Chemistry:Zeldovich number

The Zel'dovich number is a dimensionless number which provides a quantitative measure for the activation energy of a chemical reaction which appears in the Arrhenius exponent, named after the Russian scientist Yakov Borisovich Zel'dovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938. In 1983 ICDERS meeting at Poitiers, it was decided to name after Zel'dovich. It is defined as

$\beta =\frac{E_a}{R{T}_b}\cdot \frac{T_b-T_u}{T_b}$

where

• $E_a$ is the activation energy of the reaction
• $R$ is the universal gas constant
• $T_b$ is the burnt gas temperature
• $T_u$ is the unburnt mixture temperature.

In terms of heat release parameter $\alpha$, it is given by

$\beta =\frac{E_a}{R{T}_b}\alpha$

For typical combustion phenomena, the value for Zel'dovich number lies in the range $\beta \approx 8-20$. Activation energy asymptotics uses this number as the large parameter of expansion.