Effects of Ambient Pressure on the Instability of a Liquid Boiling Explosively at the Superheat Limit

The effect of ambient pressure on the dynamical behaviour of a single droplet (1-2 mm diameter) of volatile liquid boiling explosively at the limit of superheat is studied experimentally and theoretically. In a series of experiments it is shown that the evaporative instability, observed earlier by Shepherd & Sturtevant (1982) during the rapid vapourization of butane droplets at atmospheric pressure, is suppressed at high pressure. Three other fluids (pentane, isopentane, and ether) are tested to establish the generality of the instability and other transient processes previously observed. Direct evidence is obtained showing that during violently unstable boiling small liquid particles are torn from the liquid-vapour interface. This ejection of fine droplets from the evaporating surface produces a mass flux orders of magnitude greater than that characteristic of ordinary boiling. Raising the ambient pressure lowers the superheat attained at the superheat limit, which decreases the vapourization rate. At high pressure boiling consists of normal slow vapourization from a smooth interface. Observed bubble growth rates show reasonable agreement with theory. At intermediate pressures a transitional regime of stability occurs in which a drop initially vapourizes stably for several milliseconds while incipient instability waves develop on the evaporating interface. When only a small amount of liquid remains in the drop in the shape of a thin cap, heat transfer from the surrounding hot host fluid initiates violent boiling at the edge of the liquid cap. The subsequent rapid vapourization generates a radiated pressure field two orders of magnitude larger than during stable boiling, and sets the bubble into violent oscillation. The bubble is subject to the Rayleigh-Taylor instability and rapidly disintegrates into a cloud of small bubbles. Lowering the ambient pressure decreases the time delay between nucleation and onset of unstable boiling. For example, in ether at atmospheric pressure the instability is triggered less than 8 µsec after nucleation, shortly after the smooth vapour bubble contacts the droplet surface. Heterogeneous nucleation spreads out along the surface of the drop while disturbances (with a length scale of 100 µm) distort the unstably evaporating interface within the drop, substantially enhancing the vapourization rate. At early times, droplets torn from the evaporating surface evaporate before the instability-driven jet impinges upon the surrounding fluid, bulging the bubble surface. The last portion of liquid in a drop boils particularly violently and droplets ejected from the evaporating interface at this time remain intact to splatter the bubble surface. At subatmospheric pressures the most rapid vapourization occurs and temperature gradients within a drop produce spatial variations in vapourization rate. The Landau mechanism for the instability of laminar flames is adapted to the case of evaporation to investigate the effects of variable ambient pressure. A spherical version of the theory, applicable before the vapour bubble contacts the droplet surface, predicts absolute stability at atmospheric pressure. At later times the spherical constraint is inappropriate and planar theory yields results in general agreement with observation. Differences in fluid properties make some fluids more prone to instability than others. The product of the maximum growth rate with the time interval the interface is predicted to be linearly unstable measures the susceptibility to instability. For practical estimates it is suggested that a value of 3 of this parameter be taken as the lower limit for instability. The sensitivity of the instability to temperature suggests that small temperature nonuniformities may be responsible for quantitative departures of the behaviour from predictions.