Gemara

(Mishnah): When pouring a Tahor liquid into Tamei food, the top liquid remains Tahor, except for a very thick type of honey, or honey with beeswax;

Beis Shamai say, even porridge of ground or whole beans are exceptions, because they recoil when one ceases pouring.

Question (Rami bar Chama): Is a poured (solid) food considered connected?

Are the liquids in the Mishnah considered connected because drops recoil, and this does not happen to solids? Or, is it because these liquids are thick, and solids are also thick?

Pesachim 14a (Mishnah - R. Akiva): Kohanim would burn Kodesh oil that became Tamei through a Tevul Yom (one who immersed from Tum'ah today) in a lamp that is an Av ha'Tum'ah, even though this increases the oil's Tum'ah.

14b (Rava) Inference: R. Akiva holds that mid'Oraisa, liquids can Metamei other things. If they were Metamei only mid'Rabanan, the Tum'ah did not increase! The oil was already Pasul (and even now, it cannot be Metamei mid'Oraisa)!

Question: Perhaps it is Metamei mid'Rabanan. Before, it was not Metamei at all!

Answer: If so, the Mishnah would not need to say that the lamp was an Av ha'Tum'ah. Even a Rishon or Sheni makes oil a Rishon (which canbe Metamei)!

(Mishnah): The only Tum'ah that is Posel Terumah, but does not make a liquid a Rishon, is a Tevul Yom.

Chulin 107b: Rav Huna bar Sechorah sliced (or roasted) meat for Rav Hamnuna. He said 'if you were not such a Tzadik and Chacham, I would not feed you.'

Suggestion: He would trust only one zealous not to touch the food.

Rejection: He would trust only one like Rav Hamnuna to wash beforehand.

114a (Mishnah): Whey is like milk. Juice that drips from olives is like oil.

(Reish Lakish): This refers to Hechsher of food to receive Tum'ah.

Menachos 31a (Mishnah - R. Meir): Oil is (a liquid. Therefore, mid'Rabanan, whenever it is Tamei, it is) always a Rishon l'Tum'ah.

Chachamim say, even honey;

R. Shimon Shezuri says, even wine.

Question: Do the previous Tana'im say that wine is not (a liquid)?!

Correction: Rather, R. Shimon Shezuri says, (only) wine (is a liquid).

Rishonim

Rambam (Hilchos Tum'as Ochlim 1:19): Oil that congealed is not a (solid) food nor a liquid. If while it was congealed one intended for (eating) it, like a food or liquid, his opinion is Batel to that of normal people (who do not eat it).

Ra'avad: The Tosefta (Taharos 2:2) did not mention that it congealed. Perhaps it refers to oil that exuded by itself (from the olives), even if it did not congeal. In a Mishnah, R. Meir says that oil is always a Rishon, i.e. even if it congealed. Chachamim agree.

Kesef Mishneh: The Tosefta cannot refer to all oil. Oil is one of the seven liquids that are Machshir! The Rambam explains that it refers to congealed oil, rather than say that it refers to oil that exuded by itself. What is the Ra'avad's source that Chachamim agree with R. Meir? Presumably, his law was taught in his name because Chachamim disagree! Tosfos says that the Halachah follows R. Shimon Shezuri, who says that only wine is a liquid even when congealed. This is like the Rambam.

Rebuttal (Birkas ha'Zevach Menachos 31a): The Kesef Mishneh himself (below, 9:1) says that the Rambam rules unlike R. Shimon! He wrote in Perush ha'Mishnayos that 'is always a Rishon' means that if it became Tamei, it remains Tamei even if it congeals. The Tosefta teaches that while congealed it is not a liquid or food, i.e. it is not Mekabel Tum'ah. All agree that wine is Mekabel Tum'ah even when congealed.

Rambam (20):Congealed Chelev is not a food nor a liquid. If one intended for a food, it receives Tum'as Ochlim. If one intended for a liquid, his opinion is Batel.

Rambam (9:1): If wine or honey became Tamei, congealed, and melted, they are always a Rishon, like liquids, even though they froze after becoming Tamei.

Kesef Mishneh: The Rambam rules unlike R. Shimon Shezuri, for Rav Ashi (Chulin 75b) holds unlike him regarding liquids. Perush ha'Mishnayos says that they are liquids even when they are congealed.

Kaf ha'Chayim (158:27): If any liquid other than dew or water became hard and does not pour, the Radvaz (1:101) exempts from washing. It seems that the Rambam agrees. He is stringent only after they melted; he retracted from Perush ha'Mishnayos. We need not be stringent like the Kesef Mishneh.

Tosfos (Pesachim 14b DH Afilu): Here (in Pesachim) it seems that oil is a liquid. However, the Halachah follows R. Shimon Shezuri, who says that only wine is a liquid, but not oil! That Mishnah discusses wine that congealed, and later melted. The Reisha explicitly discusses gravy, grits or Chelev that congealed. Here, we discuss oil that never congealed. All agree that it is a liquid.

Poskim

Shulchan Aruch (OC 158:4): If one eats something dipped in one of the seven liquids, for which the acronym is Yad Shochat Dam (Rema - wine, honey, oil, milk, dew, blood, and water), and it is not dry, he must wash.

Magen Avraham (7): R. Shimshon (Taharos 3:1) says that it is a liquid if it is Tofe'ach Lehatfi'ach (wet enough to wet something else). If not, it is a food.

Machatzis ha'Shekel (7 DH Ayen): Tosfos said thatcongealed honey or oil is not a liquid, even if it later melted again. However, if wine congealed and melted again, it is a liquid. There are two Heterim to eat jam (from honey that was once congealed) without washing: it was intended to be a food, and it was once congealed. The Taz (7) says that this is only if it flowed by itself. If one did an act (extracted it from the hive) for the sake of a liquid, intent afterwards for a food does not help. Also, the Taz (9) does not require washing for something fried in lard, since it is not one of the seven liquids, but he requires for something fried in butter, even though it had congealed. However, the Magen Avraham proves otherwise from Tosfos.

Mishnah Berurah (14): The Poskim say that if any liquid congealed through cooking or the cold, and it is not Tofe'ach Lehatfi'ach, it is not a liquid. Tosfos says that even if it later melts, it is not a liquid, except for wine or water. The same applies to frozen milk that melted.

Rebuttal (Chazon Ish Tevul Yom 4:18): Even R. Shimon Shezuri said only that other liquids become a Sheni l'Tum'ah when they congeal, and are Tahor if they melt, but they become liquids again!

Shulchan Aruch (5): Some hold that roasted meat wet with juice is like (dry) fruit.

Beis Yosef (DH v'Hayah): The Rashba (Chulin 107b DH Ha) says that Rav Hamnuna needed to wash because Rav Huna fed him bread with the roasted meat. He did not say that the meat was wet, for the juice is not a liquid.

Chasam Sofer (OC 158:4): All agree that butter is not a liquid, even if it melted. Once it separated from its source, i.e. milk, it is no longer called milk. If one melted hardened butter in order to add it to food, it is like a liquid that comes into a food. It is like a food, since it was made for a food. Machshrin 6:5 says that whey is Machshir; it does not say that butter is Machshir.