Site Loader

Viscosity of some ?uids
Fluid Air ( at Benzene Water ( at 18 ? C ) Olive oil ( at 20 ? C ) Motor oil SAE 50 Honey Ketchup Peanut butter Tar Earth lower mantle 18 ? C ) Viscosity [ cP ] 0. 02638 0. 5 1 84 540 2000–3000 50000–70000 150000–250000 3 ? 1010 3 ? 1025

Table: Viscosity of some ?uids
Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Models with variable viscousness

General signifier: T = ?pI + 2µ ( D. T ) D
Second

( 2. 1 )

Particular theoretical accounts chiefly developed by chemical applied scientists.

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Ostwald–de Waele power jurisprudence
? Wolfgang Ostwald. Uber die Geschwindigkeitsfunktion der Viskosit?t disperser Systeme. I. Colloid Polym. Sci. . 36:99–117. a 1925 A. de Waele. Viscometry and plastometry. J. Oil Colour Chem. Assoc. . 6:33–69. 1923 µ ( D ) = µ0 |D|n?1 ( 2. 2 )

Fits experimental informations for: ball point pen ink. liquefied cocoa. aqueous scattering of polymer latex domains

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Carreau Carreau–Yasuda
Pierre J. Carreau. Rheologic equations from molecular web theories. J.
Rheol. . 16 ( 1 ) :99–127. 1972 Kenji Yasuda. Probe of the analogies between viscosimetric and additive viscoelastic belongingss of polystyrene ?uids. PhD thesis. Massachusetts Institute of Technology. Dept. of Chemical Engineering. . 1979 µ0 ? µ? ( 1 + ? |D|2 ) 2 n n?1 a

µ ( D ) = µ? +

( 2. 3 ) ( 2. 4 )

µ ( D ) = µ? + ( µ0 ? µ? ) ( 1 + ? |D|a ) Fits experimental informations for: liquefied polystyrene Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Eyring
Henry Eyring. Viscosity. malleability. and di?usion as illustrations of absolute reaction rates. J. Chem. Phys. . 4 ( 4 ) :283–291. 1936 Francis Ree. Taikyue Ree. and Henry Eyring. Relaxation theory of conveyance jobs in condensed systems. Ind. Eng. Chem. . 50 ( 7 ) :1036–1040. 1958 µ ( D ) = µ? + ( µ0 ? µ? ) arcsinh ( ? |D| ) ? |D| arcsinh ( ?1 |D| ) arcsinh ( ?2 |D| ) µ ( D ) = µ0 + µ1 + µ2 ?1 |D| ?2 |D| ( 2. 5 ) ( 2. 6 )

Fits experimental informations for: napalm ( coprecipitated aluminium salts of naphthenic and palmitic acids ; jellied gasolene ) . 1 % nitrocelulose in 99 % butyl ethanoate Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Cross

Malcolm M. Cross. Rheology of non-newtonian ?uids: A new ?ow equation for pseudoplastic systems. J. Colloid Sci. . 20 ( 5 ) :417–437. 1965 µ ( D ) = µ? + µ0 ? µ? 1 + ? |D|n ( 2. 7 )

Fits experimental informations for: aqueous polyvinyl ethanoate scattering. aqueous limestone suspension

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Sisko

A. W. Sisko. The ?ow of lubricating lubricating oils. Ind. Eng. Chem. . 50 ( 12 ) :1789–1792. 1958 µ ( D ) = µ? + ? |D|n?1 Fits experimental informations for: lubricating lubricating oils ( 2. 8 )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Barus

C. Barus. Isotherms. isopiestics and isometrics relative to viscousness. Amer. J. Sci. . 45:87–96. 1893 µ ( T ) = µref e? ( p?pref ) Fits experimental informations for: mineral oils1. organic liquids2 ( 2. 9 )

Michael M. Khonsari and E. Richard Booser. Applied Tribology: Bearing Design and Lubrication. John Wiley & A ; Sons Ltd. Chichester. 2nd edition. 2008 2 P. W. Bridgman. The e?ect of force per unit area on the viscousness of 44 pure liquids. Proc. Am. Acad. Art. Sci. . 61 ( 3/12 ) :57–99. FEB-NOV 1926 Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Ellis
Seikichi Matsuhisa and R. Byron Bird. Analytical and numerical solutions for laminal ?ow of the non-Newtonian Ellis ?uid. AIChE J. . 11 ( 4 ) :588–595. 1965 µ ( T ) = µ0 1 + ? |T? |n?1 ( 2. 10 )

Fits experimental informations for: 0. 6 % w/w carboxymethyl cellulose ( CMC ) solution in H2O. poly ( vynil chloride ) 3

T. A. Savvas. N. C. Markatos. and C. D. Papaspyrides. On the ?ow of non-newtonian polymer solutions. Appl. Math. Modelling. 18 ( 1 ) :14–22. 1994 Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Glen

J. W. Glen. The weirdo of polycrystalline ice. Proc. R. Soc. A-Math. Phys. Eng. Sci. . 228 ( 1175 ) :519–538. 1955 µ ( T ) = ? |T? |n?1 Fits experimental informations for: ice ( 2. 11 )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Seely

Gilbert R. Seely. Non-newtonian viscousness of polybutadiene solutions. AIChE J. . 10 ( 1 ) :56–60. 1964 µ ( T ) = µ? + ( µ0 ? µ? ) e ? |T? |
?0

( 2. 12 )

Fits experimental informations for: polybutadiene solutions

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Blatter
Erin C. Pettit and Edwin D. Waddington. Ice ?ow at low deviatoric emphasis. J. Glaciol. . 49 ( 166 ) :359–369. 2003 H Blatter. Velocity and stress-?elds in grounded glaciers – a simple algorithm for including deviatoric emphasis gradients. J. Glaciol. . 41 ( 138 ) :333–344. 1995 µ ( T ) = 2

A |T? | +
2 ?0
n?1 2

( 2. 13 )

Fits experimental informations for: ice

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Shear dependent viscousness Models with force per unit area dependent viscousness Models with stress dependent viscousness Models with discontinuous rheology

Bingham Herschel–Bulkley
C. E. Bingham. Fluidity and malleability. McGraw–Hill. New York. 1922 Winslow H. Herschel and Ronald Bulkley. Konsistenzmessungen von Gummi-Benzoll?sungen. Colloid Polym. Sci. . 39 ( 4 ) :291–300. O August 1926 |T?
| & gt ; ? ? |T? | ? ? ? if and merely if T? = ? ? if and merely if D=0 D + 2µ ( |D| ) D |D|

( 2. 14 )

Fits experimental informations for: pigments. toothpaste. Mangifera indica jam
Santanu Basu and U. S. Shivhare. Rheological. textural. micro-structural and centripetal belongingss of Mangifera indica jam. J. Food Eng. . 100 ( 2 ) :357–365. 2010 Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Rivlin–Ericksen ?uids

Rivlin–Ericksen
R. S. Rivlin and J. L. Ericksen. Stress-deformation dealingss for isotropic stuffs. J. Ration. Mech. Anal. . 4:323–425. 1955 R. S. Rivlin and K. N. Sawyers. Nonlinear continuum mechanics of viscoelastic ?uids. Annu. Rev. Fluid Mech. . 3:117–146. 1971 General signifier: T = ?pI + degree Fahrenheit ( A1 A2 A3. . . ) ( 3. 1 ) where A1 = 2D dAn?1 + An?1 L + L An?1 An = dt ( 3. 2a ) ( 3. 2b )

vitamin D where dt denotes the usual Lagrangean clip derivative and L is the speed gradient. Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Rivlin–Ericksen ?uids

Criminale–Ericksen–Filbey

William O. Criminale. J. L. Ericksen. and G. L. Filbey. Steady shear ?ow of non-Newtonian ?uids. Arch. Rat. Mech. Anal. . 1:410–417. 1957 T = ?pI + ?1 A1 + ?2 A2 + ?3 A2 1 ( 3. 3 )

Fits experimental informations for: polymer thaws ( explains mormal emphasis di?erences )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Rivlin–Ericksen ?uids

Reiner–Rivlin

M. Reiner. A mathematical theory of dilatancy. Am. J. Math. . 67 ( 3 ) :350–362. 1945 T = ?pI + 2µD + µ1 D2 Fits experimental informations for: N/A ( 3. 4 )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Maxwell
J. Clerk Maxwell. On the dynamical theory of gases. Philos. Trans. R. Soc. . 157:49–88. 1867

T = ?pI + S S + ?1 S = 2µD diabetes mellitus ? LM ? ML dt Fits experimental informations for: N/A M =def Josef M?lek a Non-Newtonian ?uids

( 4. 1a ) ( 4. 1b )

( 4. 2 )

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Oldroyd-B

J. G. Oldroyd. On the preparation of rheological equations of province. Proc. R. Soc. A-Math. Phys. Eng. Sci. . 200 ( 1063 ) :523–541. 1950

T = ??I + S S + ?S = ?1 A1 + ?2 A1 Fits experimental informations for: N/A

( 4. 3a ) ( 4. 3b )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Oldroyd 8-constants
J. G. Oldroyd. On the preparation of rheological equations of province. Proc. R. Soc. A-Math. Phys. Eng. Sci. . 200 ( 1063 ) :523–541. 1950 T = ??I + S ?3 ?5 ?6 ( DS + SD ) + ( Tr S ) D + ( S: D ) I 2 2 2 ?7 ( D: D ) I = ?µ D + ?2 D + ?4 D2 + 2 ( 4. 4a )

S + ?1 S +

( 4. 4b )

Fits experimental informations for: N/A
Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Warren burgers
J. M. Burgers. Mechanical considerations – theoretical account systems – phenomenological theories of relaxation and viscousness. In First study on viscousness and malleability. chapter 1. pages 5–67. Nordemann Publishing. New York. 1939

T = ??I + S S + ?1 S + ?2 S = ?1 A1 + ?2 A1 Fits experimental informations for: N/A

( 4. 5a ) ( 4. 5b )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Giesekus
H. Giesekus. A simple constituent equation for polymer ?uids based on the construct of deformation-dependent tensorial mobility. J. Non-Newton. Fluid Mech. . 11 ( 1-2 ) :69–109. 1982

T = ??I + S S + ?S ? ??2 2 S = ?µD µ

( 4. 6a ) ( 4. 6b )

Fits experimental informations for: N/A

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Phan-Thien–Tanner
N. Phan Thien. Non-linear web viscoelastic theoretical account. J. Rheol. . 22 ( 3 ) :259–283. 1978 N. Phan Thien and Roger I. Tanner. A new constituent equation derived from web theory. J. Non-Newton. Fluid Mech. . 2 ( 4 ) :353–365. 1977

T = ??I + S Y S + ?S + ?? ( DS + SD ) = ?µD 2 Y =e Fits experimental informations for: N/A Josef M?lek a Non-Newtonian ?uids

( 4. 7a ) ( 4. 7b ) ( 4. 7c )

?? ? Tr S µ

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Johnson–Segalman
M. W. Johnson and D. Segalman. A theoretical account for viscoelastic ?uid behaviour which allows non-a?ne distortion. J. Non-Newton. Fluid Mech. . 2 ( 3 ) :255–270. 1977

T = ?pI + S ( 4. 8a ) S = 2µD + S ( 4. 8b ) S +? darmstadtium + S ( W ? ad ) + ( W ? ad ) S dt = 2?D ( 4. 8c )

Fits experimental informations for: jet
Josef M?lek a Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Maxwell. Oldroyd. Burgers Giesekus Phan-Thien–Tanner Johnson–Segalman Johnson–Tevaarwerk

Johnson–Tevaarwerk
K. L. Johnson and J. L. Tevaarwerk. Shear behavior of elastohydrodynamic oil ?lms. Proc. R. Soc. A-Math. Phys. Eng. Sci. . 356 ( 1685 ) :215–236. 1977

T = ?pI + S S S + ? sinh = 2µD s0 Fits experimental informations for: lubricators

( 4. 9a ) ( 4. 9b )

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

Kaye–Bernstein–Kearsley–Zapas

Kaye–Bernstein–Kearsley–Zapas
B. Bernstein. E. A. Kearsley. and L. J. Zapas. A survey of stress relaxation with ?nite strain. Trans. Soc. Rheol. . 7 ( 1 ) :391–410. 1963 I-Jen Chen and D. C. Bogue. Time-dependent emphasis in polymer thaws and reappraisal of viscoelastic theory. Trans. Soc. Rheol. . 16 ( 1 ) :59–78. 1972 T

T=
?=??

?W ?1 ?W C+ C d? ?I ?II

( 5. 1 )

Fits experimental informations for: polyisobutylene. cured gum elastic

Josef M?lek a

Non-Newtonian ?uids

Viscosity of some ?uids Models with variable viscousness Di?erential type theoretical accounts Rate type theoretical accounts Integral type theoretical accounts Download

rotter ringer [ electronic mail protected ]: non-newtonian-models git ringer [ electronic mail protected ]: bibliography-and-macros

Josef M?lek a

Non-Newtonian ?uids

Post Author: admin