EXTINCTION THRESHOLD IN RANDOM HETEROGENEOUS
CONDENSED MIXTURES WITH AN EXTREMELY SMALL
AMOUNT OF A COMBUSTIBLE

O. S. Rabinovich and P. S. Grinchuk

UDC 536.46

A mathematical model describing the process of combustion 
of heterogeneous condensed mixtures with account for the randomness 
of the distribution of combustible particles over the system is proposed. 
The step dependence of the reaction rate on the temperature is used 
as a model of chemical kinetics. The case where the concentration 
of the particles is extremely low but the heat energy released in 
their combustion is high has been investigated. It is shown that for 
an adiabatic system there exists a concentration limit of combustion. 
The relation of this combustion limit to the geometric phase transition 
occurring in a heterogeneous condensed mixture with rare combustion 
inclusions has been demonstrated. An analytical approach to the evaluation 
of the threshold concentration of the combustible in such systems, 
based on the continual theory of percolation, is proposed.

A. V. Luikov Heat and Mass Transfer Institute, National 
Academy of Sciences of Belarus, Minsk, Belarus; email: gps@hmti.ac.by, 
orabi@hmti.ac.by. Translated from Inzhenerno-Fizicheskii Zhurnal, 
Vol. 76, No. 2, pp. 80-87, March-April, 2003. Original article 
submitted November 13, 2002.