It becomes a balance issue for the needs of the flame. To have fire, you need oxygen, fuel, and heat. If those are out of balance, you don’t have fire.
When you blow out a candle, you disrupt the balance of oxygen and heat. You provide way too much oxygen and remove the heat.
When you have a spark, it’s surrounded by fuel. A controlled blowing gives it enough oxygen to help ignite the surrounding fuel.
You remember the heat+oxygen+fuel fire triangle from school, right?
Blowing out a candle does three things:
1. It blows away the vaporised wax which is what acts as the fuel for the flame. It’s akin to taking out wood away from a campfire
2. You suddenly blow away hot air and introduce colder one in it’s place. Because enthropy causes every system to roughly equalize the heat from the flame suddenly travels into the colder air, equalizing the entire system for a brief moment lowering the heat of the flame for a short while(until more enrgy is released from the fuel)
3. You blow out the air from your own lungs, this air is generally more dense in carbon dioxide which also stifles the flame
You are reducing the balance of three main components needed for fire to exists, thus making the candle flame unsustainable with what it has in that brief moment and causing it to go out.
Meanwhile blowing a spark helps with igniting it because that spark doesn’t have all those 3 components in the first place – it has the necessary fuel and heat, but it lack the oxygen, and by blowing air on it you are forcefully moving oxygen molecules into the places near the actual heat source from which it was already used up, allowing you to sustain the flame
There are already some good answers, but I want to highlight a big difference between the candle and the “spark”.
With the candle, the wax is not burning in the solid or even liquid state. It must first vaporize and mix with air (oxygen) to burn. Once the wax is in vapor form, it mixes with air fairly easily. As others have said, when you blow on the candle it takes heat away and the vaporized wax fuel away.
If the spark is from a small piece of wood or other organic mater, then it is mostly carbon. The carbon is actually oxidizing (or burning) in the solid form. Since it’s solid, it is very hard for air to mix with it. Blowing on it gets more oxygen touching the carbon, so the carbon can burn faster. Since it’s a solid, the fuel and heat aren’t just blown away like with the vaporized candle wax.
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