Flow of Herschel-Bulkey Fluids - Colloidal Dispersions of... · August 25, 2003 Particles 2003 Herschel Bulkley Flow Effect of a yield point on flow ... Microsoft PowerPoint - Flow

August 25, 2003 Particles 2003 Herschel Bulkley Flow

The flow of Herschel-Bulkleyfluids

Ian Morrison, Cabot Corporation

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Thin polymer-filled layers coated from dispersions

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Typical shear thinning rheogramPhotoconductive Pigment in Nonaqueous Polymer Solution

Shear rate (s-1)

0.1 1 10 100 1000 10000

Visc

osity

(mPa

s)

0.001

0.01

0.1

1

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Data is reasonably fitted by a power law

10

nη η γ −=

n is the power law index and is one for a Newtonian fluid.

Photoconductive Pigment in Nonaqueous Polymer Solution

Shear rate (s-1)

0.1 1 10 100 1000 10000

Visc

osity

(mPa

s)

0.001

0.01

0.1

1

0.750.580.25n

η γ −==

August 25, 2003 Particles 2003 Herschel Bulkley Flow

The flow of a shear thinningliquid through a pipe

The reduced flow rate of a shear thinning liquid is:

1 11 3 11

nn rvn 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

Rel

ativ

e ve

loci

ty

2.5

0

PLj

10 rj

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Same data replotedShear stress versus shear rate

Shear rate (s-1)

0 200 400 600 800 1000 1200 1400 1600

Shea

r stre

ss (P

a)

0

1

2

3

4

5

6

7

August 25, 2003 Particles 2003 Herschel Bulkley Flow

How yield points approximate power law flowShear stress versus shear rate

Shear rate (s-1)

0 200 400 600 800 1000 1200 1400 1600

Shea

r stre

ss (P

a)

0

1

2

3

4

5

6

7

The slopeis the viscosity.

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Herschel-Bulkley rheology

0nmτ τ γ= +

Model the flow as shear thinning above some yield point:

Shear stress versus shear rate

Shear rate (s-1)

0 200 400 600 800 1000 1200 1400 1600

Shea

r stre

ss (P

a)

0

1

2

3

4

5

6

7

0.710.64 0.31τ γ= +

Note the value of “n” is now higher, apparently less shear thinning.

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Effect of a yield point on flow

If a fluid has a yield point, τ0, and is under pressure, p, a column of radius r and length L in the center moves as a plug. The plug radius can be calculated.

02

0 0

(2 ) or

2 2

rLprLrp P

τ ππ

τ τ

=

= =

P is the pressure drop.

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Flow of an Herschel-Bulkley fluid through a pipe

( )

0

112 20 0 0

2 3 3 3 2 2 2 3 3 20 0 0

20

40 0

2

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

2 1

4 113 3

nn n

rP

P n n R PR PRvelocity

n R P n RP R P n R P nelse

RPvelocity

RP RP

τ

τ τ ττ τ τ

τ

τ τ

+−

>

− + + − − − +=

− + + −

− =

− +

August 25, 2003 Particles 2003 Herschel Bulkley Flow

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

Rad

ial p

ositi

on fr

om c

ente

r

HBj

rj

Note: The radius of the plug is:

The fitted Herschel-Bulkley parameters:n = 0.75tau = 0.5 Pa

with a reasonable pressure dropP = 106 Pa/0.1m

5

2 0.5 Pa 110 Pa/0.1xr m

mµ= =

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Comparison of predicted flows:Power law and Herschel-Bulkley

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Some Problems Require More Study

August 25, 2003 Particles 2003 Herschel Bulkley Flow

August 25, 2003 Particles 2003 Herschel Bulkley Flow

Surface Energy Characterization ofFibers, 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, NY13210

E-mail: [email protected]

Ian D. Morrison, Cabot Corporation, 157 Concord Road,Billerica, MA 01821

E-mail: [email protected]

Philadelphia, August 22-26, 2004228th ACS National Meeting

Pennsylvania Convention Center,Philadelphia

PROGRAM CHAIR R. Nagarajan, Department ofChemical Engineering, Penn State University, UniversityPark, PA 16802 E-mail: [email protected]

Submit abstracts via Online Abstract Submittal System(OASYS) at www.acs.org/meetingsDeadline for submission of 150 words abstract is April 15,2004.