Reflux in Crohn's is likely due to intestinal inflammation. There are several likely mechanisms that could be at work and it may be that different ones apply for different people. In my case, since food seems to trigger acid problems, I have to assume that there is some sensitivity to some foods. Food sensitivities are controversial. The problem with them is that they can fade away over a fairly short period of time (weeks to months). They form in the first place because of gut permeability. The gut becomes more permeable from several causes (NSAIDs, alcohol, stress, intestinal infection like Norwalk or food poisoning and any other cause of gut inflammation - like a Crohn's flare). The foods that form sensitivities are usually the ones that you use as a main part of your diet at the time of the permeability increase. That is why wheat gluten (only proteins form antibodies) or even beef have been identified as being a problem. Once a sensitivity has formed, every time thereafter when you eat that food, it will trigger a reaction in the stomach's mast cells (front line immune cells) that causes extra acid to form. It also causes general inflammation which distorts the stomach and the esophageal valve then leaks. This can be fixed by avoiding that food trigger.
Then there is the small intestinal brake effect. Some foods when not properly digested in the stomach are sensed as being undigested and the SI slows peristalsis. The most common food here is fats and oils. With PPI's, some proteins also will slow the SI. This results in SIBO (Small Intestinal Bacteria Overgrowth) and a host of related problems. Here's a link for reference: http://www.practicalgastro.com/pdf/December08/DiBaiseArticle.pdf
The link article mentions low stomach acid (hypo- or achlorhydria) as a cause, but also strictures or low pancreatic enzymes or bile problems can all cause SIBO. All these problems initially slow the passage of food through the SI and result in backing up the digestive process and prevents the stomach from passing its contents into the SI as fast as usual. This results in normal stomach contractions pushing stomach contents back up into the esophagus - acid reflux. Once SIBO is established, diarrhea might result, or constipation could be the result. If it is constipation, the reflux problem would continue.
Once SIBO has happened, the bacteria compete with your gut for the partially digested food. In this situation, starches, sugars and other polysaccherides cause rapid bacterial growth with resulting gas/bloating and pain/sensitivity (and brain fog for me). In my experience, eliminating carbs and sugar while consuming only water - fasting - or predigested foods like clear broth or gelatin will clear the bacterial problem in a day or two. To prevent recurrence, you need to know what caused the problem and adjust your diet or supplements to fix it. The article mentions antibiotics, but there are other problems with using them (the article talks about
that a bit). It also mentions probiotics but it is short on any real information about
that. This is probably due to the complexity of the problem and individual responses.
Sorry for the long ramble - there's a lot to the subject and I have left out some conjectures.