There are two categories of mixtures in regard to nullification. The first category is a dry mixture where the foods are mixed together but do not dissolve into each other. The second category is a wet mixture, which is classified as any mixture that the two elements are dissolved in each other and not distinguishable any more.
In order for nullification to occur in a dry mixture, the majority of the food in the mixture should be permitted food. The Pitchei Teshuva says that this means a 1:2 ratio. So, if one piece of non-kosher meat got mixed up with two kosher pieces of meat, the non-kosher piece is nullified. After nullifying in this way, one is still not allowed to eat all three pieces. Rather, one may eat only one piece at a time. The Rama writes that additionally you must discard one of the pieces.
It is interesting to note that some have a custom when boiling eggs to always have at least three eggs in the pot. The reason behind this custom may be understood based on what we have just explained. If one boiled an egg and the egg had blood in it, the pot in which the egg was boiled would now be non-kosher. However, if there were three eggs in the pot, even if one egg had blood in it, it would be nullified to the other two eggs. Therefore, the pot would remain kosher.
Nullification in a liquid mixture occurs when there is sixty times more of one food than the other. Meaning, if there was one ounce of broth from chicken soup that fell into sixty ounces of milk, the kosher status of the chicken soup is not affected by the milk, and the milk is permitted to be drunk. If the food that was nullified is not recognizable but can still be removed, one should do so. An example of this is fat from meat that fell into dairy soup. If the fat is nullified and the soup is permitted, one should still cool the soup down and remove whatever congealed fat from the top that they can.
In a mixture of liquids, it will either be a mixture of ingredients that are the same (for example kosher and non-kosher meat), or a mixture of different ingredients (such as milk and chicken soup). The former is referred to as min b’mino – a mixture of one type, and the requirement to have sixty times more permitted food than forbidden food is only a rabbinic requirement. If the mixture consists of dissimilar ingredients, it is min b’eino mino – similar in dissimilar food, and the requirement to have sixty times more permitted food than the forbidden food is biblical. A rabbi may use this difference to permit certain cases if there are other reasons to be lenient alongside it.
A difference between a mixture that biblically requires nullification in sixty and a mixture that only needs sixty rabbinically occurs when the ratio of permitted food and forbidden food is in doubt. For example, if some non-kosher chicken soup dripped into a pot of milk and we don’t know exactly how much of it dripped in, since it is not the same taste it is possibly a biblical prohibition and you may not eat it. However, if some non-kosher chicken soup dripped into a pot of kosher chicken soup, since they are essentially the same taste it is min b’mino, and only requires nullification in sixty from a rabbinic viewpoint, not from a biblical view. Therefore, in a case of doubt we can be lenient and consider the soup to be kosher.
If there was a mixture of liquids and solids and the solids are recognizable in the liquid, we view the liquids and solids as two separate entities. If the liquid was kosher to start with, then in order to permit eating the liquid there has to be sixty times permitted food more than forbidden food. If there is a solid piece of forbidden food, and it is recognizable, it needs to be removed from the mixture. This must be done even though there is sixty times more permitted food than the piece of forbidden food. If there are solids of both forbidden foods and permitted foods in the mixture, the majority of the solid pieces must have originally been permitted food in order to permit eating the current mixture of solids.