The response to ambient pressure of fuel drop combustion with surface equilibrium

The burning rate response of a fuel drop to ambient pressure is determined, using the method of activation-energy asymptotics. The combustion is assumed to be quasi-steady and spherically symmetric. Other analyses of this problem have commonly, but unrealistically, assumed that the surface temperature T_s may be prescribed a priori. By contrast, the present analysis imposes vapor-liquid equilibrium at the surface of the drop, so that T_s is determined as part of the solution. The resulting response curves differ markedly from those obtained by prescribed-T_s analyses. In particular, it is shown that the burning rate actually decreases over much of the response as the ambient pressure increases. Also, in the limit of large pressure, the reaction zone moves to the surface of the drop (the Buckmaster flame), rather than evolving into the familiar Burke-Schumann equilibrium flame.