference

To understand the oscillations in the real, multi-branch pulsating heat pipe (PHP), the start-up conditions of the single branch PHP with no adiabatic section are studied theoretically and numerically. The single branch PHP is a capillary open from one end, which is connected to a reservoir at constant pressure. A gas bubble is confined between the sealed end of the capillary and the liquid. The gas is the vapor of the liquid. The gas end of the capillary is maintained at a constant temperature larger than that of the liquid end. Under certain conditions, self-sustained oscillations of the meniscus may exist in such a system. The conditions of oscillation development (i.e. of the PHP startup) are obtained via the stability analysis of an earlier proposed theoretical model. The linear instability is absent in such a system. The instability of a marginal state described by piece-wise linear equations is analyzed with the analytical averaging method. The instability boundary is presented in terms of dimensionless groups, the physical significance of which is discussed. It is found that the model describes correctly the known experimental facts. Some predictions concerning the instability threshold are formulated.