The Gemara (חולין קה) quotes Rav Chisda that one who eats meat may not eat dairy afterward. The Gemara writes that Mar Ukva would wait from one meal to the next to separate meat and dairy. The Rishonim give a few reasons for this. Rashi (חולין קה) writes that the reason for this is that the taste of the meat lingers in the mouth for an extended period of time after eating it. Tosafot explains that we are worried that if you have meat and milk in one meal you might come to eat from them together. The Rambam (רמב”ם, הל’ מאכלות אסורות ט:כח) writes that meat can remain in a person’s teeth for the amount of time that is between one meal and the next. After that time the meat is considered to be non-existent.
The halacha is that we are stringent and follow the opinion of Rashi and the Rambam. This means that if a person swallowed meat without chewing it, or chewed meat without swallowing, in either case they would not be allowed to eat dairy immediately after.