The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders

 Memento, homo, qui pulvis est et pulverem reverteris.  Genesis 3  Polvos serán, mas polvo enamorado.  Francisco de Quevedo The physics of granular materials in ambient gases is governed by interparticle forces, gas–particle interaction, geometry of particle positions and geometry of particle contacts. At low consolidations these are strongly dependent on the external forces, boundary conditions and on the assembling procedure. For dry fine powders of micron and sub-micron particle size interparticle attractive forces are typically much higher than particle weight, and particles tend to aggregate. Because of this, cohesive powders fracture before breaking, flow and avalanche in coherent blocks much larger than the particle size. Similarly the drag force for micron sized particles is large compared to their weight for velocities as low as 1 mm/s. Due to this extreme sensitivity to interstitial gas flow, powders transit directly from plastic dense flows to fluidization without passing through collisional regimes with negligible gas interaction. These two features, strong attractive forces and strong gas interaction make powder behaviour differ qualitatively from the behaviour of large, noncohesive grains. In this paper we investigate the implications of these two features on the bulk powder behaviour. More in particular, the aim of this paper is to examine the relationship between attractive interparticle forces at grain level, with solid bulk properties at low consolidations (solid fraction, stresses), fluidization (aggregation, settling) and flow regime boundaries (plastic flow, inertial flow, fluidization and suspension). Many of the experimental results reported here are for dry and uncharged fine powders made of polymer particles of the order of 10 microns in diameter. However, the basic concepts and methodology are of general applicability. Contents PAGE 1. Introduction 265 2. Scope of the paper 267 Part I: Powders at the grain level 270 3. Characterization of single powder particles 270 4. Van der Waals forces between rigid bodies 274  4.1. Van der Waals forces between two half-spaces 276   4.1.1. Surface energy 277  4.2. Van der Waals forces between a half-space and a sphere with radius R 278  4.3. Van der Waals forces between two rigid spheres 279  4.4. Van der Waals forces between two nonconforming convex bodies: the Derjaguin approximation 279  4.5. The effect of asperities 281  4.6. The effect of retardation 282  4.7. Cohesive–noncohesive particle boundary 282 5. Normal forces between deformable bodies 284  5.1. Elastic contact 285   5.1.1. Nonadhesive elastic contact: Hertz solution 286   5.1.2. Adhesive elastic contact: DMT and JKR solutions 287   5.1.3. Adhesive elastic contact: general solution 288  5.2. Indentation of elastic–ideally plastic materials: elastic–plastic and fully plastic contact 292   5.2.1. Non-adhesive elastic–plastic contact 292   5.2.2. Adhesive elastic–plastic contact 295  5.3. Unloading the adhesive contact of elastic–ideally plastic materials 296   5.3.1. Fully-plastic contact 297  5.4. The effect of asperities 298 6. Normal forces between two powder particles: AFM measurements 299 7. Normal forces: comparison between theory and experiments 305  7.1. Nature of contact 305   7.1.1. Does the contact take place between the base polymer, or through the additives? 306   7.1.2. Is the contact elastic or plastic? 308  7.2. Adhesive contact in the elastic–plastic regime: an approximate model 308  7.3. Results 310 Part II: Powders at the bulk level 312 8. Mechanical properties 312  8.1. Rigid-plastic solid 314  8.2. Elastic–plastic solid 315  8.3. Review of the techniques for measuring powder properties and flowability 318   8.3.1. Empirical techniques 318   8.3.2. Techniques of analysing powder flowability based on fundamental properties 319  8.4. The Sevilla Powder Tester: a new tool to characterize fine cohesive powders at very small consolidations 322  8.5. Experimental results 333   8.5.1. Materials 333   8.5.2. Viscosity effects in interparticle contacts 333   8.5.3. Effect of particle properties and flow additives on the cohesive properties of bulk powder 334 9. Interparticle forces versus bulk stresses: a semiquantitative approach 337  9.1. The structure of fluidized beds of fine cohesive powders 338   9.1.1. Homogeneous fluidized bed: solid-like or fluid-like? 338   9.1.2. Fluid-like domain as a function of particle size and cohesiveness 343  9.2. Aggregation in the fluid-like regime of homogeneously fluidized beds of fine cohesive powders 344   9.2.1. The settling experiments 344   9.2.2. The fluidized bed as a suspension 345   9.2.3. Estimation of average number of particles and average size of aggregates 346   9.2.4. Scaling laws for aggregates 349  9.3. Compaction of the sedimented layer 350   9.3.1. Compaction under consolidations below the sample weight 352   9.3.2. Compaction of powders subjected to consolidations above the sample weight 355  9.4. Micromechanics of granular materials 360  9.5. Correlation between the AFM and SPT measurements 362  9.6. Contact forces in the bulk: qualitative comparison with theory 365 10. Flow regime boundaries in cohesive powders 365 11. Conclusion 370 Acknowledgements 372 References 372