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


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.


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


Magnetic flux density in MRF


Magnetic flux density without sample


Specific heat


Slit height


Plate–plate gap


Solenoid current


Herschel–Bulkley parameter


Slit length


Length of yokes


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




Slope of log–log apparent flow curve (slit)

p1, p2

Pressure readings (slit)


Plate radius


Radius coordinate


Piston radius


Adiabatic temperature increase


Piston speed

\(\overline v \)

Average velocity


Volumetric flow rate


Slit width


Lateral slit coordinate


Downstream coordinate


Pressure gradient in slit


Gap between the yokes


Residence time in slit


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


Newtonian viscosity


Bingham viscosity


Casson viscosity


True shear stress


Rim shear stress (plate–plate)


Wall shear stress (slit)


Casson yield stress


Herschel–Bulkley yield stress


Bingham yield stress


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.LudwigshafenGermany

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