Abstract
The method of domain perturbation developed by Joseph is used to calculate velocity and stress profiles in a slightly misaligned cone-and-plate rheometer where the cone is spinning and the plate is stationary. Results for a Newtonian fluid, a Criminale-Ericksen-Filbey fluid, an upper-convected Maxwell fluid, and a White-Metzner fluid are presented and compared with earlier results in which the cone is stationary and the plate is spinning (Dudgeon and Wedgewood, 1993). Streamlines calculated for the Newtonian fluid show a very small recirculation region near the stationary plate. Velocity and stress contours are symmetric around the plane of largest gap width. For the elastic fluids studied, streamlines are asymmetric. The fluid response lags where the fluid is dominated by memory effects. Much larger recirculation regions are calculated for fluids dominated by shear thinning. These recirculation regions contain a large fraction of the fluid in the apparatus and have the effect of changing the shape of the flow domain for the remaining fluid that rotates around the cone's axis. Elasticity also has a pronounced effect on the stress profile, indicating that the accuracy of the cone and plate may be compromised even for small mis-alignments.
Similar content being viewed by others
References
Adams N, Lodge AS (1964) Rheological properties of concentrated polymer solutions: II. A cone-and-plate and parallel-plate pressure distribution apparatus for determining normal stress differences in steady shear flow. Phil Trans Roy Soc A256:149–184
Ascher U, Christiansen J, Russell RD (1981) Collocation software for boundary-value ODES. ACM Trans Math Softw 7(2):209–222
Beris A, Armstrong RC, Brown RA (1983) Perturbation theory for viscoelastic fluids between eccentric rotating cylinders. J Non-Newtonian Fluid Mech 13:109–148
Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, Volume 1, Fluid Mechanics, 2nd edn. Wiley, New York
Cheng DCH, Davis JB (1966) Report LR42(CE). Warren Spring Laboratory, Stevenage, Herts, UK, cited by Walters (1975)
Dudgeon DJ, Wedgewood LE (1993) Flow in the misaligned cone-and-plate rheometer. J Non-Newtonian Fluid Mech 48:21–48, as corrected in J Non-Newtonian Fluid Mech 52:99–100 (1994)
Hindmarsh AC (1983) ODEPACK: A systematized collection of ODE solvers, in Scientific Computing. Stepleman RS et al. (eds.), North-Holland, Amsterdam, pp 55–64
Joseph DD (1973) Domain perturbations: The higher order theory of infinitesimal water waves. Arch Rat Mech Anal 51:295–303
Joseph DD, Beavers GS (1977) Free surface problems in rheological fluid mechanics. Rheol Acta 16:169–189
Joseph DD, Sturges L (1975) The free surface on a liquid filling a trench heated from its side. J Fluid Mech 69:565–589
Tanner RI, Pipkin AC (1969) Intrinsic errors in pressure-hole measurements. Trans Soc Rheol 13:471–484
Walters K (1975) Rheometry. Chapman & Hall, London
Wannier GH (1950) A contribution to the hydrodynamics of lubrication. Quart Appl Math 8:1–32
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dudgeon, D.J., Wedgewood, L.E. A domain perturbation study of steady flow in a cone-and-plate rheometer of non-ideal geometry. Rheol Acta 33, 369–384 (1994). https://doi.org/10.1007/BF00366580
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00366580