Rheologica Acta

, Volume 48, Issue 7, pp 755–768 | Cite as

Combined slit and plate–plate magnetorheometry of a magnetorheological fluid (MRF) and parameterization using the Casson model

Original Contribution

Abstract

We describe a magneto-slit die of 0.34 mm height and 4.25 mm width attached to a commercial piston capillary rheometer, enabling the measurement of apparent flow curves of a magnetorheological fluid (MRF) in the high shear rate regime (apparent shear rates 276 up to 20,700 s − 1, magnetic flux density up to 300 mT). The pressure gradient in the magnetized slit is measured via two pressure holes. While the flux density versus coil current without MRF could directly be measured by means of a Hall probe, the flux density with MRF was investigated by finite element simulations using Maxwell® 2D. The true shear stress versus shear rate is obtained by means of the Weissenberg–Rabinowitsch correction. The slit die results are compared to plate–plate measurements performed in a shear rate regime of 0.46 up to 210 s − 1. It is shown that the Casson model yields a pertinent fit of the true shear stress versus shear rate data from plate–plate geometry. Finally, a joint fit of the slit and plate–plate data covering a shear rate range of 1 up to 50,000 s − 1 is presented, again using the Casson model. The parameterization of the MRF behavior over the full shear rate regime investigated is of relevance for the design of MR devices, like, e.g., automotive dampers. In the Appendix, we demonstrate the drawbacks of the Bingham model in describing the same data. We also show the parameterization of the flow curves by applying the Herschel–Bulkley model.

Keywords

Magnetorheological fluid (MRF) Slit magnetorheometer Flux density field Plate–plate magnetorheometer True flow curve Casson model Bingham model 

List of symbols

A, C, D

Parameters of fit function

B

Magnetic flux density in MRF

B0

Magnetic flux density without sample

cP

Specific heat

H

Slit height

h

Plate–plate gap

I

Solenoid current

k

Herschel–Bulkley parameter

L

Slit length

LY

Length of yokes

m

Slope of log–log apparent flow curve (plate–plate)

M

Torque

n

Slope of log–log apparent flow curve (slit)

p1, p2

Pressure readings (slit)

R

Plate radius

r

Radius coordinate

RP

Piston radius

Tad

Adiabatic temperature increase

v

Piston speed

\(\overline v \)

Average velocity

\(\dot{V}\)

Volumetric flow rate

W

Slit width

y

Lateral slit coordinate

z

Downstream coordinate

Δp

Pressure gradient in slit

Δx

Gap between the yokes

Δt

Residence time in slit

ρ

Sample density

\(\dot {\varphi }\)

Angular velocity

\(\dot {\gamma }\)

True shear rate

\(\dot {\gamma }_{\rm R} \)

Rim shear rate (plate–plate)

\(\dot {\gamma }_{\rm W} \)

Wall shear rate (slit)

\(\dot {\gamma }_{\rm a} \)

Apparent (rim or wall) shear rate

η0

Newtonian viscosity

ηB

Bingham viscosity

ηC

Casson viscosity

τ

True shear stress

τR

Rim shear stress (plate–plate)

τW

Wall shear stress (slit)

τC

Casson yield stress

τH

Herschel–Bulkley yield stress

τy

Bingham yield stress

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.LudwigshafenGermany

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