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Math Biosci. 2017 Jan;283:91-105. doi: 10.1016/j.mbs.2016.11.012. Epub 2016 Nov 16.

Particulate suspension effect on peristaltically induced unsteady pulsatile flow in a narrow artery: Blood flow model.

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Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA; Basic Science Department, Faculty of Engineering, The British University in Egypt, Al-Shorouk City, Cairo 11837, Egypt. Electronic address:
Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA.


This work is concerned with theoretically investigating the pulsatile flow of a fluid with suspended particles in a flow driven by peristaltic waves that deform the wall of a small blood artery in the shape of traveling sinusoidal waves with constant velocity. The problem formulation in the wave frame of reference is presented and the governing equations are developed up to the second-order in terms of the asymptotic expansion of Womersley number which characterizes the unsteady effect in the wave frame. We suppose that the flow rate imposed, in this frame, is a function versus time. The analytical solution of the problem is achieved using the long wavelength approximation where Reynolds number is considered small with reference to the blood flow in the circulatory system. The present study inspects novelties brought about into the classic peristaltic mechanism by the inclusion of Womersley number, and the critical values of concentration and occlusion on the flow characteristics in a small artery with flexible walls. Momentum and mass equations for the fluid and particle phases are solved by means of a perturbation analysis in which the occlusion is a small parameter. Closed form solutions are obtained for the fluid/particle velocity distributions, stream function, pressure rise, friction force, wall shear stress, instantaneous mechanical efficiency, and time-averaged mechanical efficiency. The physical explanation of the Segré-Silberberg effect is introduced and the trapping phenomenon of plasma for haemodilution and haemoconcentration cases is discussed. It has been deduced that the width of the closed plasma streamlines is increased while their number is minimally reduced in case of haemoconcentration. This mathematical problem has numerous applications in various branches in science including blood flow in small blood vessels. Several results of other models can be deduced as limiting cases of our situation.


Mechanical efficiency; Peristaltic flow; Pulsatile flow; Trapping; Two-phase flow; Wall shear stress

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