Flow of Herschel-Bulkey Fluids

8/11/2019 Flow of Herschel-Bulkey Fluids

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August 25, 2003 Particles 2003 Herschel Bulkley Flow

The flow of Herschel-Bulkley

fluids

Ian Morrison, Cabot Corporation


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Thin polymer-filled layers coated

from dispersions


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Typical shear thinning rheogram

Photoconductive Pigment in Nonaqueous Polymer Solution

Shear rate (s-1

)

0.1 1 10 100 1000 10000

Viscosity(m

Pas)

0.001

0.01

0.1

1


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Data is reasonably fitted by a power law

1

0

n

=

n is the

power law

index and

is one for a

Newtonianfluid.

Photoconductive Pigment in Nonaqueous Polymer Solution

Shear rate (s-1

)

0.1 1 10 100 1000 10000

Viscosity(mP

as)

0.001

0.01

0.1

1

0.750.58

0.25n

=

=


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The flow of a shear thinning

liquid through a pipe

The reduced

flow rate of a

shear

thinning

liquid is:

11

1 31

1

nn rv

n R

+ + = +

Macosko, Rheology, pp. 88-89, 1994.

n= 0.25

0 0.5 10

0.5

1

1.5

2

2.5

Radial postion from center

Relativevelocity

2.5

0

PLj

10 rj


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Same data replotedShear stress versus shear rate

Shear rate (s-1

)

0 200 400 600 800 1000 1200 1400 1600

Shearstress

(Pa)

0

1

2

3

4

5

6

7


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How yield points approximate power

law flowShear stress versus shear rate

Shear rate (s-1)

0 200 400 600 800 1000 1200 1400 1600

Shearstress(Pa)

0

1

2

3

4

5

6

7

The slopeis the viscosity.


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Herschel-Bulkley rheology

0

nm = +

Model the flow as

shear thinningabove some yield

point:

Shear stress versus shear rate

Shear rate (s-1

)

0 200 400 600 800 1000 1200 1400 1600

Shearstress(Pa)

0

1

2

3

4

5

6

7

0.710.64 0.31 = +

Note the value ofn is now higher,

apparently less

shear thinning.


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Effect of a yield point on flow

If a fluid has a yield point, 0,and is under pressure, p, a

column of radius rand length

L in the center moves as aplug. The plug radius can be

calculated.

02

0 0

(2 ) or

2 2

rLpr

Lr

p P

=

= =

Pis the pressure drop.


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Flow of an Herschel-Bulkley fluid through a

pipe

( )

0

11

2 2

0 0 0

2 3 3 3 2 2 2 3 3 2

0 0 0

2

0

4

0 0

2

3 1 (2 1) (( ) (Pr ) )

2 2 2

2 1

4 11

3 3

n

n n

r P

P n n R PR PRvelocity

n R P n RP R P n R P nelse

RPvelocity

RP RP

+

>

+ + +=

+ +

=

+


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Flow of Herschel Bulkley fluid

0 0.002 0.004 0.006 0.0080

0.5

1

1.5

2

2.5

Herschel-BulkleyFluid velocity

Radialpositionfromc

enter

HBj

rj

Note: The radius of the

plug is:

The fitted Herschel-Bulkley parameters:

n = 0.75

tau = 0.5 Pawith a reasonable pressure drop

P = 106 Pa/0.1m

5

2 0.5 Pa1

10 Pa/0.1

xr m

m= =


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Comparison of predicted flows:

Power law and Herschel-Bulkley


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Some Problems Require More Study


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Surface Energy Characterization of

Fibers, Fillers and Paper

D. Steven Keller, Empire State Paper Research Institute,State University of New York, College of Environmental

Science and Forestry, 1 Forestry Drive, Syracuse, NY

13210

E-mail: [email protected]

Ian D. Morrison, Cabot Corporation, 157 Concord Road,

Billerica, MA 01821E-mail: [email protected]

Philadelphia, August 22-26, 2004

228th

ACS National MeetingPennsylvania Convention Center,

Philadelphia

PROGRAM CHAIR R. Nagarajan, Department of

Chemical Engineering, Penn State University, University

Park, PA 16802 E-mail: [email protected]

Submit abstracts via Online Abstract Submittal System

(OASYS) at www.acs.org/meetings

Deadline for submission of 150 words abstract is April 15,

2004.

Flow of Herschel-Bulkey Fluids

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