Mathematical Modeling of Peristaltic Flow of Chyme in Small Intestine

Mathematical models based on axisymmetric Newtonian incompressible fluid flow are studied for the peristaltic flow of chyme in the small intestines, which is an axisymmetric cylindrical tube. The flow is modeled more realistically modeled by assuming that the peristaltic rush wave is a non-periodic mode composed of two sinusoidal waves of different wavelengths, which propagate at the same speed along the outer boundary of the tube. Both cases of flow in a tube and in an annulus that are modeled and investigated in the present paper correspond respectively to the cases of flow of chyme in the small intestine in the absence and presence of a cylindrical endoscope. For the realistic values of the parameters for these two flow cases, we determine the expressions for the leading order pressure drop, the pressure, the axial velocity, and the frictional forces at the boundaries, and evaluated the roles played by these quantities in the investigated flow systems. The presence of the two-wave peristaltic mode was found to facilitate lower positive (adverse) pressure gradient and less magnitude of the forces by the boundaries on the flow of chyme