10_non-newtonian fluids - lecture 2

8/17/2019 10_Non-Newtonian Fluids - Lecture 2

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CHE2161

Non-Newtonian Fluids


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Textbook Reference

Fluid Flow for Chemical Enineers! second edition! F" #"

Holland and R" $ra! Edward #rnold! %ondon! 1&&'"

#(ailable online at)

htt*)++www"kno(el"com"e,*rox"lib"monash"edu"au+


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/elocit 0rofiles for 0ower %aw Fluids

The (elocit *rofile for stead! full de(elo*ed! laminar flow

in a *i*e can be determined easil b usin the euation ofa *ower law fluid instead of Newton3s law of (iscosit"

For a 0ower %aw fluid)

$ combinin these! obtain a differential euation for the

(elocit radient! which can be sol(ed 4 gives velocity

profiles for various values of .


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/elocit 0rofiles for 0ower %aw Fluids

Slope of the velocity profile at the wall is

dependent of the power law index, n

Behaviour of

real fluids

lies in the

approximate

range,0.2


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Flow of Non-Newtonian Fluids in 0i*es

e alread know) all shear stress

Now what about! 7hear rate at the wall 89"

7hear rate : ;radient of the (elocit *rofile"

Shear rate at the wall !radient of the velocity profile

at the wall"

Shape of the velocity profile is different for differenttypes of fluid.

"#uation 1


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Flow of Non-Newtonian Fluids in 0i*es

Eas for Newtonian fluids) e know the (elocit *rofile


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Rabinowitsch->oone Euation

&he solution to the pro'lem of determining the wall

shear rate for a (on)(ewtonian fluid in laminar flow in atu'e"


8/13?


The wall shear rate for a non-Newtonian fluid can be

calculated from the (alue for a Newtonian fluid ha(in thesame flow rate in the same *i*e! the correction factor bein

the uantit in the suare brackets"

Clearl the flow characteristic 8or the rate of shear at thewall9 for a non-Newtonian fluid in laminar flow is not eual

to the manitude of the shear rate at the wall"

Now the flow cur(e aainst can be determined"

How@


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How@

19 >easure at (arious (alues of "

29 Calculate from the *ressure dro* measurements usin

euation 1 and the corres*ondin (alues of the flow

characteristic 89 from the flow rate measurements"

.9 0lot aainst and measure the radient 8i"e" deri(ati(e9 at

(arious *oints on the cur(e"

59 Calculate the true wall shear rate from euation 829 with

the deri(ati(e determined in ste* ." An eneral! the *lot of

aainst will not be a straiht line and the radient must bee(aluated at the a**ro*riate *oints on the cur(e"


10/131B



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Fiure shows

t*ical *lots ofaainst

and obtained

b followin

the *rocedure

abo(e"


12/1312

Exam*le 1

• For a Newtonian fluid com*are the followin *lots)

aainst and

aainst

•


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Exam*le 1

•

10_non-newtonian fluids - lecture 2

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