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The gallbladder is a sac that stores bile made by the liver in between meals. After a meal, the gallbladder squeezes the bile it has stored into the intestine. In the intestine, the bile mixes with food and fat. Bile is important because it helps with the digestion of fat and its transfer from the intestine into the body.
When the gallbladder is removed, bile made by the liver can no longer be stored between meals. Instead, the bile flows directly into the intestine anytime the liver produces it. Thus, there still is bile in the intestine to mix with food and fat. It is true that there is not as much bile, but there is enough to allow the digestion and transfer of fat. People who have had their gallbladders removed do not need to limit the fat in their diet.
The only clear side effect of removal of the gallbladder is diarrhea. This occurs in about 10% of patients. The diarrhea occurs because of the change in the way bile is delivered to the intestine once the gallbladder has been removed. Bile and the way it is delivered to the intestine appears to control the speed with which food passes through the intestine. Removing the gallbladder speeds up the passage of food and thereby may cause the diarrhea. There may be other reasons why the change in delivery of bile causes diarrhea as well.
PubMedHealth.gov. Fact sheet: Gallstones.