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Applied Bionics and Biomechanics
Volume 5 (2008), Issue 2, Pages 47-57

Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non-Uniform Annulus

K. S. Mekheimer1 and Y. Abd Elmaboud2

1Mathematics Department, Al-Azhar University, Nasr City, Cairo, Egypt
2Mathematics Department, Al-Azhar University (Assiut Branch), Assiut, Egypt

Received 27 July 2008

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ɸ, particle concentration C, the velocity constant V0 and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes.