The stratified gaseous layer established over the liquid fuel surface varies from a fuel-rich mixture to within the lean flammability limits of the vaporized fuel and air mixture. At some point above the liquid surface, if the fuel temperature is high enough, a condition corresponds to a stoichiometric equivalence ratio. For most volatile fuels this stoichiometric condition develops. Experimental evidence indicates that the propagation rate of the curved flame front that develops is many times faster than the laminar flame speed discussed earlier. There are many less volatile fuels, however, that only progress at low rates.

It is interesting to note that stratified combustible gas mixtures can exist in tunnel-like conditions. The condition in a coal mine tunnel is an excellent example. The marsh gas (methane) is lighter than air and accumulates at the ceiling. Thus a stratified air–methane mixture exists. Experiments have shown that under the conditions described the flame propagation rate is much faster than the stoichiometric laminar flame speed. In laboratory experiments simulating the mine-like conditions, the actual rates were found to be affected by the laboratory-simulated tunnel length and depth. In effect, the expansion of the reaction products of these type laboratory experiments drives the flame front that is developed. The overall effect is similar in context to the soap bubble–type flame experiments discussed in Section 4.3.5.3. In the soap bubble flame experiment measurements, the ambient condition is about 300 K and the stoichiometric flame temperature of the flame products for most hydrocarbon fuels is somewhat above 2200 K, so that the observed flame propagation rate in the soap bubble is seven to eight times the laminar flame speed. Thus, in the soap bubble experiment the burned gases drive the flame front, and of course, a small differential pressure exists across this front.

Under the conditions described for coal mine tunnel configurations, the burned gas expansion effect develops differently. To show this effect, Feng et al. [41,42] considered analytically the propagation of a fuel layer at the roof of a channel over various lengths and depths of the configuration in which the bottom layer was simply air. For the idealized infinite depth of the air layer, the results revealed that the ratio of the propagating flame speed to that of the laminar flame speed was equal to the square root of the density ratio (ρ_u/ρ_b); that is, the flame propagation for the layered configuration is about 2.6–2.8 times the laminar flame speed. Indeed the observed experimental trends [41,42] fit the analytical derivations. The same trends appear to hold for the case of a completely premixed combustible condition of the roof of a channel separated from the air layer below [41].

The physical perception derived from these analytical results was that the increased flame propagation speed over the normal flame speed was due to a fluid dynamical interaction resulting from the combustion of premixed gases; that is, after the combustible gas mixture moves through the flame front, the expansion of the product gases causes a displacement of the unburned gases ahead of the flame. This displacement results in redistributing the combustible gaseous layer over a much larger area in the induced curved, parabolic-type, flame front created. Thus, the expansion of the combustible mixture sustains a pressure difference across the flame, and the resulting larger combustible gas area exposed to the flame front increases the burning rate necessary for the elevated flame propagation rate [40,42].

The inverse of the tunnel experiments discussed is the propagation of a flame across a layer of a liquid fuel which has a low flashpoint temperature. The stratified conditions discussed previously described the layered fuel vapor−air mixture ratios. Under these conditions, the propagation rates were found to be four to five times the laminar flame speed. This increased rate compared with the other analytical results is apparently due to diffusion of air to the flame front behind the parabolic leading edge of the propagating flame [41].

Experiments [43] with very high flashpoint fuels (jet propellant, kerosene, diesel, etc.) revealed that the flame propagation occurred in an unusual manner and a much slower rate. In this situation, at ambient conditions any possible amount of fuel vapor above the liquid surface creates a gaseous mixture well outside the fuel’s flammability limits. What was discovered [44,45] was that for these fuels the flame will propagate because the liquid surface under the ignition source is raised to a local temperature that is higher than the cool ambient temperature ahead of the initiated flame. Experimental observations revealed [45] that this surface temperature variation from behind the flame front to the cool region ahead caused a variation in the surface tension of the liquid fuel. Since the surface tension of a liquid varies inversely with the temperature, a gradient in surface tension is established and creates a surface velocity from the warmer temperature to the cooler temperature. Thus, volatile liquid is pulled ahead of the flame front to provide the combustible vapor–air mixture for flame propagation. Since the liquid is a viscous fluid, currents are established throughout the liquid fluid layer by the surface movement caused by the surface tension variation. In the simplest context of thin liquid fuel films, the problem of estimating the velocities in the liquid is much like the Couette flow problem, except that movement of the viscous liquid fuel is not established by a moving plate, but by the surface tension variation along the free surface. Under such conditions at the surface the following equality exists:

The following proportionality is readily developed from the above equation:

Propagation across solid fuel surfaces is a much more complex problem because the orientation of the solid surface can be varied. For example, a sheet of plastic or wood held in a vertical position and ignited at either the top or bottom edge shows vastly different propagation rates because of gravity effects. Even material held at an angle has a different burning rate than the two possible vertical conditions. A review of this solid surface problem can be found in Refs [46–48].