# Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

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## Abstract

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.

## Keywords

Wall slip Shear thickening fluid Parallel plate rheometry## Nomenclature

*C*_{v}Volume fraction (%)

*C*_{w}Weight fraction (%)

*h*Plate separation (m)

*k*Consistency coefficient (Pa s

^{n})*n*Flow behaviour index (-)

*r*Radial position (m)

*R*Radius of plate (m)

*T*Torque (Nm)

*u*Velocity (m s

^{−1})*V*_{s}Slip velocity (m s

^{−1})*z*Vertical displacement (m)

- α
Coefficient in slip equation (m Pa

^{−β}s^{−1})- β
Index in slip equation (-)

- \(\ifmmode\expandafter\dot\else\expandafter\.\fi{\gamma}\)
Shear rate (s

^{−1})- \(\ifmmode\expandafter\dot\else\expandafter\.\fi{\gamma}_{a}\)
Apparent shear rate (s

^{−1})- η
Viscosity (Pas)

- τ
Shear stress (Pa)

- τ
_{y} Yield stress (Pa)

- ω
Angular velocity (rad s

^{−1})- θ
Angular displacement (rad)

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