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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 V 0 , whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase u f , particulate phase u p 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 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). 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.

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