(Received ?; revised ?; accepted ?. -To be entered by editorial office)During improved oil recovery, gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as 'pressure-driven growth' is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover 'pressure-driven growth' is shown to correspond to a special case of the more general 'viscous froth' model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such 'inherent' singularities can be readily incorporated into these numerical schemes.

We combine small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS) with aerodynamic levitation techniques to study in situ phase transitions in the liquid state under contactless conditions. At very high temperatures, yttria-alumina melts show a first-order transition, previously inferred from phase separation in quenched glasses. We show how the transition coincides with a narrow and reversible maximum in SAXS indicative of liquid unmixing on the nanoscale, combined with an abrupt realignment in WAXS features related to reversible shifts in polyhedral packing on the atomic scale. We also observed a rotary action in the suspended supercooled drop driven by repetitive transitions (a polyamorphic rotor) from which the reversible changes in molar volume (1.2 +/- 0.2 cubic centimeters) and entropy (19 +/- 4 joules mole(-1) kelvin(-1)) can be estimated.