General Weissenberg effect in free surface rheometry part I: analytical considerations

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Abstract

The steady free surface motion of a layered medium of viscoelastic fluids driven by a vertical rotating rod and the free surface motion of a viscoelastic fluid between vertical, eccentric, rotating cylinders is solved by means of domain perturbations. The flow field, the shape of the free surfaces and the interface and the climb at the rod are determined by expanding the stress in a series of Rivlin-Ericksen tensors and developing the theory as a perturbation of the rest state in powers of the angular frequency Ω of the rod or of the cylinders. It is shown that rheometrical measurements in the rotating rod geometry are reliably reproducible whilst concentric cylinder geometry presents important practical problems in measuring rheological constants. © 1984 Birkhäuser Verlag Basel.
Original languageEnglish
Pages (from-to)545-558
Number of pages14
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume35
Issue number4
DOIs
Publication statusPublished - 1984

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Free Surface
Rotating
rods
Viscoelastic Fluid
Vertical
Domain Perturbation
Layered Media
Fluids
Geometry
Motion
Concentric
concentric cylinders
perturbation
rotating cylinders
Flow Field
Tensors
fluids
Flow fields
eccentrics
Tensor

Cite this

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abstract = "The steady free surface motion of a layered medium of viscoelastic fluids driven by a vertical rotating rod and the free surface motion of a viscoelastic fluid between vertical, eccentric, rotating cylinders is solved by means of domain perturbations. The flow field, the shape of the free surfaces and the interface and the climb at the rod are determined by expanding the stress in a series of Rivlin-Ericksen tensors and developing the theory as a perturbation of the rest state in powers of the angular frequency Ω of the rod or of the cylinders. It is shown that rheometrical measurements in the rotating rod geometry are reliably reproducible whilst concentric cylinder geometry presents important practical problems in measuring rheological constants. {\circledC} 1984 Birkh{\"a}user Verlag Basel.",
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AB - The steady free surface motion of a layered medium of viscoelastic fluids driven by a vertical rotating rod and the free surface motion of a viscoelastic fluid between vertical, eccentric, rotating cylinders is solved by means of domain perturbations. The flow field, the shape of the free surfaces and the interface and the climb at the rod are determined by expanding the stress in a series of Rivlin-Ericksen tensors and developing the theory as a perturbation of the rest state in powers of the angular frequency Ω of the rod or of the cylinders. It is shown that rheometrical measurements in the rotating rod geometry are reliably reproducible whilst concentric cylinder geometry presents important practical problems in measuring rheological constants. © 1984 Birkhäuser Verlag Basel.

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