Investigating the effects of fire induced smoke on visibility requires an understanding of its characteristics along with the associated light obscuring properties. Mulholland provides a convenient definition of smoke as the condensed phase component of the combustion products that widely varies in appearance and structure [
12]. Light-coloured aerosols, essentially containing droplets, produced by smouldering fires and pyrolysis have a strong scattering effect on light. Dark and solid carbonaceous soot particles produced by flaming combustion from fuels such as
n-heptane, on the other hand, are highly absorbent [
13]. Both effects are induced by the particle size distribution of the aerosol, mainly related to the geometric mean volume to surface diameter of the particles [
14]. For post-flame smoke particles, the absorbing effect can be expressed in terms of an almost fuel type independent, mass-specific extinction coefficient, subsequently denoted
\(K_{\text{m}}\). This simplification assumes that soot essentially comprises spherical carbonaceous particles significantly smaller than the wavelength of light so that scattering effects are negligible [
15]. The light obscuring effect of smoke therefore is proportional to the smoke density
\(\rho _\text{s}\). Both quantities can be summarized into the extinction coefficient
\(\sigma \). It can be obtained by applying Beer–Lambert’s law, see Eq.
2, to optical measurements of the light transmission
T along a known path length
l. However, this only accounts for the damping effect on the initial light intensity
\(I_0\) to the intensity
I in the presence of smoke due to absorption and scattering, since both effects can not easily be separated.
$$\begin{aligned} T = \frac{I}{I_0} = \exp \left( - K_{\text{m}} \cdot \rho _\text{s} \cdot l\right) = \exp \left( - \sigma \cdot l\right) \end{aligned}$$
(2)
Mulholland and Croarkin estimated
\(K_{\text{m}}\) to be
\( 8700\,\text{m}^{2}\, \text{kg}^{-1}\) with an extended uncertainty of
\(1100\,\text{m}^{2}\, \text{kg}^{-1}\) as a mean value from the analysis of seven studies involving 29 fuels in flaming fires [
15]. It is frequently referenced as a default quantity in various numerical fire models, such as FDS [
16]. Optical measurements each were performed at a wavelength of
\(\lambda = {633}\, \text{nm}\) in post-flame generated smoke from stoichiometric or over-ventilated combustion. For smoulder and pyrolysis generated smoke, the value is reported to be much lower and more variable. A similar study was conducted by Widmann based on a literature review of data from stoichiometric and over-ventilated combustion [
17]. He deduced a correlation of
\(K_{\text{m}}\) with wavelength
\(\lambda \), based on the least square fit of measurements mainly in the visible spectrum and in the near infrared range, described by Eq.
3.
$$\begin{aligned} K_{\text{m}}= 4.8081 \cdot \lambda ^{-1.0088} \end{aligned}$$
(3)
The value of
\(K_{\text{m}}\) can change over time caused by ageing processes of the aerosol. Due to agglomeration, the particle concentration decreases while the size distribution shifts towards a larger mean particle diameter [
18]. The difference in scattering and absorption characteristics of particles at different wavelengths can be used to estimate the mean particle size diameter. A potential approach relying on a combination of optical measurements and theoretical calculations based on Mie scattering theory is presented in [
19,
20]. These procedures follow a correlation of the logarithms of the measured light transmission at different wavelengths with the calculated extinction efficiency as a function of the particle diameter. Węgrzyński et al. have examined several multi-wavelength densitometers following a similar approach in a literature study [
21]. They summarized that most of the apparatus are connected to bench-scale experimental setups like cone calorimeters, while only few devices exist that are meant to be used in compartment scale fires. Still, such investigations are even more important in terms of modelling visibility, since scaling effects regarding the extinction coefficient can not be precluded.