Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Primary Normal StressDifferences in Magnetic Inks

Meihua Piao and John M. WiestDepartment of Chemical Engineering

Magnetic inks (dispersions of acicular ferromagnetic particles in a solvent with an anti-flocculating polymer) are coated onto a flexible substrate in the manufacture of magnetic tape.

The inks are non-Newtonian and viscoelastic, and their rheology plays a fundamental role in coating operations. It is also a sensitive indicator of dispersion structure and quality.

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

vx = Ý γ (t)y

Shear Flow

Steady Inception

Ý γ = constant

η = −τ xy Ý γ

Ψ1 = −(τ xx −τ yy ) Ý γ 2

Ψ2 = −(τ yy −τ zz ) Ý γ 2

Ý γ = Ý γ 0H(t)

η+ = −τ xy Ý γ 0

Ψ1+ = −(τ xx −τ yy) Ý γ 0

2

Ψ2+ = −(τ yy −τ zz) Ý γ 0

2

Friction

Tension along streamlines

Tension across streamlines

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

MaterialsDispersions were prepared containing cyclohexanone as a solvent, a commercial binderpolymer (Nippon Zeon Co. MR110), and metal particles (MP) The particles areprimarily iron with saturation magnetization of 750-900 e mu/cc, coercivity 1300-2200Oe, specific surface are 42 m2/g, length 200nm, aspect ratio (L/d) 8, and dens ity 5.7cm3.The MR110 bind er polymer is a PVC-acetate copolymer commonly used in magneticdispersions. It has 0.7 wt% sulfonic acid groups, 0.6 wt% hydroxyl groups, and 3.0 w t%of an epoxy component. Its weight average molecular weight is 26,000, and its numberaverage molecular weight is 12,000.

Steady shear and inception of shear flow measurements on the dispersions wereperformed on an ARES controlled strain rheometer using a cone and plate geometry(50 mm diameter, 0.04 rad. cone angle). The viscosity of the supernatants wasmeasured using a Carri-MED controlled stress rheometer (60 mm diameter, 1 degreecone angle).

0.00543.2MP3.2

0.00583.9MP3.9

0.00584.4MP4.4

0.00664.8MP4.8

ηs(Pa s)φ (%)Sample

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

0.00001

0.001

0.1

10

1000

100000

10000000

1000000000

0.001 0.01 0.1 1 10 100 1000

MP4.8MP4.4MP3.9MP3.2

Ý γ (s-1)

0.01

0.1

1

10

100

1000

10000

100000

0.001 0.01 0.1 1 10 100 1000

MP4.8MP4.4MP3.9MP3.2

Ý γ (s-1)

Shear thinning in viscosity a consequence of network reformation time being greater than characteristic time of flow.

The network is weaker, but re-forms more rapidly, at lower particle volume fractions.

Steady Shear Flow

Shear thinning in first normal stress differencea consequence of network reformation time being greater than characteristic time of flow.

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Inception of Shear Flow

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16t(s)

MP4.8MP4.4MP3.9MP3.2

Ý γ =1s−1

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Inception of Shear Flow

φ = 0.044

Ý γ 0

0.0

0.5

1.0

1.5

2.0

2.5

0.01 0.1 1 10 100 1000 10000

t(s)

10 (1/s)1 (1/s)0.1 (1/s)0.01 (1/s)

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

shear strain

φ = 0.044

Ý γ 0

0.0

0.5

1.0

1.5

2.0

2.5

0.01 0.1 1 10 100

10/s1/s0.1/s0.01/s

= Ý γ 0t

Inception of Shear Flow

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Inception of Shear Flow

0

50

100

150

200

250

0.1 1 10 100 1000

MP4.8MP4.4MP3.9MP3.2

t(s)

Ý γ =1s−1

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Inception of Shear Flow

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.01 0.1 1 10 100 1000

10/s1/s0.1/s0.01/s

t(s)

Ý γ 0

φ = 0.044

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Inception of Shear Flow

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.01 0.1 1 10 100 1000

10/s1/s0.1/s0.01/s

Ý γ 0

strain

φ = 0.044

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

Observations

• Stress overshoot in both viscosity and normalstress coefficient; more pronounced at higher particle loading.

• Inflection points in stress growth functions prior to overshoots.

• Overshoot in normal stress occurs after the overshoot in the shear stress.

• Inflection point in normal stress occurs after the overshoot in the shear stress.

Center For Materials For Information TechnologyAn NSF Materials Research Science and Engineering CenterTHE UNIVERSITY OF ALABAMA

An Explanation

Inter-floc links in the velocity gradient direction break (inflection point in viscosity) and the flocs arrange into loose planes (inflection point in normal stress coefficient).

small time

intermediate time

long time

Flocs deform into the shear planes (viscosity overshoot). Flocs then rearrange in shear planes (normal stress coefficient overshoot).