Flame Challenge

Posted: 29th June 2012 by seanmathmodelguy in Blog

A few months ago I submitted an entry to Alan Alda’s flame challenge.  Although I was not a finalist I wanted to share the submission.  I hope you enjoy it.

[dropcap style=”1″ size=”3″]C[/dropcap]onsider the flame from a simple candle. If you stare very closely at the wick, you will see wax bubbling away on its surface and if you look even closer, perhaps you will observe the bubbles evaporating away into the flame. What is really going on here just beyond what you can observe with your eyes? How is the wax sustaining the flame and where is the wax going?

The story starts with the wax fuel for the flame. Wax itself consists of long chain carbon molecules almost like rows upon rows of chorus line dancers moving in time with their arms interlocked. When heated, these chains become agitated and if the temperature is high enough, they leave the wick by evaporation. If you continue to apply heat then the chains break into shorter strands as they jostle and bang into each other. If a chain of dancers breaks into fragments then the dancers on the ends of the chain have a free arm to rejoin with another fragment. The same is true with the chain fragments. At the ends where the chains break, it is a bit sticky and the fragments of chain can rejoin into long tangled chains that we identify as soot.

Having left the wick, these chain fragments drift drift up and away, occasionally either getting a little bit shorter through a collision or sticking to a forming soot particle, driven by the buoyancy of the heat of the flame until they meet an oxygen drifting inwards from the region outside the flame.

When these two, carbon and oxygen, meet under lower temperatures when there is not so much jostling going on, they pass by each other without combining. However, if there is enough jostling then they get close enough and snap together in a violent chemical reaction that produces a lot of heat. This consumes the oxygen and produces carbon monoxide and enough heat to cause even more jostling and other snapping together of oxygen and carbon in a run-away process that sustains the flame. As well as producing heat, there is a characteristic blue light that is emitted from the excited products of this reaction. This region of the flame, where this reaction is taking place, is the bluish band you see in the candle flame. This band marks the boundary between the inner dark zone of the flame where the chain fragments are diffusing away from the candle and the outer zone where oxygen is diffusing towards the candle. This inner region is called the dark zone since no light is produced in part of the flame.

All of the soot and particle fragments rise with the rising air and this pulls more oxygen in from below the flame to sustain the process. The large soot particles consist of tangled masses of recombined fragments from the wax and they absorb a lot of the heat given off. If you shine a light on a flame, you can observe a shadow which indicates that the flame has some large particles within it — these very soot particles we have been discussing. When they get hot, they begin to glow and decompose by reacting with more oxygen as they rise, and if there is enough heat, then they completely decompose into carbon dioxide and carbon monoxide. If the temperature reduces, say with a wayward breeze, then the soot does not completely decompose and some of it escapes.

So you can see that there are really three regions of the flame. An inner dark zone where the fuel breaks into shorter strands and soot begins to form; a thin reaction region of a particular colour that characterizes the chemical reactions taking place there; and an outer region, called the carbon zone, where glowing soot particles decompose as they float away from the flame. This whole process is an example of a buoyancy driven flow and has an interesting parallel with a waterfall.  In this case the driving force is not buoyancy but rather gravity. As the water falls in a sheet it breaks into smaller and smaller droplets and if you look carefully you can see an arc separating the the bulk flow of the water and the region of droplets. There is no chemical reaction going on, but what you are looking at has the same structure as a flame but pointing down in the direction of the gravitational driving force rather than upwards as you see in the household candle.

Next time you look at a flame think of the wonderful tiny dance that is going on.  Fragments of fuel, like long lines of dancers, either breaking into smaller strips and tangling with other fragments or a tiny piece whizzing off to meet their fate with an oxygen in a violent reaction that produces the heat of the flame. This heat reflected back to the tangled fragment that make up the soot causing then to glow in response as they are systematically disassembled by more oxygen as they rise through the flame.

Depending on the type of fuel and whether or not it is oxygen that completes the reaction, the temperature and colour of a flame can vary greatly. However, the basic structure remains the same and the beauty of it remains intact.