10/11/2015bae2023 physical properties of biological materials lecture 10 viscosity 1 this chapter is...
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04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
1
This chapter is a study of the shear stress as a function of the
shear rate for Newtonian and non-Newtonian biological
materials.
Lecture 9 – Viscosity and Flow (Ch. 2 and notes)
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 9
Viscosity
2
• “When a fluid or semisolid is subjected to a constant shearing force it flows, ie., it deforms continuously at a velocity that increases as the applied shearing force increases.”
• Viscosity: quantifies the resistance of the fluid to flow
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Liquids and semisolids are usually pumped during processing
• Viscosity plays a huge part in pump and conveyance system design
• Viscosity may be dependent on moisture content, concentration, composition and prior treatments.
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Newtonian Fluids (Newton 1687)
– Simplest model– Covers most, but not all, ag products– Velocity behaves linearly w/ distance– Shear stress is linear function of the shear
rate– Dynamic viscosity: proportionality constant
for this relationship
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• The viscosity can be measured where the fluid of interest is sheared between two flat plates which are parallel to one another
• Known as planar Couette flow. The shear stress is the ratio of the tangential force F needed to maintain the moving plate at a constant velocity V to the plate area A.
• Couette flow:Low-speed, steady motion of a viscous fluid between two
infinite plates moving parallel to each other.
Lecture 9 – Viscosity and Flow
•http://www.answers.com/topic/viscosity?cat=biz-fin
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Dynamic viscosity (Figure 6.1)2
1
; where =shear stress (N/m = Pa),
=shear rate (s ),
proportionality constant
zyz
z
dv
dy
dv
dy
aka dynamic viscosity (Pa-s)
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Kinematic viscosity: dynamic viscosity/density
(no force involved)
2,m s stokes
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Non-Newtonian Fluids• Relationship between shear stress and shear rate is NOT linear
• Some also have a yield stress which must be obtained before flow begins.
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
9
• Most common: pseudoplastic…convex curve towards the shear stress axis (Fig. 6.1b)
–Apparent viscosity will decrease as shear rate increases
• Dilatant fluids: concave toward shear stress axis (corn flour, wet beach sand: stiffens when walked on..select pumps carefully!)
–Apparent viscosity increases as shear rate increases
• Plastic: linear but intercept is at the yield stress (toothpaste: must stay on brush but must be exudable)
• Casson-type plastic: has a yield stress but is not linear (chocolate)
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
10
• Apparent viscosity = shear rate ratio at any given shear rate
• Pseudoplastic and Dilatant materials, eqtn. 6.2, Table 6.2)
• Newtonian: n=1, k=dynamic viscosity
; : =shear stress
k=consistency coefficient
n=flow behavior index
ndv
k wheredy
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Plastic and Casson-type plastic behavior (more general case…Herschel-Bulkley model, eqtn. 6.3 Table 6.3)
• Chocolate and other Casson materials follows this where N = ½ and the yield stress is taken to the ½ power
0 0; : =shear stress, yield stress
k=consistency coefficient
n=flow behavior index
ndv
k wheredy
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
12
• Temperature Dependency:– Viscosity decreases with an increase in Temp.– Typically 2% per degree C– For some materials (fruit juices) the T effect follows
an Arrhenius relationship (Eqtn. 6.5 page 193)
exp , viscosity, Pa-s Ea
RT
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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•Time dependent Viscosity (figure 6.2 page 196)
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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•Time dependent Viscosity–Thixotropic examples (viscosity decreases with time)
»Gelatin, shortening, cream, paints–Rheopectic examples (viscosity increases with time)
»Highly concentrated starch solutions…gravy
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Flow in a pipe:• Darcy-Weisbach
– Newtonian
– -Non-newtonian
2
2
L vH f
d g
4 8n
K L VP
d d
Lecture 9 – Viscosity and Flow
04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10
Viscosity
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• Examples of viscometers
Lecture 9 – Viscosity and Flow