Each troop type has a set amount of food that a single troop eats per day. For example, 1 Vanquisher eats 6 units of food per day.
When enlisting troops in your city, the amount of food that they eat per day will be divided by 24, and given per hour as part of your net food income. The breakdown of your net food income can be seen in each city's food tooltip.
For example, if you have 100 vanquishers, each eating 6 units of food per day:
6*100 /24 = 25 food per hour, eaten by your vanquishers.
If a city's troop count means that it is expending more food per hour from troops eating, than it is making with farm estates, then that city's net food balance will be negative, and will be displayed in red in the left-hand panel in-game.
If this happens, there is a chance that your city could run out of food, if you do not keep it topped up with surplus food!
If your city runs out of food and you can no longer feed all of your troops, your troops will gradually begin to abandon your city, and go to look for work somewhere else! Your troops will abandon at a rate of 10% of your total city force, per hour.
From the time that your city first runs out of food, the first troop abandonment can occur within anywhere up to 15 minutes.
If your troops are sent to reinforce other cities, they will still eat from their home city, unless the city that they are reinforcing comes under siege.
If a city with reinforcing troops comes under siege, ALL troops residing in that city will begin to eat from that city. As such, if you have a city under siege, keep an eye on your food counter! Your food count can reduce far more quickly if you are under siege - depending on how many reinforcements you have!