Thermal explosion characteristics of a gelled hypergolic droplet

TL;DR

This paper analyzes the thermal explosion behavior of a gelled hypergolic droplet, deriving conditions for ignition and steady-state, with explicit formulas for ignition delay times in different regimes.

Contribution

It provides an analytical framework for predicting explosive versus steady-state behavior in hypergolic droplet systems, including explicit ignition delay formulas.

Findings

Critical conditions for explosion vs. steady state are derived.

Explicit ignition delay formulas are provided for different regimes.

The model employs activation-energy asymptotics to analyze interface temperature evolution.

Abstract

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.