Mathematical model of reaction rate oscillations on a chain of nm-sized catalyst particles

2003 ◽  
Vol 118 (19) ◽  
pp. 8882-8890 ◽  
Author(s):  
N. V. Peskov ◽  
M. M. Slinko ◽  
N. I. Jaeger
Keyword(s):  
Mathematical Model ◽  
Reaction Rate ◽  
Rate Oscillations ◽  
A Chain

The theory of flame phenomena with a chain reaction

1956 ◽  
Vol 249 (957) ◽  
pp. 1-25 ◽  
Keyword(s):  
Reaction Zone ◽  
Flame Propagation ◽  
Reaction Rate ◽  
Laminar Flame ◽  
Combustible Mixture ◽  
Flame Speed ◽  
Spontaneous Ignition ◽  
Chain Reaction ◽  
Hydrazine Decomposition ◽  
A Chain

For single-step reactions there is a unique relation between reaction rate and reactedness for a given combustible mixture at a specified pressure and initial temperature. This paper examines whether the relation is still unique when chain reactions are present, by considering three types of flame—spontaneous ignition, laminar-flame propagation, and the homogeneous steady-flow reaction zone—with a chain-reaction scheme proposed by Adams & Stocks for the decomposition of hydrazine. It is found that the relation is not unique but that similarities exist between the relation for laminar-flame propagation and the relation for the homogeneous reaction zone. Incidentally, a general method of calculating laminar-flame speeds with reaction schemes of arbitrary complexity is presented. When applied to the hydrazine decomposition flame the predictions of the theory are in fair agreement with experimental results. In particular, the variation of flame speed with temperature is correctly predicted. It is shown that the use of the Karman-Penner 'steady-state assumption' would lead to an overestimate of the flame speed. Consideration of the changes which would result if the chain reaction should branch shows that there would once again tend to be a unique reaction rate versus reactedness relation, and that the laminar-flame speed would be increased by a factor of about three for the hottest flame considered but by larger factors for cooler flames.

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