Could biochar be used to clear fog?

Could biochar be used to clear fog? After the biochar dust has fallen to the ground the ground should be more fertile.
Fog: Shipping and aviation is sometimes delayed by fog. Fog will reflect some sunlight and absorb some infrared. If you distributed fine biochar particles in the fog these would absorb most of the solar energy (light and infrared) and the fog should heat up and disperse. The Japanese use biochar on snow to help melt snow. The biochar decreases the albedo of the snow and so it absorbs solar energy and melts days sooner.
Calculations: Wikipedia says that in fog there is typically 50 000 kg of water per cubic kilometre of fog (liquid water content of fog is typically 0.05 g per cubic metre). 2257 kJ is needed to vaporise 1 kg of water.
To vaporize this 50 000 kg of water takes about 50 000x2257 kJ=112 850 000 kJ = 112 850 000/3600 kWh = 31347 kWh.
Say the fog is 100 m deep. Then an area of 10 square kilometres has a cubic kilometre of fog. Say the solar energy falling per square metre of ground is 2 kWh per day. Then 2x10x1000000 kWh = 20000000 kWh falls on the 10 square kilometres. This is far more than the 31347 kWh needed to vaporize the fog. Of course not all the solar energy will be absorbed by the fog with biochar dust in and some solar energy must go into heating air as well, but there is a lot of solar energy to spare (31347 kWh needed for vaporization and 20 000 000 kWh available from the sun).