PART 2 ELECTRORHEOLOGICAL SUSPENSIONS

ELECTRORHEOLOGICAL SUSPENSIONS

 SUMMARY – Review of electrorheological suspensions (ERS) – Classification of ERS – Mechanisms of the ER effect proposed by several researchers – potential applications – modelling

ELECTROACTIVE MATERIALS

 An electro-active material is a suspension where a semiconductive material (particulate or liquid) is dispersed in a dielectric liquid medium.

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

ELECTROACTIVE MATERIALS

 Since the rheological properties can be easily controlled within a wide range, many scientific and technological applications may be 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 APLICATIONS

 Clutch, brake and damping systems, actuators, fuel injections systems  Joints and hands of robotic arms  photonic crystals.

 Microswitches.

 Mechanical-electronic interfaces C. F.Zukoski, Annu.Rev.Matter.Sci.

23

(1993)45 T.C. Halsey Science

23

(1992) 761

Schematic illustration of structure change of ERS

Before an external electric field is applied Structure of an electrorheological material after an electric field is applied E

ERF Phenomena

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

+

Increase in Viscosity

Continue experimental 4. Estructural arrangement observations

Classification of Electrorheological Materials

ERF Liquid Phase Dispersed Phase Additive Liquid Solid Water Anhydrous Homogeneous Fluid Heterogeneous Fluid Liquid Crystalline Emulsion a Microemulsion Oxide Inorganic Non-Oxide Organic Polymeric

Experimental Characteristics of an Electrorheological fluid

Liquid Phase Particle ER Suspension Relative dielectric constant Conductivity (S/m) Viscosity at no electric field Pa.s

2 10 -10 to10 -16 0.01 to 10 2 to10000 10 -7 10 -9 to10 -16 0.1 to 10

CRITICAL PARAMETERS

 Electric Field Strength, E – two effects in competition for explain the changes in the yield stress,  y, after applying the electric field  Frequency of Electric Field,  – DC is mostly used to generate detectable ER effect – AC is used to study the ER mechanisms – ER effect is function of  through  and   Particle Conductivity,  – determines J and it peaks  at  o

CRITICAL PARAMETERS

 Particle Dielectric Property,  – the polarization depends on  .

– the electric double layer overlap is the reason – the dielectric constant changes with electrolytes  Particle Volume Fraction,  –  y and  depend on  , and exhibit a maximum – Percolation theory was used to understand this phenomenon

CRITICAL PARAMETERS

 Temperature – Changes the polarizability of ERF because changes  and  .

– Impact particle thermal motion  Liquid medium – sedimentation, viscosity, conductivity and permitivity of liquid causes pronounced differences for the ER effect.

 Water content

FORCES RELEVANT TO THE ER EFFECT

 After ER fluid is submitted to an electric field the particles should be polarized and appears a electrostatic force. However hydrodynamic, Brownian, van der Waals, DLVO and other forces act too.  Dimensionless groups that describe the relative importance of those forces. Eg.

– Mason, Mn = 6  /(  0  sm  E 2 ) – Peclet, Pe = 6  sm 

a

2  /kT

PHASE TRANSITION

 As increase the ERS changes from a disordered state to coexistence with a crystalline phase  Laser diffraction method and confocal scanning laser microscopy were employed to determine the crystal structure within fibrilated columns

POLARZATION PROCESS

 Four kinds of polarization exist – electronic – atomic – Debye – Interfacial  The dielectric constant is   D +  I =  E +  A +

Results

Rheological properties

Viscosity vs shear rate 10 4 10 3 10 2 10 1 10 0

SF-14 20 wt %

E = kV/mm 0.25

0.50

0.75

1.0 1.5 2.0 2.5 10 -1 10 -2 a 10 -1 10 0 10 1 Shear rate (s -1 ) 10 2 10 3 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2

SF-14 (A-1100) 20 wt %

E = kV/mm 0.25KV

0.5 KV 0.75KV

1.0 KV 1.5 KV 2.0 KV 2.5 KV 10 -1 10 0 10 1 Shear rate (s -1 ) 10 2 b 10 3

Shear stress vs shear rate Continue results

10 4 10 3 10 2 10 1 10 0 10 -1 10 -2

SF-14 20 wt %

10 -1 10 0 10 1 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 10 2 10 3 a 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2

SF-14 (A-1100) 20 wt %

10 -1 10 0 10 1 Shear rate (s -1 ) E = kV/mm 0.0 V 0.25 0.5 0.75

1.0 1.5 2.0 2.5 10 2 10 3 b

Model of ER suspensions

Bingham model  =  y +  plastic  .

Krieger-Dougherty  plastic =  0 [1  /  m ] – [ ] m  =  y +  0  .

[1  /  m ] – [ ] m J. W. Goodwin et.al. J Phys. Chem. B, 1997, 101, 1961-1967 L. Rejon. PhD Thesis, 1998, UNAM.

BKD Model

10 4

SF-14 (A1100) 20 wt %

10 3 2.5 Kv/mm 10 2 0.5 Kv/mm Experimental Model 10 1 10 -1 10 0 10 1 Shear rate (s -1 ) 10 2 10 3

Kinetic chain model. [ Martin, J.E.; Odinek, J. J. Rheol. 1995 ,

39

, 995].

   The kinetics of aggregation and fragmentation follows a phenomenological expression

dN dt

(

t

) 

N k

(

t

)   1 

N N

(

t

(

t

) 2 ) 2   maximum stable size of the chains N(t)max, max The aggregation process is induced by the dipolar forces and hence the kinetic constant k is given by 

k M



k

0

M

( 8  0 

f

 2

E

0 2 /  0 )

 This model predicts a viscosity proportional to the electric field squared and to inverse shear rate according to  3 6  

A rheological kinetic model for electrorheological suspensions    ´ (  ,

D

)    2

G

0  ´ (  ,

D

)

D

 ´(  ,

D

) 

A

 1  0

dA dt W F

 1  ( 1 

A

) 

k

0 ' (  0     :

D



A

)

W F



k

1 ' (  0 

E



A

)

W E W E



E



P

  0  2

E

2    

p

 ( 1   ) 

f

k

0 '  1 

k

2  0

k

0  2 

E

2

k

1 ' 

k

1 

dA



dt

( 1  

A

) 

k

0 1 (  0 

k

2 /   0    2

A

)  

E

: 2

D



k

1 (  0 / 

E



A

)  0  2 

E

2

 For weak electric fields and low shear rates, the viscosity grows slowly as a function of time with rate proportional to E*E. Under strong electric fields, the viscosity growth with time is exponential, and at long times the viscosity approaches the limit     0 ( 

E

/  0 )  

E

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

t c

  /

E

2

Strong flow limit

   1   0 2

bt

   Initially, the reference viscosity is the zero shear-rate viscosity. Asymptotic analysis of the model shows that at long times, for weak electric fields, the viscosity decreases with a rate proportional to 1/( )

t

whereas under strong electric fields, the viscosity is proportional to

E

 

t

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

Weak flow

  

E

 ( 1 

E

0  

k

1  0 

k

1  0   2  2 

E

2 )

E

2 

y



G

0 ( 1 

k

1  0  2 

E

2 )( 1   /  

k

2  0  2 

E

2 ) 

y

0 

G

0    

y

 

y

0

k

1

k

2   0  2 

E

2

Conductivity contributions to the electrorheological effect.

k

0 '  1 

k

2 ( 1 

k

3 

k

0

E

)  0  2 

E

2

k

1 '  

k

1 ( 1 

k

3 

E

)   

p

 ( 1   ) 

f

10000

A

1000 100 0 200 400 S100



=0.08

E (kV/mm) 0.5 1.0 1.5 600 time (s) 800 1000 1200

100000 10000 1000 100 10 0.0

Influence of electric field strength on ER response

0.5

1.0

E (kV/mm) 1.5

2.0

 Red  =0.03

 Black   =0.16

 Silicon 100 DOP  TCP  There are two effects in competition

100000 10000 1000 100 10

Influence of fraction of particles

0.0

on ER response

 Black E=0.5

 Red E=1.0

 Green E=1.5

 Blue E=2.0  Silicon 100  DOP  TCP

0.1



Comparison between experimental data and model

10 3

Comparison between experimental data and model

10 2 = 0.03

S100, R 2 = 0.99

DOP, R 2 = 0.96

TCP, R 2 = 0.97

10 1 10 0 10 -2



E 2 10 -1

Comparison between experimental data and model

10 2 = 0.03

S100, R 2 = 0.99

DOP, R 2 = 0.96

TCP, R 2 = 0.97

10 1 10 0 10 -2



E 2 10 -1