Ignition of Heterogeneous Mixtures in Gravitational Fields

Abstract

A solid mixture is ignited from above. Melting of some of the components results in a reactive liquid suspension containing condensed phase particles whose density exceeds the density of the liquid. Thus, under the influence of gravity, sedimentation occurs, i.e., particles descend, displacing fluid, which then flows upward. We consider the problem of ignition in the presence of gravitational forces, employing a two-velocity model which describes the relative motion of the components of the mixture. Whether or not ignition occurs depends on the relative time scales of reaction and sedimentation. Thus, we introduce a parameter v g , which is the ratio of the reaction and sedimentation time scales. We study the problem both analytically and numerically. We determine whether or not ignition occurs, by determining a critical ignition condition, i.e., by determining a critical value of v g as a function of parameters such as the strength of the heat source, the initial temperature, the strength of the gravitational field, the diameter of the particles, the viscosity of the fluid, the difference in the densities of the fluid and the particles, and the kinetic parameters, etc. Below (above) The critical value ignition will (will not) occur. In the case that ignition does occur, we estimate the ignition time. In addition, we numerically determine the dynamics of the ignition process as a function of the parameters of the problem. We show that it is necessary to modify standard ignition criteria in order to account for gravitational effects. Finally, we describe how to adapt the model to other heterogeneous mixtures, e.g., to gas–condensed phase suspensions.