Dynamic response of geometrically constrained vapor bubbles

We consider a two-dimensional model of a vapor bubble between two horizontal parallel boundaries held at different temperatures. When the temperatures are constant, a steady state can be achieved such that evaporation near the contact lines at the hot bottom plate is balanced by condensation in colder areas of the interface near the top. The dynamic response of the bubble is probed by treating the case of time-dependent wall temperatures. For periodic modulations of the wall temperature the bubble oscillates about the steady state. In order to describe such time-dependent behavior we consider the limit of small capillary number, in which the effects of heat and mass transfer are significant only near the contact lines at the bottom plate and in a small region near the top. When the bottom temperature is modulated and the top temperature is held fixed, the amplitude of forced oscillations is constant for low-frequency modulations and then rapidly decays in the high-frequency regime. When the top temperature is modulated with fixed bottom temperature, the dynamic-response curve is flat in the low-frequency regime as well, but it also flattens out when the frequency is increased. This shape of the response curve is shown to be the result of the nonmonotonic behavior of the thickness of the liquid film between the bubble interface and the top plate: when the temperature is decreased, the film thickness increases rapidly, but then slowly decays to a value which is smaller than the initial thickness. The dynamic response is also studied as a function of the forcing amplitude.