PART 2 PART 2 ELECTRORHEOLOGICAL ELECTRORHEOLOGICAL

SUSPENSIONSSUSPENSIONS

ELECTRORHEOLOGICAL ELECTRORHEOLOGICAL SUSPENSIONSSUSPENSIONS

SUMMARYSUMMARY– Review of electrorheological Review of electrorheological

suspensions (ERS)suspensions (ERS)– Classification of ERSClassification of ERS– Mechanisms of the ER effect proposed Mechanisms of the ER effect proposed

by several researchersby several researchers– potential applicationspotential applications– modellingmodelling

ELECTROACTIVE MATERIALSELECTROACTIVE MATERIALSAn electro-active material is a An electro-active material is a

suspension where a semiconductive suspension where a semiconductive material (particulate or liquid) is material (particulate or liquid) is dispersed in a dielectric liquid dispersed in a dielectric liquid medium.medium.

The rheological properties change in The rheological properties change in reversible form by several orders of reversible form by several orders of magnitude under external electric magnitude under external electric fields.fields.

ELECTROACTIVE MATERIALSELECTROACTIVE MATERIALS Since the rheological properties can Since the rheological properties can

be easily controlled within a wide be easily controlled within a wide range, many scientific and range, many scientific and technological applications may be technological applications may be developed.developed.

T. Hao , Adv. Colloid Interface Sci. 1-35, 97 (2002)H. Block, J.P. Kelley, J. Phys. D, 1661, 21(1988)A. P. Gast, C. F.Zukoski,Adv. Colloid Interface Sci.153,30(1989)T.C. Halsey Science 761,23(1992)

POTENTIAL APLICATIONSPOTENTIAL APLICATIONSClutch, brake and damping systems, Clutch, brake and damping systems,

actuators, fuel injections systemsactuators, fuel injections systems Joints and hands of robotic armsJoints and hands of robotic arms photonic crystals.photonic crystals.Microswitches.Microswitches.Mechanical-electronic Mechanical-electronic interfacesinterfaces

C. F.Zukoski, Annu.Rev.Matter.Sci.23(1993)45T.C. Halsey Science 23(1992) 761

Schematic illustration of structure Schematic illustration of structure change of ERSchange of ERS

E

Before an external electric field is applied

Structure of an electrorheological material after an electric field is applied

ERF PhenomenaERF Phenomena

Without Electric Field With Electric field (E)DC ó AC

E

+

-

Increase in Viscosity

Continue Continue experimentalexperimental

4. Estructural arrangement observations

Classification of Electrorheological MaterialsClassification of Electrorheological MaterialsERF

Liquid Phase

Additive

Water Anhydrous

Dispersed Phase

Liquid

Homogeneous Fluid

Liquid Crystalline Emulsion

a

Microemulsion

Solid

Heterogeneous Fluid

Inorganic

Oxide Non-Oxide

Organic

Polymeric

Experimental CharacteristicsExperimental Characteristicsof an Electrorheological fluidof an Electrorheological fluid

Liquid Phase Particle ERSuspension

Relative dielectricconstant

2 2to10000

Conductivity (S/m) 10 -10 to10 -16 10 -7 10 -9 to10 -16

Viscosity atno electric field Pa.s

0.01 to 10 0.1 to 10

CRITICAL PARAMETERSCRITICAL PARAMETERS Electric Field Strength, EElectric Field Strength, E

– two effects in competition for explain the changes two effects in competition for explain the changes in the yield stress, in the yield stress, y,y, after applying the electric after applying the electric field field

Frequency of Electric Field, Frequency of Electric Field, – DC is mostly used to generate detectable ER effectDC is mostly used to generate detectable ER effect– AC is used to study the ER mechanismsAC is used to study the ER mechanisms– ER effect is function of ER effect is function of through through and and

Particle Conductivity, Particle Conductivity, – determines determines JJ and it peaks and it peaks yy at at o o

CRITICAL PARAMETERSCRITICAL PARAMETERS Particle Dielectric Property,Particle Dielectric Property,

– the polarization depends on the polarization depends on ..– the electric double layer overlap is the reasonthe electric double layer overlap is the reason– the dielectric constant changes with the dielectric constant changes with

electrolyteselectrolytes Particle Volume Fraction, Particle Volume Fraction, yy and and depend on depend on , and exhibit a maximum, and exhibit a maximum– Percolation theory was used to understand Percolation theory was used to understand

this phenomenonthis phenomenon

CRITICAL PARAMETERSCRITICAL PARAMETERS TemperatureTemperature

– Changes the polarizability of ERF Changes the polarizability of ERF because changes because changes and and ..

– Impact particle thermal motionImpact particle thermal motion Liquid mediumLiquid medium

– sedimentation, viscosity, conductivity sedimentation, viscosity, conductivity and permitivity of liquid causes and permitivity of liquid causes pronounced differences for the ER effect.pronounced differences for the ER effect.

Water content Water content

FORCES RELEVANT TO THE FORCES RELEVANT TO THE ER EFFECTER EFFECT

After ER fluid is submitted to an electric After ER fluid is submitted to an electric field the particles should be polarized field the particles should be polarized and appears a electrostatic force. and appears a electrostatic force. However hydrodynamic, Brownian, van However hydrodynamic, Brownian, van der Waals, DLVO and other forces act der Waals, DLVO and other forces act too. too.

Dimensionless groups that describe the Dimensionless groups that describe the relative importance of those forces. Eg.relative importance of those forces. Eg.– Mason, Mn = 6Mason, Mn = 6/(/(00smsmEE22))– Peclet, Pe = 6Peclet, Pe = 6smsmaa22/kT/kT

PHASE TRANSITIONPHASE TRANSITION

As increase the ERS changes from a As increase the ERS changes from a disordered state to coexistence with a disordered state to coexistence with a crystalline phasecrystalline phase

Laser diffraction method and confocal Laser diffraction method and confocal scanning laser microscopy were scanning laser microscopy were employed to determine the crystal employed to determine the crystal structure within fibrilated columns structure within fibrilated columns

POLARZATION PROCESSPOLARZATION PROCESS

Four kinds of polarization existFour kinds of polarization exist– electronicelectronic– atomicatomic– DebyeDebye– InterfacialInterfacial

The dielectric constant is The dielectric constant is = = E E + + AA + + DD + + II

ResultsResultsRheological propertiesViscosity vs shear rate

ba10-2 10-1 100 101 102 10310-1

100

101

102

103

104

SF-14 (A-1100) 20 wt %

Rel

ativ

e vi

scos

ity

Shear rate (s-1)

E = kV/mm 0.25KV 0.5 KV 0.75KV 1.0 KV 1.5 KV 2.0 KV 2.5 KV

10-2 10-1 100 101 102 10310-1

100

101

102

103

104

SF-14 20 wt %

Rel

ativ

e vi

scos

ity

Shear rate (s-1)

E = kV/mm 0.25 0.50 0.75 1.0 1.5 2.0 2.5

Continue Continue resultsresults

Shear stress vs shear rate

b

10-2 10-1 100 101 102 10310-1

100

101

102

103

104

SF-14 20 wt %

(P

a)

Shear rate (s-1)

E = kV/mm 0.O KV 0.25KV 0.5 KV 0.75KV 1.0 KV 1.5 KV 2.0 KV 2.5 KV

a

10-2 10-1 100 101 102 10310-1

100

101

102

103

104

SF-14 (A-1100) 20 wt %

(P

a)

Shear rate (s-1)

E = kV/mm 0.0 V 0.25 0.5 0.75 1.0 1.5 2.0 2.5

Model of ER suspensionsModel of ER suspensions

= y + plastic

plastic = 0 [1- /m]

Bingham model

Krieger-Dougherty

= y + 0 [1- /m]

.

– [m

J. W. Goodwin et.al. J Phys. Chem. B, 1997, 101, 1961-1967L. Rejon. PhD Thesis, 1998, UNAM.

– [m

.

BKD ModelBKD Model

10-1 100 101 102 103101

102

103

104

2.5 Kv/mm

0.5 Kv/mm

SF-14 (A1100) 20 wt %

(P

a)

Shear rate (s-1)

Experimental Model

Kinetic chain model. [ Martin, J.E.; Kinetic chain model. [ Martin, J.E.; Odinek, J. Odinek, J. J. Rheol. J. Rheol. 19951995, , 3939, 995]., 995]. The kinetics of aggregation and The kinetics of aggregation and

fragmentation follows a fragmentation follows a phenomenological expressionphenomenological expression

The aggregation process is induced The aggregation process is induced

by the dipolar forces and hence the by the dipolar forces and hence the kinetic constant kinetic constant k k is given byis given by

max2

2

)()(1

)()(

tNtN

tNk

dttdN

)/8( 02

02

00 Ekk fMM

maximum stable size of the chains N(t)max,

This model predicts a viscosity This model predicts a viscosity proportional to the electric field proportional to the electric field squared and to inverse shear rate squared and to inverse shear rate according toaccording to

is the volume fraction of particlesis the volume fraction of particles1

20

2010

63

Ef

A rheological kinetic model for A rheological kinetic model for electrorheological suspensionselectrorheological suspensions

DDGD ),(2),( ´0

´

01),´( AD

EE

F WAkWAkAdtdA )()()1(1 0'

10'

0

DWF :

220 EPEWE

fp )1(

2202

0'0 1 Ek

kk

1'

1 kk

2200122

02

00 )/(1

:)/()1( EAkEkDAkA

dtdA

E

For weak electric fields and low shear rates, the For weak electric fields and low shear rates, the viscosity grows slowly as a function of time with viscosity grows slowly as a function of time with rate proportional to rate proportional to E*EE*E. Under strong electric . Under strong electric fields, the viscosity growth with time is fields, the viscosity growth with time is exponential, and at long times the viscosity exponential, and at long times the viscosity approaches the limitapproaches the limit

At short times and in the case where , the model At short times and in the case where , the model gives the proportionality of the characteristic time gives the proportionality of the characteristic time for structure formation with the viscosity and for structure formation with the viscosity and electric field, i.e.,.electric field, i.e.,.

EE )/( 00

2/ Etc

Strong flow limitStrong flow limit

Initially, the reference viscosity is the zero Initially, the reference viscosity is the zero shear-rate viscosity. Asymptotic analysis of the shear-rate viscosity. Asymptotic analysis of the model shows that at long times, for weak model shows that at long times, for weak electric fields, the viscosity decreases with a electric fields, the viscosity decreases with a rate proportional torate proportional to

1/( )1/( ) whereas under strong electric fields, the whereas under strong electric fields, the

viscosity is proportional to viscosity is proportional to

In the latter case, the ratio of the electric field In the latter case, the ratio of the electric field to the shear rate controls the viscosity to the shear rate controls the viscosity decrease with time.decrease with time.

bt210

t

t

E

Weak flowWeak flow

2201

0

2201 )1(

Ek

EkE

E

/

)1)(1( 2202

2201

0EkEk

Gy

00 Gy

220210 Ekkyy

Conductivity contributions to the Conductivity contributions to the electrorheological effect.electrorheological effect.

22032

0'0 )1(1 EEkk

kk

)1( 31'1 Ekkk

fp )1(

0 200 400 600 800 1000 1200100

1000

10000

r

time (s)

S100=0.08E (kV/mm)

0.5 1.0 1.5

A

Influence of electric field Influence of electric field strength on ER responsestrength on ER response

0.0 0.5 1.0 1.5 2.0

10

100

1000

10000

100000

(E

)

E (kV/mm)

Red Red =0.03=0.03Black Black =0.16 =0.16 Silicon 100 Silicon 100 DOP DOP TCP TCP

There are There are two effects in two effects in competition competition

Influence of fraction of particles Influence of fraction of particles on ER responseon ER response

Black E=0.5Black E=0.5Red E=1.0Red E=1.0Green Green

E=1.5E=1.5Blue E=2.0 Blue E=2.0

Silicon Silicon 100 100 DOP DOP TCP TCP

0.0 0.1

10

100

1000

10000

100000

(E

)

Comparison between Comparison between experimental data and model experimental data and model

predictionspredictions

10-6 1x10-51x10-4 10-3 10-2 10-1 100 101 102 103

100

101

102

103

p/

L = 1 x 106

S100, = 0.03

E = kV/mm 0.5 1.5 2.0

L

Mn

Comparison between Comparison between experimental data and model experimental data and model

predictionspredictions

10-2 10-1100

101

102

= 0.03S100, R2 = 0.99DOP, R2 = 0.96TCP, R2 = 0.97

Yiel

d st

ress

(Pa)

E2

Comparison between Comparison between experimental data and model experimental data and model

predictionspredictions

10-2 10-1100

101

102

= 0.03S100, R2 = 0.99DOP, R2 = 0.96TCP, R2 = 0.97

Yiel

d st

ress

(Pa)

E2