# Markstein number

The Markstein number is a term used in combustion engineering and explosion studies. It characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature.

The dimensionless Markstein number is defined as:

${\displaystyle \mathrm {Ma} ={\frac {L_{b}}{\delta _{f}}}}$

where ${\displaystyle L_{b}}$ is the Markstein length, and ${\displaystyle \delta _{f}}$ is the characteristic laminar flame thickness. The larger the Markstein length, the greater the effect of curvature on localised burning velocity.

It is named after George Markstein (1911—2011), who showed that thermal diffusion stabilized the curved flame front and proposed a relation between the critical wavelength for stability of the flame front, called the Markstein length, and the thermal thickness of the flame.[1]

Phenomenological Markstein numbers with respect to the combustion products are obtained by means of the comparison between the measurements of the flame radii as a function of time and the results of the analytical integration of the linear relation between the flame speed and either flame stretch rate or flame curvature.[2][3][4]

The burning velocity is obtained at zero stretch, and the effect of the flame stretch acting upon it is expressed by a Markstein length. Because both flame curvature and aerodynamic strain contribute to the flame stretch rate, there is a Markstein number associated with each of these components.[5]