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Flow between eccentric cylinders: a shear-extensional controllable flow

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Abstract

In this work the non-Newtonian fluid between eccentric cylinders is simulated with finite element method. The flow in the annular gap between the eccentric rotating cylinders was found to be a shear-extensional controllable flow. The influence of rotating speed, eccentricity as well as the radius ratio on the extensional flow in the vicinity of the minimum gap between the inner and outer cylinder was quantitatively investigated. It was found that both the strengths of shear flow and extensional flow could be adjusted by changing the rotating speed. In respect to extensional flow, it was also observed that the eccentricity and radius ratio exert significant influences on the ratio of extensional flow. And it should be noted that the ratio of extensional flow in the mix flow could be increased when increasing the eccentricity and the ratio of shear flow in the mix flow could be increased when increasing the radius ratio.

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References

  • Ballal, B.Y. and R.S. Rivlin, 1962, Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects, Arch. Ration. Mech. An. 62, 237–294.

    Google Scholar 

  • Ballal, B.Y. and R.S. Rivlin, 1975, Flow of a viscoelastic fluid between eccentric cylinders. I. Rectilinear shearing flow, Rheol. Acta. 14, 484–492.

    Article  Google Scholar 

  • Boonen, E., P. Van Puyvelde, and P. Moldenaers, 2009, Droplet dynamics in sub-critical complex flows, Rheol. Acta. 48, 359–371.

    Article  Google Scholar 

  • Boonen, E., P. Van Puyvelde, and P. Moldenaers, 2010, Droplet dynamics in mixed flow conditions: Effect of shear/elongation balance and viscosity ratio, J. Rheo. 54, 1285–1306.

    Article  Google Scholar 

  • Bouquey, M., C. Loux, R. Muller, and G. Bouchet, 2011, Morphological study of two-phase polymer blends during compounding in a novel compounder on the basis of elongational flows, J. Appl. Polym. Sci. 119, 482–490.

    Article  Google Scholar 

  • Cogswell, F.N., 1972a, Converging flow of polymer melts in extrusion dies, Polym. Eng. Sci. 12, 64–73.

    Article  Google Scholar 

  • Cogswell, F.N., 1972b, Measuring the extensional rheology of polymer melts, Trans. Soc. Rheol. 16, 383–403.

    Article  Google Scholar 

  • Domurath, J., M. Saphiannikova, F. Julien, G. Ausias, and G. Heinrich, 2015, Stress and strain amplification in a dilute suspension of spherical particles based on a Bird–Carreau model, J. Non-Newton. Fluid Mech. 221, 95–102.

    Article  Google Scholar 

  • Dris, I.M. and E.S.G. Shaqfeh, 1996, On purely elsatic instabilities in eccentric cylinder flows, J. Non-Newton. Fluid Mech. 56, 349–360.

    Article  Google Scholar 

  • Dris, I.M. and E.S.G. Shaqfeh, 1998a, Experimental and theoretical observations of elastic instabilities in eccentric cylinder flows: local versus global instability, J. Non-Newton. Fluid Mech. 80, 1–58.

    Article  Google Scholar 

  • Dris, I.M. and E.S.G. Shaqfeh, 1998b, Flow of a viscoelastic fluid between eccentric cylinders: impact on flow stability, J. Non-Newton. Fluid Mech. 80, 59–87.

    Article  Google Scholar 

  • Feigl, K., S.F.M. Kaufmann, P. Fischer, and E.J. Windhab, 2003, A numerical procedure for calculating droplet deformation in dispersing flows and experimental verification, Chem. Eng. Sci. 58, 2351–2363.

    Article  Google Scholar 

  • Grecov, D.R. and J.R. Clermont, 2002, Numerical study of flows of complex fluids between eccentric cylinders using transformation functions, Int. J. Numer. Meth. Fluids 40, 669–695.

    Article  Google Scholar 

  • Grecov, D. and J.R. Clermont, 2005, Numerical simulations of non-Newtonian flows between eccentric cylinders by domain decomposition and stream-tube method, J. Non-Newton. Fluid Mech. 126, 175–185.

    Article  Google Scholar 

  • Grecov, D. and J.R. Clermont, 2008, Numerical simulations of non-stationary flows of non-Newtonian fluids between concentric and eccentric cylinders by stream-tube method and domain decomposition, Rheol. Acta. 47, 609–620.

    Article  Google Scholar 

  • Hosseinalipour, S.M., A. Tohidi, M. Shokrpour, and N.M. Nouri, 2013, Introduction of a chaotic dough mixer, part A: mathematical modeling and numerical simulation, J. Mech. Sci. Technol. 27, 1329–1339.

    Article  Google Scholar 

  • Ibarra-Gómez, R., R. Muller, M. Bouquey, J. Rondin, C.A. Serra, F. Hassouna, Y.E. Mouedden, V. Toniazzo, and D. Ruch, 2015, Processing of nanocomposites PLA/graphite using a novel elongational mixing device, Polym. Eng. Sci. 55, 214–222.

    Article  Google Scholar 

  • Jia, S.K., J.P. Qu, W.F. Liu, C.G. Wu, R.Y. Chen, S.F. Zhai, and Z. Huang, 2014, Thermoplastic polyurethane/polypropylene blends based on novel vane extruder: A study of morphology and mechanical properties, Polym. Eng. Sci. 54, 716–724.

    Article  Google Scholar 

  • Larson, R.G., E.S.G. Shaqfeh, and S.J. Muller, 1990, A purely elastic instability in Taylor–Couette flow, J. Fluid Mech. 218, 573–600.

    Article  Google Scholar 

  • Li, X.K., 2014, Non-Newtonian lubrication with the Phan-Thien–Tanner model, J. Eng. Math. 87, 1–17.

    Article  Google Scholar 

  • Qu, J.P., H.Z. Chen, S.R. Liu, B. Tan, L.M. Liu, X.C. Yin, Q.J. Liu, and R.B. Guo, 2013, Morphology study of immiscible polymer blends in a vane extruder, J. Appl. Polym. Sci. 128, 3576–3585.

    Article  Google Scholar 

  • Qu, J.P., G.Z. Zhang, H.Z. Chen, X.C. Yin, and H.Z. He, 2012a, Solid conveying in vane extruder for polymer processing: Effects on pressure establishment, Polym. Eng. Sci. 52, 2147–2156.

    Article  Google Scholar 

  • Qu, J.P., X.Q. Zhao, J.B. Li, and S.Q. Cai, 2012b, Power consumption in the compacting process of polymer particulate solids in a vane extruder, J. Appl. Polym. Sci. 127, 3923–3932.

    Article  Google Scholar 

  • Rajagopalan, D., J.A. Byars, R.C. Armstrong, R.A. Brown, J.S. Lee, and G.G. Fuller, 1992, Comparison of numerical simulations and birefringence measurements in viscoelastic flow between eccentric rotating cylinders, J. Rheol. 36, 1349–1375.

    Article  Google Scholar 

  • Rauwendaal, C., T. Osswald, P. Gramann, and B. Davis, 1999, Design of dispersive mixing devices, Int. Polym. Proc. 14, 28–34.

    Article  Google Scholar 

  • Rondin, J., M. Bouquey, R. Muller, C.A. Serra, G. Martin, and P. Sonntag, 2014, Dispersive mixing efficiency of an elongational flow mixer on PP/EPDM blends: Morphological analysis and correlation with viscoelastic properties, Polym. Eng. Sci. 54, 1444–1457.

    Article  Google Scholar 

  • Wei, X., J.R. Collier, and S. Petrovan, 2007, Shear and elongational rheology of polyethylenes with different molecular characteristics. II. Elongational rheology, J. Appl. Polym. Sci. 104, 1184–1194.

    Article  Google Scholar 

  • Yanovsky, Y.G., 2009, Polymer Rheology: Theory and Practice, Springer, London.

    Google Scholar 

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Correspondence to Gang Jin.

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Tian, G., Wang, M., Wang, X. et al. Flow between eccentric cylinders: a shear-extensional controllable flow. Korea-Aust. Rheol. J. 28, 139–148 (2016). https://doi.org/10.1007/s13367-016-0013-8

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  • DOI: https://doi.org/10.1007/s13367-016-0013-8

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