Casually known as "Steakhouse Syndrome" and more formally Eosinophilic Esophagitis EoEthere can be damage to the esophagus in the form of scaring or narrowing.
This can cause food to become lodged on the way to the stomach. Often, drinking water can help the food to pass through but other times the water just sits on top of the obstruction.
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Soda is sometimes attempted with the idea that the acid in the drink will dissolve the food enough to let it pass. A mild sedative can also help by relaxing the muscles around the esophagus.
These techniques worked in a severe case I had. Afterward, I had another procedure in which a long rubber cone is used to expand the esophagus a bit which seemed to help me.]