Shepherd, J. J.; Chiera, C.; Connell, H. J. Perturbation analysis of the helical flow of non-Newtonian fluids with application to a recirculating coaxial cylinder rheometer. (English) Zbl 0805.35099 Math. Comput. Modelling 18, No. 10, 131-140 (1993). Summary: This paper analyzes the flow of non-Newtonian fluids between infinitely long coaxial cylinders, when the inner cylinder rotates with given angular velocity \(\Omega\), and a given axial flow rate, \(Q\), is superimposed on this rotational motion. Such helical flow is of significance in the modelling of the action of a recirculating coaxial cylinder rheometer, where the axial flow is superimposed on the standard cup-and-bob rheometer to allow accurate rheological measurements involving fluids that are settling in nature. Cited in 1 Document MSC: 35Q35 PDEs in connection with fluid mechanics 76U05 General theory of rotating fluids 35R30 Inverse problems for PDEs Keywords:perturbation parameter; Reiner-Rivlin relation; flow of non-Newtonian fluids PDF BibTeX XML Cite \textit{J. J. Shepherd} et al., Math. Comput. Modelling 18, No. 10, 131--140 (1993; Zbl 0805.35099) Full Text: DOI References: [1] Langlois, W.E., Slow visous flows, (1964), MacMillan & Sons New York [2] Coleman, B.D.; Noll, W., Helical flow of general fluids, J. app. phys., 30, 1508-1512, (1959) [3] Dierckes, A.C.; Schowalter, W.R., Helical flow of non-Newtonian polyisobutylene solution, I. & E.C. fundamentals, 5, 263-271, (1966) [4] Bird, R.B.; Armstrong, R.C.; Hassager, O., Dynamics of polymeric liquids, Vol. 1, (1987), John Wiley & Sons [5] Huilgol, R.R., Helical flow of non-Newtonian fluids, Proc. 5^th nat. conf. rheology, 43-46, (1990), Melbourne [6] Bhattacharya, S.N.; Chryss, A.; Connell, H.J.; Shepherd, J.J., Rotational rheometer for multiphase mixtures, Proc. 5^th nat. conf. rheology, 15-18, (1990), Melbourne [7] Huilgol, R.R., Continuum mechanics of viscoelastic liquids, (1975), Hindustan Publ. Corp Delhi, India · Zbl 0353.76003 [8] Shepherd, J.J.; Connell, H.J., On the helical flow of a power law fluid between coaxial cylinders with small radial separation, RMIT math. dept. res. rept. no. 12, (1991) [9] Chiera, C.; Connell, H.J.; Shepherd, J.J., Perturbation analysis of a Herschel-Bulkley model fluid in a rotational rheometer at low axial flow rates, RMIT math. dept. res. rept. no. 9, (1991) [10] Chiera, C.; Connell, H.J.; Shepherd, J.J., Note on a nonlinear equation in helical flow theory, RMIT math. dept. res. rept. no. 3, (1991) · Zbl 1195.76014 [11] Wilkinson, W.L., Non-Newtonian fluids: fluid mechanics, mixing and heat transfer, (1960), Pergamon Press London · Zbl 0124.41802 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.