IGNITION OF HETEROGENEOUS MIXTURES IN GRAVITATIONAL-FIELDS

A solid mixture is ignited from above. Melting of some of the componen ts 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 desce nd, displacing fluid, which then flows upward. We consider the problem of ignition in the presence of gravitational farces, employing a two- velocity model which describes the relative motion of the components o f the mixture. Whether or not ignition occurs depends on the relative time scales of reaction and sedimentation. Thus, we introduce a parame ter v(g), which is the ratio of the reaction and sedimentation time sc ales. We study the problem both analytically and numerically. We deter mine whether or not ignition occurs, by determining a critical ignitio n condition, i.e., by determining a critical value of v(g) as a functi on 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 densi ties of the fluid and the particles, and the kinetic parameters, etc. Below (above) The critical value ignition will (will not) occur. Ln th e case that ignition does occur, we estimate the ignition time. In add ition, we numerically determine the dynamics of the ignition process a s a function of the parameters of the problem. We show that it is nece ssary to modify standard ignition criteria in order to account for gra vitational effects. Finally, we describe how to adapt the model to oth er heterogeneous mixtures, e.g., to gas-condensed phase suspensions. ( C) 1998 by The Combustion Institute.