(409d) Shear-Induced Dilation of Constrained Consolidated Powder Beds | AIChE

(409d) Shear-Induced Dilation of Constrained Consolidated Powder Beds


Thomas, A. - Presenter, Freeman Technology
Thornton, T., Micromeritics
Brockbank, K., Freeman Technology
Clayton, J., Freeman Technology Ltd
Dilatancy, the phenomenon by which compacted dense granular materials, including powders expand when sheared was first observed by Reynold [1] in 1885. This phenomenon is attributed to the formation of stress chains, consisting of interlocking particles, which rotate during shear, resulting in the expansion of the powder bed [2]. Whilst this behaviour is well recognised, the bulk of scientific investigation on dilatancy has been conducted from a viewpoint of soil (and sand) mechanics rather than powders, as such these consider dilatancy at significantly higher consolidation loads then those routinely encountering during powder handling [3, 4].

The limited studies on powder bed dilatancy have primary used Discrete Element Method (DEM) models or similar [5-7]. Based on these studies, alongside some experimental work, it is generally accepted the particle size will affect the degree of bed expansion during shear, with larger particles resulting in increased dilation [8-10].

Other studies have focused on the impact of inter-particular friction on dilatancy, as this will influence the ability of the powder to from stable stress chains. Again, there is general agreement that increasing inter-particular friction will increase bed dilation [5, 6, 11].

Finally, the impact of Applied Normal Load (ANL) has also been investigated, however the results are conflicting, with several studies showing that the ANL has little to no effect, while other studies have demonstrated a link between Applied Load and dilatancy [8, 12].

Interestingly, the majority of these studies have not considered constrained systems where there is limited or no free volume for the powder to expand into. Therefore, the main aim of this study was to investigate the impact of the ANL on powder bed dilation in constrained systems. Further to this, the impact of particle size and powder flow properties were also investigated.

Using a modified shear cell test, Calcium Carbonate samples (Eskal 500 to Eskal 150) were critically consolidated at ANL values ranging from 0.25kPa up to 20kPa. The ANL was then reduced to 0.01kPa and the powder bed sheared at constant volume. The resultant Generated Normal Stress (GNS) and Shear Stress (SS) values were recorded, alongside changes in the bulk density. Flow properties (Dynamic Flow, Aeration and Shear Cell analysis) and bulk properties (Permeability and Compressibility) were also evaluated for these samples using an FT4 Powder Rheometer® (Freeman Technology, Gloucestershire, UK).

The results demonstrate that the GNS, resulting from dilation of a fixed volume bed, correlates with bulk density changes, rather than a direct correlation with ANL. This would explain the conflicting results for previous studies as bulk density changes are also related to ANL, as further demonstrated by the Compressibility results. At lower ANL, the powder bed exhibited larger relative changes in bulk density and subsequently a greater degree of dilation. As ANL increases, the relative change in bulk density decreases and eventually plateaus, with a similar trend observed in GNS values.

Interestingly, the ratio of GNS to ANL is substantially higher at lower ANL values, with GNS even exceeding ANL in some cases. This was most notable for the larger grades of Eskal, which is consistent with the literature. These results also suggest that consideration of powder bed dilation is required when undertaking Shear Cell analysis at low Applied Normal Load as dilation will have a greater influence on achieving and maintaining the target ANL, especially due to the rapid increase in stress during shear, and will also be variable. In terms of measuring Shear Stress at lower ANL, good correlation was observed between the GNS and SS values, with most Eskal grades exhibiting either a linear or 2nd order polynomial relationship.

As discussed, GNS typically increased with particle size, however, the smallest grade of calcium carbonate, Eskal 500 (D50 0.5µm), deviated from this trend, presenting higher than expected GNS values. This sample was far more compressible than the other grades, exhibiting greater changes in bulk density. Whilst this may explain the larger GNS values at higher ANL, higher compressibility values are typically associated with less efficient particle packing and entrained air. A looser packed powder bed might be expected to accommodate displaced particles more easily in the shear zone, thereby reducing dilation and GNS. Comparison of Specific Energy (SE), a measure of mechanical interlocking and inter-particular friction [13], was notably higher for this sample. Results from previous studies [5, 6, 11] suggest that increased inter-particular friction and mechanical interlocking likely contributed towards the higher than expected GNS values for this sample. As such dilatancy can still be problematic when handling powders of smaller particle size.

The use of a modified shear cell was demonstrated to be a suitable approach for investigating powder dilation in constrained systems. Using this technique, it was possible to investigate the relationship between ANL, bulk density and dilation. The results reinforced the results of previous DEM studies, demonstrating that both particle size and inter-particular friction can influence powder bed dilation.

  1. Reynolds, O., LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1885. 20(127): p. 469-481.
  2. Schulze, D., Powders and Bulk Solids: Behavior, Characterization, Storage and Flow. 2021: Springer International Publishing.
  3. Tsegaye, A.B., Cyclic stress-dilatancy relations and associated flow for soils based on hypothesis of complementarity of stress-dilatancy conjugates. arXiv preprint arXiv:2101.04601, 2021.
  4. Szypcio, Z., Stress-Dilatancy for Soils. Part I: The Frictional State Theory. Studia Geotechnica et Mechanica, 2017. 38(4): p. 51-57.
  5. Shi, H., et al., Steady state rheology of homogeneous and inhomogeneous cohesive granular materials. Granular matter, 2020. 22(1): p. 1-20.
  6. Yang, Z.X., J. Yang, and L.Z. Wang, On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis. Granular Matter, 2012. 14(3): p. 433-447.
  7. Amirpour Harehdasht, S., et al., Influence of particle size and gradation on shear strength–dilation relation of granular materials. Canadian Geotechnical Journal, 2019. 56(2): p. 208-227.
  8. Louati, H., et al., Qualitative and quantitative DEM analysis of cohesive granular material behaviour in FT4 shear tester. Chemical Engineering Research and Design, 2019. 148: p. 155-163.
  9. Faqih, A., et al., Flow - induced dilation of cohesive granular materials. AIChE Journal, 2006. 52(12): p. 4124-4132.
  10. Obregón, L., A. Realpe, and C. Velázquez, Mixing of granular materials, part II: effect of particle size under periodic shear. Powder Technology, 2010. 201(3): p. 193-200.
  11. Babu, V., et al., Dilatancy, shear jamming, and a generalized jamming phase diagram of frictionless sphere packings. Soft Matter, 2021. 17(11): p. 3121-3127.
  12. Mofiz, S.A., M.R. Taha, and D.C. Sharker. Mechanical stress-strain characteristics and model behavior of geosynthetic reinforced soil composites. in 17th ASCE Eng. Mechanics Conf. 2004.
  13. Freeman, R., Measuring the flow properties of consolidated, conditioned and aerated powders — A comparative study using a powder rheometer and a rotational shear cell. Powder Technology, 2007. 174(1–2): p. 25-33.