Abstract
A viscous flow in a long pipe of a circular cross-section, driven by a time-dependent pressure drop at the ends of the pipe and the deformation of the pipe walls, is investigated. This kind of a flow is relevant to the peristaltic transport of blood, with the effect of the oscillating pressure gradient due to the heart pumping included. An explicit solution is obtained within the framework of lubrication theory approximation, and some numerical simulations to illustrate the model are carried out. In order to account for inertia effects, an approximation based on an a priori parabolic flow pattern across the pipe, is also derived.
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References
Rath, H.J. (1980). Peristaltische Stromungen, Springer-Verlag, Berlin.
Provost, A.M. and Schwartz, W.H. (1994). A theoretical study of viscous effects in peristaltic pumping, J. Fluid Mech., 279: 177–195.
Pozrikidis, C. (1987). A study of peristaltic flow, J. Fluid Mech., 180: 515–527.
Takabatake, S., Ayukawa, K. and Mori, A. (1988). Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech., 193: 267–283.
Brasseur, J. G. Corrsin, S. and Lu, N.Q (1987). The influence of peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. J. Fluid Mech., 174: 495–519.
Bohme, G. and Friedrich, R. (1983). Peristaltic flow of vicoelastic liquids. J. Fluid Mech., 128: 109–122.
Shapiro, A.H., Jaffrin, M.Y. and Weinberg, S.L. (1969). Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech., 37: 799–825.
Brown, T.D. and Hung, T.K. (1977). Computational and experimental investigations of two-dimensional nonlinear peristaltic flows. J. Fluid Mech., 83:249-272.
Chow, T.S. (1970). Peristaltic transport in a circular cylindrical pipe. Trans. ASMEJ: J.Appl Mech., 37: 901–905.
Fung, Y.C. and Yih, C.S. (1968). Peristaltic transport. Trans. ASMEJ: J. Appl. Mech., 35: 669–675.
Shukla, J.B. and Gupta, S.P. (1982). Peristaltic transport of a power-law fluid with variable consistency. Trans. ASME K: J. Biomech. Engng., 104: 182–186.
Jaffrin, M.Y. and Shapiro, A.H. (1971). Peristaltic pumping. Ann. Rev. Fluid Mech., 3: 13–36.
Awon, M. P. Review of the literature with formulation of a theory for regulation of blood supply. (Private communication).
Kapitsa, P. L. (1948). Wave flow of thin layers of viscous liquid. Zh. Eksper. Teoret. Fiz., 18(1): 3–28.
Levich, V.G. (1967). Physico-Chemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ
Demekhin, E.A. and Shkadov, V. Ya. (1984). On three-dimensional unsteady waves in a moving liquid film. Izv. AN Nauk SSSR Ser. Mekh. Zhidk. Gaza, 5:21–27.
Antanovskii, L.K. (1987). Generalized equations for a flow in a film on a plane wall. Dinamika Sploshnoi Sredy, 81: 37–42. [In Russian].
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Ramkissoon, H., Antanovskii, L.K. (1998). Peristaltic Transport in a Finite Circular Pipe. In: Ramkissoon, H. (eds) IUTAM Symposium on Lubricated Transport of Viscous Materials. Fluid Mechanics and its Applications, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5248-8_9
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DOI: https://doi.org/10.1007/978-94-011-5248-8_9
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