Blowing out a candle
|Blowing out a candle slowed down 20x|
As you can see the wind first makes the flame better oxygenated, and it burns much bluer, it then starts to get blown away from the wick. There are two things which can stop the flame burning, one is if the air is moving faster than the flame can move through the air, which means that the flame is literally blown away from the wick. And secondly the cold air can just cool the fuel and air down so much that they cease to burn. It doesn't cool the wick down immediately as after the candle is blown out there is still lots of wax vapor produces which condenses as smoke.