The run-off condition for the non-Newtonian rimming flow

Sergei Fomin, John Watterson, Eileen Harkin-Jones, S. Raghunathan

Research output: Contribution to journalConference article

Abstract

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. The Weissenberg number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The Theological models, which show Newtonian behaviour at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit the Newtonian behaviour near the free surface and power-law behaviour near the wall of the rotating cylinder.

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Non Newtonian flow
Shear deformation
Shear thinning
Newtonian liquids
Liquid films
Lubrication
Shear stress
Reynolds number

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title = "The run-off condition for the non-Newtonian rimming flow",
abstract = "Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. The Weissenberg number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The Theological models, which show Newtonian behaviour at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit the Newtonian behaviour near the free surface and power-law behaviour near the wall of the rotating cylinder.",
author = "Sergei Fomin and John Watterson and Eileen Harkin-Jones and S. Raghunathan",
year = "2001",
month = "12",
day = "1",
language = "English",
volume = "369",
pages = "271--278",
journal = "American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD",
issn = "0272-5673",
number = "3",

}

The run-off condition for the non-Newtonian rimming flow. / Fomin, Sergei; Watterson, John; Harkin-Jones, Eileen; Raghunathan, S.

In: American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, Vol. 369, No. 3, 01.12.2001, p. 271-278.

Research output: Contribution to journalConference article

TY - JOUR

T1 - The run-off condition for the non-Newtonian rimming flow

AU - Fomin, Sergei

AU - Watterson, John

AU - Harkin-Jones, Eileen

AU - Raghunathan, S.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. The Weissenberg number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The Theological models, which show Newtonian behaviour at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit the Newtonian behaviour near the free surface and power-law behaviour near the wall of the rotating cylinder.

AB - Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. The Weissenberg number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The Theological models, which show Newtonian behaviour at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit the Newtonian behaviour near the free surface and power-law behaviour near the wall of the rotating cylinder.

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M3 - Conference article

VL - 369

SP - 271

EP - 278

JO - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

T2 - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

JF - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

SN - 0272-5673

IS - 3

ER -