Computational Rheometry of Yielding and Viscoplastic Flow in Vane-and-Cup Rheometer Fixtures
A planar two-dimensional computational analysis is presented to qualify traditional and fractal vane-in-cup geometries for accurate rheometry of simple viscoplastic fluids with and without slip. Numerical simulations based on an adaptive augmented Lagrangian scheme are used to study the two-dimensio...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
08.02.2022
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Subjects | |
Online Access | Get full text |
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Summary: | A planar two-dimensional computational analysis is presented to qualify
traditional and fractal vane-in-cup geometries for accurate rheometry of simple
viscoplastic fluids with and without slip. Numerical simulations based on an
adaptive augmented Lagrangian scheme are used to study the two-dimensional flow
field of yield-stress fluids within and around vane tools with N=3 to 24 arms
for a wide range of Bingham numbers, B (i.e. the ratio of the yield stress over
the characteristic viscous stress). This allows for accurate calculations of
the velocity and stress fields around vanes with various geometries, as well as
direct comparison to experimental observations of the output torque measured by
a rheometer, revealing sources of variation and error. We describe the impact
of the vane structure on the fluid velocity field, from few-arm cruciform vanes
(N < 6) that significantly perturb the flow away from ideal azimuthal
kinematics, to many-arm fractal vanes (N > 12) in which the internal structural
features are successfully ``cloaked" by a yield surface. This results in the
shearing of an almost-circular ring of viscoplastic fluid that is
indistinguishable from the annular ring of fluid deformed around a slip-free
rotating cylindrical bob and leads to more accurate rheometric measurements of
the material flow curve. Moreover, in direct comparison with data from previous
literature, we show that slip conditions on the vane surface do not impact the
velocity field or measured overall torque T, whereas slip conditions on the
smooth outer wall have significant impact on data, even when using a vane
geometry. Finally, we describe the impact of vane topography and Bingham
number, B, on the measured torque and rheometric accuracy of vane-in-cup
geometries for ``simple" (inelastic) yield-stress fluids described by either
the Bingham plastic or Herschel-Bulkley constitutive model. |
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DOI: | 10.48550/arxiv.2202.04255 |