# Rheology of powders and nanopowders through the use of a Couette four-bladed vane rheometer: flowability, cohesion energy, agglomerates and dustiness

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## Abstract

A new four-bladed vane powder rheometer is proposed to study powder and nanopowder rheology at low and high shear rates. As shear rates increase, the powder flow will evolve from a Newtonian regime (low shear rates) to a Coulombic regime (moderate shear rates) and then to a kinetic regime (high shear rates) at which the powder may become self-fluidized because of intense particles collisions. Viscosity measurements of noncohesive glass beads at low shear rates (Newtonian and Coulombic regimes) do not strongly depend upon the particle size and can reach values much larger than commonly used viscosities in some CFDs models. Since, in the kinetic regime, the shear stress is a strong function of the particle size, agglomerate particle size of cohesive powders can be directly inferred from rheograms. Cohesive carbon black and silica nanopowders have been tested and compared to noncohesive glass beads microparticles, chosen as reference. For noncohesive glass bead micropowders, the “agglomerate” diameter average values found from rheological measurements are of the same order of magnitude as the primary diameters of the powder. This indicates that the kinetic theory of granular flows describes well these high shear rate regimes and that such theory can be used to estimate agglomerate diameters. It is also found that estimated agglomerate sizes of nanometric cohesive materials can reach sizes of hundred micrometers depending upon their cohesion strength. Such agglomerate size measurements have been corroborated with those made by microscopy.

## Keywords

Nanopowder Rheology Nanosafety Cohesion energy Agglomerates Viscosity Dustiness## List of symbols

*C*Torque (N m)

*d*_{agg}Agglomerate diameter (m)

*d*_{p}Primary particle diameter (m)

*D*_{f}Fractal dimension

*E*_{v}Energy of the vibrations (J)

*F*Frequency of the vibrations (Hz)

*G*Powder elasticity (Pa)

*k*_{f}Structure factor of the agglomerate

*k*_{g}Structural coefficient

*K*_{σ}Couette-analogy stress coefficient

*K*_{γ}Couette-analogy rate coefficient

*M*Mass of powder in the cell (kg)

*m*_{b}Mass of sheared powder (kg)

*n*_{agg}Number of particles in an agglomerate

*n*_{b}Total number of particles in the powder

*V*_{agg}Agglomerate volume (m

^{3})*V*_{b}Volume of the shearing cell (m

^{3})*h*Mean height of powder in the cell (m)

## Greek symbols

*α*Angle of repose

*ɛ*_{sint}Inner solids volume fraction of the agglomerate

*ɛ*_{s}Total solids volume fraction of the powder

*ɛ*_{smax}Maximum packing solids volume fraction of the powder

- \(\dot{\gamma }\)
Shear rate (s

^{−1})- \(\dot{\gamma }_{\text{c}}\)
Critical shear rate (s

^{−1}) in Eq. 3- \(\dot{\gamma }_{t}\)
Transition shear rate between the Coulombic and the kinetic regime (s

^{−1}) in Eq. 4- \(\dot{\gamma }_{ \hbox{max} }\)
Maximal shear rate delivered by the rheometer (s

^{−1})*Γ*_{agg}Agglomeration stress (Pa)

*Γ*_{c}Cohesion stress (Pa)

*Η*Powder viscosity (Pa s)

*η*_{0}Constant viscosity in Newtonian state (Pa s)

*μ*Viscosity, Coefficient of friction

- Θ
Amplitude of the vibrations (m)

*θ*Internal friction angle

*ρ*_{p}Density of the particles (kg m

^{−3})*ρ*_{b}Bulk density (kg m

^{−3})*σ*Shear stress (Pa)

*σ*_{f}Transition shear stress in Coulombic/kinetic regime (Pa)

- \(\dot{\varOmega }\)
Rheometer angular rate (s

^{−1})- \(\dot{\varOmega }_{ \hbox{max} }\)
Rheometer maximal angular rate delivered (s

^{−1})

## Notes

### Acknowledgments

This work has been performed within the French research program P190 funded by the French Ministry of Ecology and Sustained Development. We thank L. Perrin and O. Dufaud of the LRGP for constructive advices concerning this work.

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