A mathematical model developed earlier for the time-dependent circular tube flow of compressible polymer melts subject to pressure-dependent wall slip [Tang and Kalyon, J. Rheol52, 507525 (2008)] was applied to the tube flow of polymeric suspensions with rigid particles. The model relies on the apparent slip mechanism for suspension flow with the additional caveat that the polymeric binder slips at the wall according to a pressure-dependent wall slip condition. The numerical simulations of the tube flow of concentrated suspensions suggest that steady flow is generated when the flow boundary condition at the wall is a contiguous strong slip condition along the entire length of the tube wall. The findings of the simulations are consistent with the experimental flow curves and flow instability data collected on suspensions of a poly (dimethyl siloxane), which itself exhibits wall slip, compounded with rigid and hollow spherical particles in the 10–40% by volume range. Increasing the concentration of rigid particles gives rise to the expansion of the range of flow rates over which the flow remains stable, as consistent with the experimental observations.

1.
Adams
,
S.
,
W. J.
Frith
, and
J. R.
Stokes
, “
Influence of particle modulus on the rheological properties of agar microgel suspensions
,”
J. Rheol.
48
,
1195
1213
(
2004
).
2.
Allende
,
M.
, and
D.
Kalyon
, “
Assessment of particle-migration effects in pressure-driven viscometric flows
,”
J. Rheol.
44
,
79
90
(
2000
).
3.
Aral
,
B.
, and
D. M.
Kalyon
, “
Effects of temperature and surface roughness on time-dependent wall slip in steady torsional flow of concentrated suspensions
,”
J. Rheol.
38
,
957
972
(
1994
).
4.
Aral
,
B.
, and
D. M.
Kalyon
, “
Rheology and extrudability of very concentrated suspensions: Effects of vacuum imposition
,”
Plast. Rubber Process. Applic.
24
,
201
210
(
1995
).
5.
Benbow
,
J. J.
, and
P.
Lamb
, “
New aspects of melt fracture
,”
SPE Trans.
3
,
7
17
(
1963
).
6.
Bernstein
,
B.
,
E.
Kearsley
, and
L.
Zapas
, “
A study of stress relaxation with finite strain
,”
Trans. Soc. Rheol.
7
,
391
410
(
1963
).
7.
Birinci
,
E.
, and
D.
Kalyon
, “
Development of extrudate distortions in poly(dimethyl siloxane) and its suspensions with rigid particles
,”
J. Rheol.
50
(
3
),
313
326
(
2006
).
8.
Brandrup
,
J.
,
E.
Immergut
, and
E.
Grulke
,
Polymer Handbook
, 4th ed. (
Wiley
,
New York
,
1999
).
9.
Cohen
,
Y.
, and
A. B.
Metzner
, “
Apparent slip flow of polymer solutions
,”
J. Rheol.
29
,
67
102
(
1985
).
10.
Denn
,
M. M.
, “
Extrusion instabilities and wall slip
,”
Annu. Rev. Fluid Mech.
33
,
265
287
(
2001
).
11.
Den Doelder
,
C. J.
,
R. J.
Koopmans
, and
J.
Molenaar
, “
Quantitative modeling of HDPE spurt experiments using wall slip and generalized Newtonian flow
,”
J. Non-Newtonian Fluid Mech.
79
,
503
514
(
1998
).
12.
Friend
,
J. P.
, and
R. J.
Hunter
, “
Plastic flow behavior of coagulated suspensions treated as a repeptization phenomenon
,”
J. Colloid Interface Sci.
37
,
548
556
(
1971
).
13.
Gadala-Maria
,
F.
, and
A.
Acrivos
, “
Shear-induced structure in a concentrated suspension of solid spheres
,”
J. Rheol.
24
,
799
814
(
1980
).
14.
Gevgilili
,
H.
, and
D. M.
Kalyon
, “
Step strain flow: Wall slip effects and other error sources
,”
J. Rheol.
45
,
1
9
(
2001
).
15.
Gevgilili
,
H.
, “
Development of the wall slip condition and its ramifications for polymers and other complex fluids
,” Thesis,
Stevens Institute of Technology
, Hoboken, NJ (
2003
).
16.
Georgiou
,
G. C.
, “
The time-dependent, compressible Poiseuille and extrusion-swell flows of a Carreau fluid with slip at wall
,”
J. Non-Newtonian Fluid Mech.
109
,
93
114
(
2003
).
17.
Hatzikiriakos
,
S. G.
, and
J. M.
Dealy
, “
Role of slip and fracture in the oscillating flow of HDPE in a capillary
,”
J. Rheol.
36
,
845
884
(
1992a
).
18.
Hatzikiriakos
,
S. G.
, and
J. M.
Dealy
, “
Wall slip of molten high density polyethylenes. II. Capillary rheometer studies
,”
J. Rheol.
36
,
703
741
(
1992b
).
19.
Hatzikiriakos
,
S. G.
, and
K. B.
Migler
, Editors,
Polymer Processing Instabilities: Control and Understanding
(
Dekker
,
New York
,
2005
).
20.
Jana
,
S.
,
B.
Kapoor
, and
A.
Acrivos
, “
Apparent wall-slip velocity coefficients in concentrated suspensions of noncolloidal particles
,”
J. Rheol.
39
,
1123
1132
(
1995
).
21.
Kalika
,
D. S.
, and
M. M.
Denn
, “
Wall slip and extrudate distortion in linear low density polyethylene
,”
J. Rheol.
31
,
815
834
(
1987
).
22.
Kalyon
,
D. M.
,
D.
Yu
, and
J.
Yu
, “
Melt rheology of two engineering thermoplastics: Poly(ether imide) and Poly(2,6-Dimethyl-1,4-phenylene ether)
,”
J. Rheol.
32
,
789
811
(
1988
).
23.
Kalyon
,
D. M.
,
R.
Yazici
,
C.
Jacob
,
B.
Aral
, and
S. W.
Sinton
, “
Effects of air entrainment on the rheology of concentrated suspensions during continuous processing
,”
Polym. Eng. Sci.
31
,
1386
1392
(
1991
).
24.
Kalyon
,
D. M.
,
P.
Yaras
,
B.
Aral
, and
U.
Yilmazer
, “
Rheological behavior of a concentrated suspension: A solid rocket fuel simulant
,”
J. Rheol.
37
,
35
53
(
1993
).
25.
Kalyon
,
D.
,
H.
Gokturk
,
P.
Yaras
, and
B.
Aral
, “
Motion analysis of development of wall slip during die flow of concentrated suspensions
,” Society of Plastics Engineers ANTEC Technical Papers,
41
,
1130
1134
(
1995
).
26.
Kalyon
,
D.
, and
H.
Gevgilili
, “
Wall slip and extrudate distortion of three polymer melts
,”
J. Rheol.
47
(
3
),
683
699
(
2003
).
27.
Kalyon
,
D.
, “
Apparent slip and viscoplasticity of concentrated suspensions
,”
J. Rheol.
49
,
621
640
(
2005
).
28.
Kalyon
,
D.
, and
H. S.
Tang
, “
Inverse problem solution of squeeze flow for parameters of generalized Newtonian fluid and wall slip
,”
J. Non-Newtonian Fluid Mech.
143
,
133
140
(
2007
).
29.
Karnis
,
A.
, and
S. G.
Mason
, “
The flow of suspensions through tubes VI. Meniscus effects
,”
J. Colloid Interface Sci.
23
,
120
133
(
1967
).
30.
Knudsen
,
M.
,
The Kinetic Theory of Gases
, 3rd ed. (
Methuen
,
London
,
1950
).
31.
Kok Hartman
,
P. J. A.
,
S.
Kazarian
,
C. J.
Lawrence
, and
B. J.
Briscoe
, “
Near-wall particle depletion in a flowing colloidal suspension
,”
J. Rheol.
46
,
481
493
(
2002
).
32.
Krieger
,
I. M.
, and
T. J.
Dougherty
, “
A mechanism for Non-Newtonian Flow in suspensions of rigid spheres
,”
Trans. Soc. Rheol.
3
,
137
152
(
1959
).
33.
Laun
,
H. M.
, “
Description of the nonlinear shear behavior of a low density polyethylene melt by means of an experimentally determined strain dependent memory function
,”
Rheol. Acta
17
,
1
15
(
1978
).
58.
Lawal
,
A.
, and
D. M.
Kalyon
, “
Compressive squeeze flow of viscoplastic fluids with apparent wall slip
,”
Int. Polym. Process.
15
,
63
71
(
2000
).
34.
Leighton
,
D.
, and
A.
Acrivos
, “
The shear-induced migration of particles in concentrated suspensions
,”
J. Fluid Mech.
275
,
155
199
(
1987
).
35.
Lu
,
G.
,
D.
Kalyon
,
I.
Yilgör
, and
E.
Yilgör
, “
Rheology and processing of BaSO4 filled medical-grade thermoplastic polyurethane
,”
Polym. Eng. Sci.
44
,
1941
1948
(
2004
).
36.
Meeker
,
S. P.
,
R. T.
Bonnecaze
, and
M.
Cloitre
, “
Slip and flow in pastes of soft particles: Direct observation and rheology
,”
J. Rheol.
48
,
1295
1320
(
2004
).
37.
Mewis
,
J.
, “
Rheology of concentrated dispersions
,”
Adv. Colloid Interface Sci.
6
,
173
200
(
1976
).
38.
Nott
,
P. R.
, and
J. F.
Brady
, “
Pressure-driven flow of suspensions: Simulations and theory
,”
J. Fluid Mech.
275
,
157
199
(
1994
).
39.
Osaki
,
K.
,
Proceedings of the Seventh International Congress on Rheology
,
C.
Klason
and
J.
Kubat
, eds. (
Tages Anzeiger, Götenburg
,
1976
), pp.
104
109
.
40.
Person
,
T. J.
, and
M. M.
Denn
, “
The effect of die materials and pressure-dependent slip on the extrusion of linear low-density polyethylene
,”
J. Rheol.
41
,
249
265
(
1997
).
41.
Phillips
,
R. J.
,
R. C.
Armstrong
,
R. A.
Brown
,
A. L.
Graham
, and
J. R.
Abbott
, “
A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration
,”
Phys. Fluids A
4
,
30
40
(
1992
).
42.
Reiner
,
M.
,
Deformation, Strain and Flow
(
H. K. Lewis
,
London
,
1960
).
44.
Robert
,
L.
,
Y.
Demay
, and
B.
Vergnes
, “
Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry
,”
Rheol. Acta
43
,
1435
1528
(
2004
).
45.
Rosenbaum
,
E. E.
,
S. K.
Randa
,
S. G.
Hatzikiriakos
,
C. W.
Stewart
,
D. L.
Henry
, and
M.
Buckmaster
, “
Boron nitride as a processing aid for the extrusion of polyolefins and fluoropolymers
,”
Polym. Eng. Sci.
40
,
179
190
(
2000
).
46.
Rough
,
S. L.
,
J.
Bridgwater
, and
D. I.
Wilson
, “
Effects of liquid phase migration on extrusion of microcrystalline cellulose pastes
,”
Int. J. Pharm.
204
,
117
126
(
2000
).
47.
Tabuteau
,
H.
,
J.
Baudez
,
F.
Bertrand
, and
P.
Coussot
, “
Mechanical characteristics and origin of wall slip in pasty biosolids
,”
Rheol. Acta
43
,
2
,
168
174
(
2004
).
48.
Tang
,
H. S.
, and
D. M.
Kalyon
, “
Time-dependent development of flow instabilities of non-Newtonian melts and suspensions with rigid particles
,”
Proceedings of AICHE Annual Meeting
,
Austin, Texas
(
2004a
).
49.
Tang
,
H. S.
, and
D. M.
Kalyon
, “
Estimation of the parameters of Herschel-Bulkley fluid under wall slip using a combination of capillary and squeeze flow viscometers
,”
Rheol. Acta
43
,
80
88
(
2004b
).
50.
Tang
,
H. S.
, and
D. M.
Kalyon
, “
Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip
,”
J. Rheol.
52
,
507
525
(
2008
).
51.
Tyrrell
,
J. W. G.
, and
P.
Attard
, “
Images of nanobubbles on hydrophobic surfaces and their interactions
,”
Phys. Rev. Lett.
87
,
176104
(
2001
).
52.
Vinogradov
,
G. V.
, and
L. I.
Ivanova
, “
Viscous properties of polymer melts and elastomers exemplified by ethylene-propylene copolymer
,”
Rheol. Acta
6
,
209
222
(
1967
).
53.
Wagner
,
M. H.
, “
Analysis of the time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt
,”
Rheol. Acta
15
,
136
142
(
1976
).
54.
Yaras
,
P.
,
D. M.
Kalyon
, and
U.
Yilmazer
, “
Flow instabilities in capillary flow of concentrated suspensions
,”
Rheol. Acta
33
,
48
59
(
1994
).
59.
Yaras
,
P.
, “
Rheological behavior and twin screw extrusion flow of non-colloidal concentrated suspensions
,” Ph.D. thesis,
Stevens Institute of Technology
, Hoboken, NJ (
1995
).
55.
Yilmazer
,
U.
, and
D. M.
Kalyon
, “
Slip effects in capillary and parallel disk torsional flows of highly filled suspensions
,”
J. Rheol.
33
,
1197
1212
(
1989
).
56.
Yilmazer
,
U.
,
C.
Gogos
, and
D. M.
Kalyon
, “
Mat formation and unstable flows of highly filled suspensions in capillaries and continuous processors
,”
Polym. Compos.
10
,
242
248
(
1989
).
57.
Zarraga
,
I. E.
,
D. A.
Hill
, and
D. T.
Leighton
, Jr.
, “
The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids
,”
J. Rheol.
44
,
185
220
(
2000
).
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