Abstract
The problem of blood flow induced by peristaltic waves in a uniform small diameter tube has been investigated. Blood has been represented by a two-fluid model consisting of a core region of suspension of all the erythrocytes, assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. The expressions for dimensionless pressure drop and friction force have been obtained. The results obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories both analytically and numerically.
Similar content being viewed by others
References
Bertuzzi A, Salinari P, Mancinelli R, Pescatori M (1983) Peristaltic transport of a solid bolus. J Biomech 16:459–464
Böhme G, Friedrich R (1983) Peristaltic flow of viscoelastic liquids. J Fluid Mech 128:109–122
Brasseur JG, Corrsin S, Lu NQ (1987) The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. J Fluid Mech 174:495–519
Bugliarello G, Kapur C, Hsiao G (1965) The profile viscosity and other characteristics of blood flow in a non-uniform shear field. Proc IVth Int Cong on Rheol 4, Symp of Biorheol (Ed. Copley AL), pp 351–370, Interscience, New York
Bugliarello G, Sevilla J (1970) Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes. Biorheol 7:85–107
Charm SE, Kurland GS (1974) Blood flow and microcirculation. John Wiley, New York
Chien S, Usami S, Taylor HM, Lundberg JL, Gregerson MT (1965) Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. J Appl Physiol 21:81–87
Cokelet GR (1972) The rheology of human blood: biomechanics (Ed. Fung YC). Prentice Hall Publ., Englewood Cliffs, NJ
Friedrich R (1983) Peristaltic flow of viscoelastic fluids. ZAMM 63:T249-T252
Latham TW (1966) Fluid motion in peristaltic pump. MS Thesis, MIT, Cambridge, Mass
Li M, Brasseur JG (1993) Non-steady peristaltic transport in finite length tubes. J Fluid Mech 248:129–151
Longuet-Higgins MS (1983) Peristaltic pumping in water waves. J Fluid Mech 137:199–215
Merrill FW, Benis AM, Gilliland ER, Sherwood TK, Salzman EW (1965) Pressure-flow relations of human blood in hollow fibers at low flow rates. J Appl Physiol 20:954–967
Ohlson L (1989) Morphological dynamics of ureteral transport: 2. Peristaltic patterns in relation to flow rate. Am J Physiol 256:R29-R34
Pozrikidis C (1987) A study of peristaltic flow. J Fluid Mech 180:515–527
Rand PW, Lacombe E, Hunt HE, Austin WH (1964) Viscosity of normal blood under normothermic and hypothermic conditions. J Appl Physiol 19:117–122
Rath HJ (1980) Peristaltic Strömungen. Springer-Verlag, Berlin Heidelberg New York
Samy RP (1986) Peristaltic flow of generalized viscoplastic fluids in tubes with varying cross-sections and its applications. Biorheol 23:223 (Abstract)
Shapiro AH, Jaffrin MY, Wienberg SL (1969) Peristaltic pumping with long wavelength at low Reynolds number. J Fluid Mech 37:799–825
Shen MC, Ebell D (1987) Asymptotic method for peristaltic transport of a heat conducting fluid. J Math Anal Appl 127:49–71
Shukla JB, Chandra P, Sharma R, Radhakrishnamacharya G (1988) Effects of peristaltic and longitudinal wave motion of the channel wall on the movement of micro-organisms: application to spermatozoa transport. J Biomech 21:947–954
Shukla JB, Parihar RS, Rao BRP (1980a) Effects of stenosis on non-Newtonian flow of blood in an artery. Bull Math Biol 42:283–294
Shukla JB, Parihar RS, Rao BRP, Gupta SP (1980b) Effects of peripheral layer viscosity on peristaltic transport of a bio-fluid. J Fluid Mech 97:225–237
Srivastava LM (1986) Peristaltic transport of a couple stress fluid. Rheol Acta 25:638–641
Srivastava LM, Srivastava VP (1985a) Peristaltic transport of a non-Newtonian fluid: applications to vas deferens and small intestine. Annals Biomed Engng 13:137–153
Srivastava LM, Srivastava VP (1985b) Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube. J Biomech 18:247–253
Srivastava LM, Srivastava VP (1988) Peristaltic transport of a power-law fluid: application to the ductus efferentes of the reproductive tracts. Rheol Acta 27:428–433
Srivastava LM, Srivastava VP (1989) Peristaltic transport of a particle-fluid suspension. Trans ASME J Biomech Engng 111:157–165
Srivastava LM, Srivastava VP, Sinha SN (1983) Peristaltic transport of a physiological fluid, part I: non-uniform geometry. Biorheol 20:153–166
Srivastava VP, Saxena M (1994) Two-layered model of Casson fluid flow through stenotic vessels: applications to cardiovascular system. J Biomech 28 (in press)
Takabatake S, Ayukawa K, Mori A (1988) Peristaltic pumping in circular cylindrical tubes. A numerical study of fluid transport and its efficiency. J Fluid Mech 193:267–283
Tang D, Shen MC (1989) Peristaltic transport of a heat conducting fluid subject to Newtonian cooling law at the boundary. Int J Engng Sci 27:809–825
Thomas HW, French RJ, Groom AC, Rowlands S (1965) The flow of red cell's suspensions through narrow tubes. The (extra corporeal) determination of the difference in mean velocities of red cells and their suspension phase. Proc IVth Int Cong on Rheol 4, Symposium on Biorheol (Ed. Copley AL), pp 381–391, Interscience, New York
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Srivastava, V.P., Saxena, M. A two-fluid model of non-Newtonian blood flow induced by peristaltic waves. Rheol Acta 34, 406–414 (1995). https://doi.org/10.1007/BF00367155
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00367155