Peristaltic transport of a newtonian fluid through a uniform and non-uniform annulus

الملخص EN

The problem of peristaltic transport of a viscous incompressible fluid through a uniform and non-uniform annulus has been investigated under zero Reynolds number condition with the long wavelength approximation.

The inner tube is uniform, rigid, and moving with a constant velocity V 0 , while the outer non-uniform tube has a sinusoidal wave traveling down its wall.

This analysis can model the gastric juice motion in the small intestine when an endoscope is inserted through it.

Expressions for the axial velocity and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ϕ , the velocity constant V 0 and the radius ratio ε , (the ratio between the radius of the inner tube and the radius of the outer one at the inlet).

Furthermore ،the pressure rise and friction force on the inner and the outer tubes have been computed numerically and the pumping regions (peristaltic, augmented, and retrograde) have been discussed.

The results show that the pressure rise for the endoscope increases as the radius ratio increases and also as the inner tube moves in the direction of the peristaltic wave.

The pressure rise, in case of non-uniform geometry, is found to be much smaller than the corresponding value for uniform geometry.