zbMATH — the first resource for mathematics

Helical flow of a Bingham fluid arising from axial Poiseuille flow between coaxial cylinders. (English) Zbl 07167900
Summary: The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.
76 Fluid mechanics
74 Mechanics of deformable solids
Full Text: DOI
[1] Bingham, E. C., Fluidity and Plasticity (1922), McGraw-Hill: McGraw-Hill New York
[2] Abu-Jdayil, B.; Banat, F.; Jumah, R.; Al-Asheh, S.; Hammad, S., A comparative study of rheological characteristics of tomato paste and tomato powder solutions, Int. J. Food Prop., 7, 3, 483-497 (2004)
[3] Kurdowski, W., Cement and Concrete Chemistry (2014), Springer Science & Business
[4] Fisher, K. A.; Wakeman, R. J.; Chiu, T. W.; Meuric, O. F.J., Numerical modelling of cake formation and fluid loss from non-newtonian muds during drilling using eccentric/concentric drill strings with/without rotation, Chem. Eng. Res. Des., 78, 5, 707-714 (2000)
[5] Bown, D. J.; Middlelberg, A. P.J.; Nguyen, Q. D., A flow rheometer for industrial slurries, Proceedings of the 12th International Conference on Slurry Handling and Pipeline Transport (Hydrotransport 12), 343-352 (1993), Brugge Belgium
[6] Nguyen, Q. D.; Devasagayam, C.; Brown, D. J., Development of an on-line flow rheometer for mineral slurries, Extr. Metall. Rev., 20, 1, 75-91 (2000)
[7] Langlois, W. E., Slow Viscous Flow (1964), The Macmillan Company: The Macmillan Company New York
[8] Coleman, B. D.; Noll, W., Helical flow of general fluids, J. Appl. Phys., 30, 10, 1508-1512 (1959)
[9] Fredrickson, A. G., Helical flow of an annular mass of visco-elastic fluid, Chem. Eng. Sci., 11, 252-259 (1960)
[10] Fredrickson, A.; Bird, R. B., Non-Newtonian flow in annuli, Ind. Eng. Chem., 50, 3, 347-352 (1958)
[11] Liu, Y. Q.; Zhu, K. Q., Axial couette – poiseuille flow of bingham fluids through concentric annuli, J. Non Newton. Fluid Mech., 165, 21, 1494-1504 (2010) · Zbl 1274.76041
[12] Filip, P.; David, J., Axial couette – poiseuille flow of power-law viscoplastic fluids in concentric annuli, J. Pet. Sci. Eng., 40, 3, 111-119 (2003)
[13] Rao, D. K.M., Helical flow of a bingham plastic, J. Indian Inst. Sci., 47, 3, 97-105 (1965)
[14] Bittleston, S. H.; Hassager, O., Flow of viscoplastic fluids in a rotating concentric analysis, J. Non Newton. Fluid Mech., 42, 19-36 (1992) · Zbl 0748.76015
[15] Bhattacharya, S. N.; Chryss, A.; Connell, H. J.; Shepherd, J. J., Rotational rheometer for settling multiphase mixtures, Proceedings of the 5th National Conference on Rheology, 15-18 (1990), Melbourne
[16] Shepherd, J. J.; Chiera, C.; Connell, H., Perturbation analysis of the helical flow of non-Newtonian fluids with application to a recirculating coaxial cylinder rheometer, Math. Comput. Model., 18, 10, 131-140 (1993) · Zbl 0805.35099
[17] Farrugia, M. T.; Shepherd, J. J.; Stacey, A. J., A perturbation analysis of the flow of a Powell-Eyring fluid between coaxial cylinders, ANZIAM J., 52, C257-C270 (2011) · Zbl 1386.76009
[18] Shepherd, J. J.; Stacey, A. J.; Khan, A. A., Helical flow arising from the yielded annular flow of a Bingham fluid, Appl. Math. Model., 38, 5382-5391 (2014)
[19] Alharbi, F. M., Helical Flow of Yield Stress Fluids (2016), RMIT University: RMIT University Melbourne, Australia, Ph.d. thesis
[21] Bird, R. B.; Armstrong, R. C.; Hassager, O., Dynamics of Polymeric Liquids. Volume 1: Fluid Mechanics (1977), A Wiley-Interscience Publication, John Wiley & Sons
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.