2. Casson model was discussed in class in the context of blood rheology. This phenomenological model is often used to describe the shear stress vs. shear rate relationship in colloidal suspensions where particle aggregation might cause the measured viscosity to increase at low shear rates. In an experiment, data for the shear stress rand the applied shear rate S were fitted to the Casson model written below (in a slightly different form compared to that given in the lecture notes): √r = √²₁ + √as. (1) constant constent The best least square fit parameters to the experimental data were found to be 40 mPa for the yield stress and 2.5 mPas for the parameter a, which is referred to as the plastic viscosity. a. Using Eq. (1), derive an expression for the fluid viscosity μ as a function of S. b. Plot the viscosity of the fluid as a function of S for 0.1s¹
2. Casson model was discussed in class in the context of blood rheology. This phenomenological model is often used to describe the shear stress vs. shear rate relationship in colloidal suspensions where particle aggregation might cause the measured viscosity to increase at low shear rates. In an experiment, data for the shear stress rand the applied shear rate S were fitted to the Casson model written below (in a slightly different form compared to that given in the lecture notes): √r = √²₁ + √as. (1) constant constent The best least square fit parameters to the experimental data were found to be 40 mPa for the yield stress and 2.5 mPas for the parameter a, which is referred to as the plastic viscosity. a. Using Eq. (1), derive an expression for the fluid viscosity μ as a function of S. b. Plot the viscosity of the fluid as a function of S for 0.1s¹
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Transcribed Image Text:2. Casson model was discussed in class in the context of blood rheology. This
phenomenological model is often used to describe the shear stress vs. shear rate relationship
in colloidal suspensions where particle aggregation might cause the measured viscosity to
increase at low shear rates. In an experiment, data for the shear stress rand the applied
shear rate S were fitted to the Casson model written below (in a slightly different form
compared to that given in the lecture notes):
√t=√₁+√as.
(1)
The best least square fit parameters to the experimental data were found to be 40 mPa for the yield
stress and 2.5 mPas for the parameter a, which is referred to as the plastic viscosity.
a. Using Eq. (1), derive an expression for the fluid viscosity u as a function of S.
b. Plot the viscosity of the fluid as a function of S for 0.1s¹ <S≤ 10 s¹.
c. Based on class discussion on fluid classification, how would you characterize this fluid?
Definition of
Viscosity
Viscosity
I ₂ Sty
S = V = dv₁
H
dy
= Rate of
change
T: Shear stress, S: Shear rate
= M = dz
ds
of shear stress w shear rate
Vse Excel etc
from E₂1, find modt
=
ds
3
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