Abstract
Results are given of the numerical solution of the equations which describe in the quasione-dimensional approximation the motion of a fluid in a pipe made of a viscoelastic material with a nonmonotonic S-shaped static characteristic curve. Some possible ways are considered for obtaining simpler models with lumped parameters for such flows. There is a discussion of the application of the theory to the problem of the tone of blood vessels.
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The Physiology of Man and Animals, Vol. 23: The Regulation of Vascular Tone [in Russian], VINITI, Moscow (1979).
E. Basar and C. Weiss, Vasculature and Circulation, Elsevier, Amsterdam (1981).
S. A. Regirer, I. M. Rutkevich, and P. I. Usik, “A model of vascular tone,” Mech. Polim., No. 4, 585 (1975).
S. A. Regirer and I. M. Rutkevich, “Wave motions of a fluid in pipes made of viscoelastic material. Waves of small amplitude,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 45 (1975).
I. M. Rutkevich, “Wave motions of a fluid in pipes made of a viscoelastic material. Steady nonlinear waves,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 86 (1975).
S. A. Regirer, “Mechanical aspects of the local regulation of blood circulation,” in: The Regulation of Blood Circulation in Skeletal Muscles [in Russian], Zinatne, Riga (1980), pp. 113–117.
M. E. Burrows and P. C. Johnson, “Diameter, wall tension and flow in mesenteric arterioles during autoregulation,” Am. J. Physiol.,241, H829 (1981).
I. M. Skobeleva, “A model of vascular tone (numerical experiment),” Mekh. Kompozitnykh Materialov, No. 1, 107 (1980).
E. E. Kireeva and B. N. Klochkov, “A nonlinear model of vascular tone,” Mekh. Kompozitnykh Materialov, No. 5, 887 (1982).
B. N. Klochkov, “Automatic wave processes in blood vessels of the muscular type,” in: Autowave Processes in Systems with Diffusion [in Russian], Gor'kii (1981), pp. 233–242.
E. E. Kireeva, B. N. Klochkov, A. M. Reiman, L. A. Rozenblyum, and Yu. A. Stepanyants, “The possibility of autowave motions in small blood vessels with an active muscular wall,” in: Abstracts of Stand Communications at the First All-Union Biophysical Congress, Vol. 2 [in Russian], Moscow (1982), p. 159.
B. N. Klochkov, A. M. Reiman, and Yu. A. Stepanyants, “The mathematical simulation of wave phenomena in arterioles,” in: Abstracts of Papers at the Third All-Union Conference on Problems in Biomechanics, Vol. 1 [in Russian], Riga (1983), pp. 220–222.
E. E. Kireeva, S. A. Regirer, B. N. Klochkov, A. M. Reiman, and Yu. A. Stepanyants, Studies in Biomechanics. The Mechanics of Muscle Tissue: Flow in Active Pipes, No. 2818 [in Russian], Otchet Inst. Mekhaniki, Moscow State University (1983).
V. A. Vasil'ev, Yu. M. Romanovskii, and V. G. Yakhno, “Autowave processes in distributed kinetic systems,” Usp. Fiz. Nauk,128, 625 (1979).
E. E. Kireeva and S. A. Regirer, “Wave motions of a fluid in pipes made of viscoelastic material. Forced oscillations,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 94 (1984).
P. C. Johnson and M. Intaglietta, “Contributions of pressure and flow sensitivity to autoregulation in mesenteric arterioles,” Am. J. Physiol.,231, 1686 (1976).
V. M. Paskonov, “A standard program for the solution of boundary layer problems,” in: Numerical Methods in Gas Dynamics, No. 2 [in Russian], Izd. Moscow State University (1963), pp. 110–116.
I. M. Skobeleva, “Possible regimes of flow in a Newtonian fluid in pipes made of active material,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 88 (1985).
G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, New York (1977).
R. S. Sonina and V. M. Khayutin, “The behavior of microscopic arterial vessels in the submaxillary muscle of a frog during its contraction,” in: The Current Problems of Breakdowns in Haemodynamics and the Regulation of Microcirculation in Clinical Practice and Experiment [in Russian], Moscow (1984), pp. 197–198.
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 94–102, May–June, 1985.
In the present study account has been taken of remarks and suggestions by S. A. Regirer made in the course of discussion of the results and the manuscript.
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Klochkov, B.N., Reiman, A.M. & Stepanyants, Y.A. Unsteady flows in a fluid in pipes made of viscoelastic active material. Fluid Dyn 20, 416–423 (1985). https://doi.org/10.1007/BF01049995
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DOI: https://doi.org/10.1007/BF01049995