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0 constant
velocity field
shear rate:
0
H
x1 (t )
the advantage of subjecting every x1 fluid particle to the same deformation x (t t )
1
This has v1 ( x x2 2)
3
x2 x1
path lines
© Faith A. Morrison, Michigan Tech U.
By definition, viscosity is measured in pure, homogeneous shear flow Means, the shear rate force=F is the same at every v1 ( H ) V 0 H position in space
r z 2R well-developed flow
exit region
1
© Faith A. Morrison, Michigan Tech U.
Shear Rheometry Goal:
Measure the viscosity of a very viscous, non-Newtonian fluid.
Strategy:
Use capillary flow experiments (pressure drop versus flow rate) to infer viscosity
Implications:
•The flow is not the simple shear flow assumed when viscosity was defined; •We need to analyze the flow with as few assumptions as possible; •We need to design the apparatus to conform to the assumptions we make; •When our assumptions are only approximately satisfied, we must correct the data where possible.
Strategy:
Design experiments making the fewest assumptions possible so that the design is applicable to all (most) fluids. Begin with: What is the definition of viscosity?
Hee Eon Park, works on a high-pressure sliding plate rheometer, the only instrument of its kind in the world.
Even though producing the parallel plate geometry is tricky, it has been done: J. M. Dealy and S. S. Soong J. Rheol. 28, 355 (1984); doi:10.1122/1.549756 A Parallel Plate Melt Rheometer Incorporating a Shear Stress Transducer (Sliding Plate Rheometer) 10
v1 x2
V x2 x1
0 x2 v 0 0 123
21 F / A 0 V / H
5
path lines
© Faith A. Morrison, Michigan Tech U.
By definition, viscosity is measured in pure, homogeneous shear flow Means, the shear rate force=F is the same at every v1 ( H ) V 0 H position in space
v1 x2
0 x2 v 0 0 V 123 (just in case it matters
to the measurement of viscosity)
x1
x2
path lines
21 F / A 0 V / H
6
© Faith A. Morrison, Michigan Tech U.
Difficulty:
Because we do not know the rheological behavior of our sample (whether it is Newtonian, power-law, etc.) we do not know how it will behave. If we do not know how it will behave, it is difficult to design an experiment to measure its behavior (Catch 22).
0 constant
0
H
v1 ( x2 )
x2 x1
v1 x2
x1 (t )
x1 (t t )
V x2 x1
0 x2 v 0 0 123
21 F / A 0 V / H
8
path lines
© Faith A. Morrison, Michigan Tech U.
Can we use an alternate, easier geometry?
9
© Faith A. Morrison, Michigan Tech U.
Sliding Plate Rheometer
Image from: www.mcgill.ca/photos/2006/february/
John Dealy McGill University
© Faith A. Morrison, Michigan Tech U.
Image from:
5
CM4655 Morrison Lecture 2 2014
Shear is fundamentally a sliding flow
We can infer a viscosity from any sliding flow if we can relate the data back to homogeneous shear flow
7
© Faith A. Morrison, Michigan Tech U.
By definition, viscosity is measured in pure, homogeneous shear flow force=F
velocity field
v1 ( H ) V 0 H
shear rate:
0 constant
v1 ( x2 ) x2 x1
velocity field
shear rate:
0
H
v1 x2
x1 (t )
x1 (t t )
V x2 x1
0 x2 v 0 0 123
21 F / A 0 V / H
4
path lines
© Faith A. Morrison, Michigan Tech U.
2
CM4655 Morrison Lecture 2 2014
By definition, viscosity is measured in pure, homogeneous shear flow Means, the shear rate force=F is the same at every v1 ( H ) V 0 H position in space
x2
Cartesian geometry
x1
(parallel plates)
r r2
Cylindrical geometry
z R r1
r3
Telescoping sliding flow (capillary flow)
11
© Faith A. Morrison, Michigan Tech U.
0 constant
velocity field
shear rate:
0
H
x1 (t )
the advantage of subjecting every x1 fluid particle to the same deformation x (t t )
1
This has v1 ( x x2 2)
0 constant
velocity field
shear rate:
0
H
x1 (t )
the advantage of subjecting every x1 fluid particle to the same deformation x (t t )
1
This has v1 ( x x2 2)
CM4655 Morrison Lecture 2 2014
CM4655 Polymer Rheology Lab
entrance region
Shear Viscosity Measurement in a Capillary Rheometer
Prof. Faith A. Morrison Michigan Technological University
