Rimming flow of the non-Newtonian fluid on the inner surface of a horizontal rotating cylinder is investigated. Simple lubrication theory is applied since the Reynolds number is small and liquid film is thin. For the steady-state flow of a power-law fluid the mathematical model reduces to a simple algebraic equation regarding the thickness of the liquid film. The qualitative analysis of this equation is carried out and the existence of two possible solutions is rigorously proved. Based on this analysis qualitative analysis, different regimes of the rimming flow are defined and analyzed analytically.

Volume Subject Area:
Fluids Engineering
Topics:
Flow (Dynamics), Fluids, Liquid films, Non-Newtonian fluids, Steady state, Algebra, Cylinders, Lubrication theory, Reynolds number
1.
Thoroddsen
S. T.
&
Mahadevan
L.
,
Experimental study of coating flows in a partially filled horizontally rotating cylinder
,
Experiments in Fluids
23
(
1997
)
1
–
13
.
2.
Hosoi
A. E.
&
Mahadevan
L.
,
Axial instability of a free-surface front in a partially filled horizontal rotating cylinder
,
Phys. Fluids
11
(
1999
)
97
–
106
.
3.
Moffatt
H. K.
,
Behaviour of viscous film on the surface of a rotating cylinder
,
J. Mecanique
16
(
1977
)
651
–
673
4.
Preziosi
L.
and
Joseph
D. D.
,
The Run-Off Condition for Coating and Rimming Flows
,
J. Fluid. Mech.
,
187
, (
1988
)
99
–
113
.
5.
O’Brien
S. B. G.
&
Gath
E. G.
,
Location of a shock in rimming flow
,
Phys. Fluids
10
(
1998
)
1040
–
1042
6.
Johnson
R. E.
, “
Steady-State Coating Flows Inside a Rotating Horizontal Cylinder
”,
J. Fluid. Mech.
,
190
, (
1988
)
321
–
342
.
7.
Fomin
S.
,
Watterson
J.
,
Raghunathan
S.
and
Harkin-Jones
E.
,
Steady-State Rimming Flow of the Generalized Newtonian Fluid
,
Physics of Fluids
,
14
(
9)
, (
2002
)
3350
–
3353
.
8.
Fomin
S.
, “
Three Regimes of Non-Newtonian Rimming Flow
”,
ASME Journal of Fluids Engineering
, v.
128
, (
2006
),
107
–
112
9.
Ross
A. B.
,
Wilson
S. K.
&
Duffy
B. R.
,
Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder
,
J. Fluid Mech.
430
(
2001
)
309
–
333
.
10.
Ruschak
K. J.
&
Scriven
L. E.
,
Rimming flow of liquid in a rotating horizontal cylinder
,
J. Fluid Mech.
76
(
1976
)
113
–
125
.
11.
Rajagopalan
D.
,
Phillips
R.
,
Armstrong
R.
,
Brown
R.
&
Bose
A.
,
The influence of viscoelasticity on the existence of steady solutions in two-dimensional rimming flow
,
J. Fluid Mech.
235
(
1992
)
611
–
642
.
12.
Lawrence
C. J.
&
Zhou
W.
,
Spin coating of non-Newtonian fluids
,
J. Non-Newtonian Fluid Mech.
39
(
1991
)
137
–
187
.
13.
Melo
F.
,
Localized states in film-dragging experiments
,
Phys. Rev. E.
48
(
1993
)
2704
–
2712
.
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