Misra, J. C.; Pandey, S. K. Peristaltic transport of a particle-fluid suspension in a cylindrical tube. (English) Zbl 0811.76100 Comput. Math. Appl. 28, No. 4, 131-145 (1994). The flow of an incompressible Newtonian viscous fluid containing a suspension of small particles along a long circular cylindrical tube of uniform cross-section is considered. Peristaltic motion is modelled by assuming that the tube wall is subjected to a sinusoidal wave. By assuming that the wave amplitude is small compared with the tube radius, a perturbation method is developed to obtain a set of ordinary differential equations. For pumping of initially stationary fluid the equations simplify, and the solution is shown to depend on Bessel functions. The Bessel functions are represented by polynomials to obtain a solution. Numerical results are presented in graphical form for flow in the ureter. It is claimed that reverse flow may occur at the boundary in contrast to the two-dimensional case. Reviewer: G.Eason (Glasgow) Cited in 10 Documents MSC: 76Z05 Physiological flows 92C35 Physiological flow 76T99 Multiphase and multicomponent flows Keywords:incompressible Newtonian viscous fluid; sinusoidal wave; perturbation method; ordinary differential equations; Bessel functions; polynomials; flow in the ureter; reverse flow PDFBibTeX XMLCite \textit{J. C. Misra} and \textit{S. K. Pandey}, Comput. Math. Appl. 28, No. 4, 131--145 (1994; Zbl 0811.76100) Full Text: DOI References: [1] Hung, T. K.; Brown, T. D., Solid-particle motion in two-dimensional peristaltic flows, J. Fluid Mech., 73, 77-96 (1976) [2] Srivastava, L. M.; Srivastava, V. P., Peristaltic transport of a particle-fluid suspension, J. Biomech. Engg., 111, 157-165 (1989) [3] Drew, D. A., Stability of a Stokes layer of a dusty gas, Phys. Fluids, 22, 2081-2084 (1979) · Zbl 0434.76062 [4] Tam, C. K.W., The drag on a cloud of spherical particles in low Reynolds number flow, J. Fluid Mech., 38, 537-546 (1969) · Zbl 0184.52701 [5] Charm, S. E.; Kurland, G. S., Blood Flow and Micro-Circulation (1974), John Wiley: John Wiley New York [6] Yin, F.; Fung, Y. C., Peristaltic waves in a circular cylindrical tube, J. Applied Mech., 36, 93-112 (1969) [7] Orkins, L. A., Trauma in the Ureter: Pathogenesis and Management (1964), F.A. Davis Co: F.A. Davis Co Philadelphia, PA [8] Bergeman, H., The Ureter (1967), Harper & Row: Harper & Row New York [9] Boyarsky, S., Neurogenic Bladder (1967), Williams and Wilkins Co: Williams and Wilkins Co Baltimore [10] Griffiths, D. J., Flow of urine through the ureter: A collapsible, muscular tube undergoing peristalsis, J. Biomech. Engg., 111, 206-211 (1989) [11] Weinberg, S. R., Physiology of the Ureter, (Bergeman, H., The Ureter (1967), Harper & Row), 48-66 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.