10/11/2015BAE2023 Physical Properties of Biological Materials Lecture 10 Viscosity 1 This chapter is a study of the shear stress as a function of the shear.

04/19/23 BAE2023 Physical Properties of Biological Materials Lecture 10

Viscosity

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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

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• “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

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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

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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

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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

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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

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• Kinematic viscosity: dynamic viscosity/density

(no force involved)

2,m s stokes

Lecture 9 – Viscosity and Flow

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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

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• 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

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• 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

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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

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• 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

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•Time dependent Viscosity (figure 6.2 page 196)

Lecture 9 – Viscosity and Flow

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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

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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

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• Examples of viscometers

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Viscosity and Flow of Liquids and Semisolids…Chapter 6