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

- 467 Downloads
- 5 Citations

## 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.

## References

- 2011/696/EU (2011) RECOMMENDATIONS COMMISSION RECOMMENDATION of 18 October 2011 on the definition of nanomaterial (Text with EEA relevance). Off J Eur Union L 275/238Google Scholar
- Abbott M (1966) An introduction to the method of characteristics. American Elsevier, New yorkGoogle Scholar
- Andreotti B, Forterre Y, Pouliquen O (2011) Les milieux granulaires: entre fluide et solide. EDP SciencesGoogle Scholar
- Bakhtiyarov SI, Overfelt RA, Reddy S (1996) Study of the apparent viscosity of fluidized sand. In: Siginer DAA, Advani SG (eds) 1996. Proceedings in Rheology and Fluid Mechanics of Nonlinear Materials. ASME International Mechanical Engineering Congress, New York, United Engineering Center, pp 243–249Google Scholar
- Barnes HA, Nguyen QD (2001) Rotating vane rheometry—a review. J Non Newton Fluid Mech 98(1):1–14CrossRefGoogle Scholar
- Barois-Cazenave A, Marchal P, Falk V, Choplin L (1999) Experimental study of powder rheological behaviour. Powder Technol 103(1):58–64CrossRefGoogle Scholar
- Bouillard JX, Gidaspow D (1991) On the origin of bubbles and Geldart’s classification. Powder Technol 68(1):13–22CrossRefGoogle Scholar
- Bouillard JX, Lyczkowski RW, Gidaspow D (1989) Porosity distribution in a fluidized bed with an immersed obstacle. AIChE 35:908–972Google Scholar
- Bouillard J, Vignes A, Dufaud O, Perrin L, Thomas D (2010) Ignition and explosion risks of nanopowders. J Hazard Mater 181(1–3):873–880Google Scholar
- Bruni G, Colafigli A, Lettieri P, Elson T (2005) Torque measurements in aerated powders using a mechanically stirred fluidized bed rheometer (msFBR). Chem Eng Res Des 83(11):1311–1318Google Scholar
- Bruni G, Barletta D, Poletto M, Lettieri P (2007) A rheological model for the flowability of aerated fine powders. Chem Eng Sci 62:397–407Google Scholar
- Daniel RC, Poloski AP, SÃ¡ez AE (2008) Vane rheology of cohesionless glass beads. Powder Technol 181(3):237–248Google Scholar
- ECHA (2012a) Guidance on Information requirements and chemical safety assessment—Appendix R8-15: recommendations for nanomaterials applicable to chapter R8 Characterisation of dose (concentration) response for human healthGoogle Scholar
- ECHA (2012b) Guidance on information requirements and chemical safety assessment: Appendix R14-4: recommendations for nanomaterials applicable to chapter R.14: Occupational Exposure estimationGoogle Scholar
- Geldart D (1973) Types of gas fluidization. Powder Technol 7:285–292Google Scholar
- Gidaspow D (1994) Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic Press, New YorkGoogle Scholar
- Heirman G, Hendrickx R, Vandewalle L, Van Gemert D, Feys D, De Schutter G, Desmet B, Vantomme J (2009) Integration approach of the Couette inverse problem of powder type self-compacting concrete in a wide-gap concentric cylinder rheometer: Part II. Influence of mineral additions and chemical admixtures on the shear thickening flow behaviour. Cem Concr Res 39(3):171–181Google Scholar
- Henry F (2013) Dynamique des systèmes nanodispersés: application au cas de l’agglomération des nanoparticules. Thesis in Chemical Engineering, Institut Polytechnique de Loraine, France, NancyGoogle Scholar
- Henry F, Bouillard J, Marchal P, Vignes A, Dufaud O, Perrin L (2013) Exploring a new method to study the agglomeration of powders: application to nanopowders. Powder Technol 250:13–20. doi: 10.1016/j.powtec.2013.08.010 Google Scholar
- ISO/TS-27687 (2008) International standards organization, nanotechnologies—terminology and definitions for nano-objects: nanoparticle, nanofibre and nanoplateGoogle Scholar
- Jenike AW (1987) A theory of flow of particulate solids in converging and diverging channels based on a conical yield function. Powder Technol 50(3):229–236. doi: 10.1016/0032-5910(87)80068-2 Google Scholar
- Johanson JR (1964) Stress and velocity fields in the gravity flow of bulk solids. J Appl Mech 31(3):499–506. doi: 10.1115/1.362966 Google Scholar
- Linsinger TR, Guilland D, Calzolai L, Rossi F, Gibson N, Klein C (2012) JRC reference report: requirement on measurements for the implementation of the European Commission definition on the term “Nanomaterial”. Institute o = for reference materials and measurementsGoogle Scholar
- Lochmann KOL, Stoyan D (2006) Statistical analysis of random sphere packings with variable radius distribution. Solid States Sci 8:1397–1413Google Scholar
- Lun CKK, Savage SB, Jeffrey DJ, Chepurnity N (1984) Kinetic theory for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J Fluid Mech 140:223–235Google Scholar
- Makkawi YW, Ocone R (2004) Comparative analysis of experimental and modelling of gas-solid flow hydrodynamics: effect of friction and interparticle cohesion forces. In: AICHE Proceedings, 2004Google Scholar
- Marchal PCL (2004) Eléments de physique statistique appliqués à la rhéologie des milieu granulaires non cohésifs: le modèle du château de sables mouvants. Rhéologie 5:10–26Google Scholar
- Marchal PSN, Choplin L (2009) Rheology of dense-phase vibrated powders and molecular analogies. J Rheol 53:1–29Google Scholar
- Marchal PC, Choplin L, Smirani N (2005) System and method for rheological characterization of granular materials. USA PatentGoogle Scholar
- Mewis J, Wagner NJ (2012) Colloidal suspension rheology. Cambridge University Press, CambridgeGoogle Scholar
- REACH (2006) REGULATION (EC) No 1907/2006 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 18 December 2006 concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH), establishing a European Chemicals Agency, amending Directive 1999/45/EC and repealing Council Regulation (EEC) No 793/93 and Commission Regulation (EC) No 1488/94 as well as Council Directive 76/769/EEC and Commission Directives 91/155/EEC, 93/67/EEC, 93/105/EC and 2000/21/ECGoogle Scholar
- Savage SB, Jeffrey DJ (1981) The stress tensor in a granular flow at high shear rates. J Fluid Mech 110:255–272Google Scholar
- Sokolovskii SB (1965) Statitics of granular media. Pergamon Press, Oxford, UKGoogle Scholar
- Tsardaka KDJER (1993) Apparent viscosity of particulate solids determined using creep analysis. Powder Technol 76:221–224Google Scholar