title: Zeldovich–Liñán model
text: # Zeldovich–Liñán model
  
  In combustion, Zel'dovich–Liñán model is a two-step reaction model for the combustion processes, named after Yakov Borisovich Zel'dovich and Amable Liñán. The model includes a chain-branching and a chain-breaking (or radical recombination) reaction. The model was first introduced by Zel'dovich in 1948 and later analysed by Liñán using activation energy asymptotics in 1971. The mechanism reads as
  
      ${\begin{aligned}{\rm {{F}+{\rm {X}}}}&\rightarrow 2{\rm {X}}\\{\rm {{X}+{\rm {{X}+{\rm {M}}}}}}&\rightarrow 2{\rm {{P}+{\rm {M}}}}\end{aligned}}$
  
  where ${\rm {F}}$ is the fuel, ${\rm {X}}$ is an intermediate radical, ${\rm {M}}$ is the third body and ${\rm {P}}$ is the product. The first reaction is the chain-branching reaction, which is considered to be auto-catalytic (consumes no heat or releases no heat), with very large activation energy and the second reaction is the chain-breaking (or radical-recombination) reaction, where all of the heat in the combustion is released, with almost negligible activation energy.
  
  