Sleeping positions on the right or left might have an influence on digestion if the digestive problems are related to gastroesophageal reflux per research mentioned below.
Per Katz LC et.al.'s research in 1994 into whether there is a difference in the amount of gastroesophageal reflux when lying with the right versus the left side down, 'the direct comparison of the two positions demonstrated that the total amount of reflux time was significantly greater with subjects in the right decubitus position than in the left'.
Per Khoury RM et.al.'s research in 1999 into influence of spontaneous sleep positions on nighttime recumbent reflux in patients with gastroesophageal reflux disease, the conclusions were 'the left lateral decubitus position is preferred in patients with nocturnal GER'.
Several studies have shown that gastroesophageal reflux is increased in patients in the right lateral decubitus position along with the risk factors of exposure to tobacco, alcohol, chocolate, and high-fat meals influencing reflux.
The reason for this phenomenon is not completely clear, but it may be related to increased transient LES relaxations in the right position, or possibly that the gastroesophageal junction lies above the level of gastric acid in the left lateral position. Specifically, total reflux time, average acid clearance, and LES relaxations are significantly prolonged in patients lying on their right side compared with the left lateral decubitus position.