  When a sphere of one reactant is placed in the medium of another reactant
with which it is hypergolic, a chemical reaction (modeled here as a
zeroth-order one-step irreversible Arrhenius reaction) occurs at the common
interface of the two reactants, and the heat generated at the interface then is
transmitted away from it by thermal conduction. Depending on the nature of the
problem, the system may approach an explosive mode, or it may settle into a
steady-state mode. The critical condition defining the transition between these
two states is determined analytically. In particular, explicit formulas for the
ignition delay time for the explosive mode are provided for two limits, one in
which an appropriately defined Damk\"ohler number is large and the other in
which it is closer to the critical conditions. This is accomplished here by
deriving and solving an integral equation for the time evolution of the
interface temperature, employing activation-energy asymptotics.
