Actually Neil, the exact opposite happens. Blood flow is restricted to all of the digestive organs. The blood flow is directed to the muscles, the skin, the brain and respiratory organs - where it is most needed. The body has no need to be digesting when it enters the 'fight or flight' mode, which is what occurs when it is suddenly confronted by something that it percieves as a threat. As a point of interest: In extreme situations it is known for the body to completley neglect and lose controll over the digestive system. As an example, back in World War II, it was noticed that in the American soldiers that were assaulting the beaches in the Pacific against the Japanese, it would be very common for the soldiers to deficate and urinate uncontrollably. It was concluded that due to the extreme stress of the situation their bodies shut down everything that was not necessary for their survival on the battlefield. The digestive system and subsequent sphincters were such things.