Fluid flow in tubes with elastic walls

Physico-mathematical aspects of fluid flow in elastic thin-walled tubes have been examined and nonlinear equations describing it have been derived and solved. It is shown that an auto-oscillating flow-regime (flutter) can occur and mathematical models of solitons (pulse waves) based on the Korteveg-de Vries equation and on the modified nonlinear Schroedinger equation have been developed. The appropriateness of using the elastic thin-walled tube model for the description of blood flow in major blood vessels is discussed.

PACS: 87.45.-k
DOI: 10.1070/PU1995v038n02ABEH000069
URL: https://ufn.ru/en/articles/1995/2/c/
Web of Science

A1995QR33900003
Citation: Volobuev A N "Fluid flow in tubes with elastic walls" Phys. Usp. 38 169–178 (1995)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Волобуев А Н «Течение жидкости в трубках с эластичными стенками» УФН 165 177–186 (1995); DOI: 10.3367/UFNr.0165.199502c.0177

References (19) ↓ Cited by (14) Similar articles (20)

Pedli T Gidrodinamika Krupnykh Krovenosnykh Sosudov (M.: Mir, 1983); Pedley T J The Fluid Mechanics Of Large Blood Vessels (Cambridge: Cambridge University Press, 1980)
Brankov G Osnovy Biomekhaniki (M.: Mir, 1981)
Karo K, Pedli T, Shroter R, Sid U Mekhanika Krovoobrashcheniya (M.: Mir, 1981); Caro C G et al. The Mechanics Of The Circulation (Oxford: Oxford University Press, 1978)
Laitfut E Yavleniya Perenosa v Zh Ivykh Sistemakh (M.: Mir, 1977); Lightfoot E N Transport Phenomena And Living Systems. Biomedical Aspects Of Mom Entum And Mass Transport (New York: John Wiley, 1973)
Vladimirov Yu A, Roshchupkin D I, Potapenko A Ya, Deev A I Biofizika (M.: Meditsina, 1983) p. 152, 171
Levtov V A, Regirer S A, Shadrina N X Reologiya Krovi (M.: Meditsina, 1982)
Volobuev A N, Pirogov V P, Koshev V I, Petrov E S Biofizika 33 675 (1988)
Budak B M, Samarskii A A, Tikhonov A N Sbornik Zadach Po Matematicheskoi Fizike (M.: Nauka, 1980) p. 161
Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986) p. 36, 55
Shlikhting G Teoriya Pogranichnogo Sloya (M.: Nauka, 1974) p. 227
Ablovits M, Sigur X Solitony, Metod Obratnoi Zadachi (M.: Mir, 1987) p. 316; Ablowitz M J, Segur H Solitons And The Inverse Scattering Transform (Philadelphia, PA: SIAM, 1981)
Levich V G, Vdovin Yu A, Myamlin V A Kurs Teoreticheskoi Fiziki Vol. 2 (M.: Fizmatgiz, 1962) p. 364
Uizem Dzh Lineinye i Nelineinye Volny (M.: Mir, 1977) p. 575; Whitham G B Linear And Nonlinear Waves (New York: John Wiley, 1974)
Kaptsov O V Zh. Eksp. Teor. Fiz. 98 532 (1990); Kaptsov O V Sov. Phys. JETP 71 276 (1990)
Rashmer R Dinamika Serdechno-sosudistoi Sistemy (M.: Meditsina, 1981); Rushmer R F Cardiovascular Dynamics 3rd ed. (Phildelphia, PA: Saunders, 1970)
Folkov V, Nil E Krovoobrashchenie (M.: Meditsina, 1976); Folkow B, Neil E Circulation (New York: Oxford University Press, 1971)
Dzhonson P Perifericheskoe Krovoobrashchenie (M.: Meditsina, 1982); Johnson P C Peripheral Circulation (New York: John Wiley, 1978)
Konradi G P Regulyatsiya Sosudistogo Tonusa (L.: Nauka, 1973) p. 38, 158, 168
Nerem R M et al. "Fluid dynamic aspects of arterial disease" Proc. of Specialists Meeting, Columbus, Ohio, 1974 (1974)