Abstract
In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Shapiro AH, Jaffrin MY, Weinberg SL (1969) J Fluid Mech 37:799
Jaffrin MY (1973) Int J Engng Sce 11:681
Burns JC, Parkes T (1967) J Fluid Mech 29:731
Fung YC, Yih CS (1968) J Appl Mech 35:669
Zien TF, Ostrach S (1970) J Biomechanics 3:63
Ayukawa K, Takabatake S (1982) Bull JSME 25:1061
Brown TD, Hung TK (1977) J Fluid Mech 83:249
Hung TK, Brown TD (1976) J Fluid Mech 73:77
Takabatake S, Ayukawa K (1982) J Fluid Mech 122:439
Takabatake S, Ayukawa K, Mori A (1988) J Fluid Mech 193:267
Tong P, Vawter D (1972) J Appl Mech 39:857
Latham TW (1966) SM Thesis, MIT, Cambridge, MA
Weinberg SL, Eckstein EC, Shapiro AH (1971) J Fluid Mech 49:461
Yin FCP, Fung YC (1971) J Fluid Mech 47:93
Jaffrin MY, Shapiro AH (1971) In: Annual review of fluid mechanics. Annual Review Palo Alto Publications, CA, v3, p13
Rath HJ (1980) Peristaltische Strömungen. Springer, Berlin
Srivastava LM, Srivastava VP (1984) J Biomechanics 17:821
Böhme G, Friedrich R (1983) J Fluid Mech 128:109
Raju KK, Devanathan R (1972) Rheol Acta 11:170
Raju KK, Devanathan R (1974) Rheol Acta 13:944
Shukla JB, Gupta SP (1982) J Biomechanical Eng 104:182
Siddiqui AM, Provost A, Schwarz WH (1991) Rheol Acta 30:249
Coleman BD, Noll W (1960) Arch Ratl Mech Anal 6:355
Joseph DD (1980) Fluid dynamics of viscoelasic fluids. Springer, New York Berlin Heidelberg
Bruce C (1969) Ph D Dissertation Stanford University, Stanford CA
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Siddiqui, A.M., Schwarz, W.H. Peristaltic motion of a third-order fluid in a planar channel. Rheologica Acta 32, 47–56 (1993). https://doi.org/10.1007/BF00396676
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00396676