The Zel'dovich number is a

dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

which provides a quantitative measure for the

activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...

of a

chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...

which appears in the Arrhenius exponent, named after the

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

scientist A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosoph ...

Yakov Borisovich Zel'dovich Yakov Borisovich Zeldovich ( be, Я́каў Бары́савіч Зяльдо́віч, russian: Я́ков Бори́сович Зельдо́вич; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet physicist of Bel ...

, who along with

David A. Frank-Kamenetskii David Albertovich Frank-Kamenetskii (russian: Давид Альбертович Франк-Каменецкий, August 3, 1910 – June 2, 1970) was a Soviet theoretical physicist and chemist, professor and doctor of physical, chemical and mathe ...

, first introduced in their paper in 1938. In 1983 ICDERS meeting at Poitiers, it was decided to name after Zel'dovich.Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59. It is defined as :

\beta = \frac   \cdot \frac

where *

E_a

is the

of the reaction *

R

is the

universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

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 \alpha

For typical

combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combus ...

phenomena, the value for Zel'dovich number lies in the range

\beta\approx 8-20

Activation energy asymptotics Activation energy asymptotics (AEA), also known as large activation energy asymptotics, is an asymptotic analysis used in the combustion field utilizing the fact that the reaction rate is extremely sensitive to temperature changes due to the large ...

uses this number as the large parameter of expansion.

References

{{Reflist, 30em Chemical kinetics Combustion Dimensionless numbers of fluid mechanics Fluid dynamics Dimensionless numbers Dimensionless numbers of chemistry