Compaction simulation
Compaction simulation is the modelling of granular matter is compressed into a dense state that is achieved through the reduction of the air void.
Three stages are included in the compaction process those are filling or packing, compaction and ejection. During the compaction process, if the loading pressure is increasing straightly, the powder assembly will experience three stages. First of all, particles are filling the voids and set up contacts with the adjacent particles. This stage is termed rearrangement stage. After most contacts are set up, the initial compaction started. Elastic deformation and plastic deformation happens and the loading pressure increases sharply. The third stage is breakage where the particles breaks into fragments.
Discrete Element Method (DEM) is an explicit numerical model capable of tracking the motion and interaction of individual modeled particles.[1] DEM has enhanced rapidly our understanding of granular system by producing quantitative predictions rather than only qualitative description, increased our insight into particle assemblies by providing both microscopic and macroscopic information.[2][3] DEM has been proved to be of great potential in scientific tasks and industries,[4][5] including chemical and mechanical engineering, food industry, geo-sciences and agriculture.
The translational and rotational movement of each particle can be calculated by Newton’s second law of motion. Forces involved are normally particle gravity and inter-particle contact forces including normal and tangential force. Other forces are van der Waals force and capillary force for fine and wet particles system respectively.
The whole simulation process includes compaction and breakage, involves four stages: packing, compaction, relaxation and crushing. At the beginning of packing stage, modeled particles were generated randomly in a square space and allowed to fall under gravity with a small initial velocity to form a packing. There are no overlaps between the particles, and the walls. Then the packing bed is compressed by a modeled plane at a low speed, most of the time, it is set to 10d/s. When the compact density reaches the set value, for example 0.75, the loading process stops and the plane goes up with the speed 5d/s. The compaction stage is ended when the top plane leaves the highest particle. In the recently research, periodical boundaries are used during the packing and compaction stages to exclude the effect of wall.
Bold text==Stages of Compaction / Events occurring during Compaction==
a. Particle rearrangement / inter-particle slippage / transitional repacking
b. Deformation at Points of Contact
c. Fragmentation and Deformation
d. Bonding
e. Deformation of the solid body
f. Decompression
g. Ejection
a. Particle rearrangement / inter-particle slippage / transitional repacking At low pressures, relative volume of powder bed is reduced and close packing attained due to:
• Small particles flow into voids between larger particles. • Particles also acquire proper orientation.
Spherical particles undergo less particle rearrangement than irregular particles. Granules are made spherical or oval; thus, particle rearrangement and the energy expended in rearrangement are minor considerations in the total process of compression. As pressure increases, relative particle movement becomes impossible, inducing deformation.
b. Deformation at Points of Contact
Change of form or deformation of particles occurs due to applied forces. If the deformation disappears completely (returns to the original shape) upon release of the stress, it is an elastic deformation. A de-formation that does not completely recover after release of the stress is known as a plastic deformation. Both plastic and elastic deformation may occur although one type predominates for a given material. Deformation increases the area of true contact and the formation of potential bonding areas.
c. Fragmentation and Deformation
Fracture and fragmentation occurs at higher pressure. Fragmentation cause further densification of the material.
Fragmentation increases the number of particles and forms new, clean surfaces which serve as potential bonding areas. With some materials fragmentation does not occur because the stresses are relieved by plastic deformation.
Initially specific surface area increases due to fragmentation but later on specific surface area decreases as particles become bonded with each other.
d. Bonding
(i) Mechanical theory – mechanical interlocking of irregular shaped particles. (ii) Intermolecular theory – molecules can come very close to each other (less than 50 nm) at the points of true contact allowing development of • van der Waals forces • Hydrogen bonds, if possible • This process is called cold welding.
(iii) Liquid-surface film theory – binding occurs as a result of a thin liquid film, produced by fusion or solution, at the surface of the particles induced by the energy of compression. This process is called fusion welding. Pres¬sure-induced melting and solubility is important in tableting. Water-insoluble materials – poor compressibility. Water-soluble materials – good compressibility. Moisture in granules plays an important role in fusion welding. Moisture may be retained from • granulating solution after drying • adsorption from the atmosphere. Granulations that are absolutely dry have poor compression characteristics.
e. Deformation of the solid body As the applied pressure is further increased, the bonded solid is con¬solidated toward a limiting density by plastic and/or elastic deformation of the tablet within the die.
f. Decompression As the upper punch is withdrawn from the die cavity, the tablet is confined in the die by a radial pressure. Consequently, any dimensional change during decompression must occur in the axial direction. The stress resulting from the axial elastic recovery and the radial contraction can be relieved by plastic deformation. Capping may occur if sufficient plastic deformation is absent. Stress relaxation is time dependant. Materials having fast rates of stress relaxation produce intact tablets. Tablets may crack with materials having slow rates of stress relaxation. If stress relaxation is slow and cracking is a problem, a slower operational speed provides more time for stress relaxation. Selection of tablet shape may be useful to reduce stress gradients within the tablet. Flat faced punches work better than deep concave or oval punches to solve tableting problems.
g. Ejection
Capping may also occur during ejection. This may happen because that portion of the tablet removed from the die undergoes elastic recovery with an increase (2 to 10%) in the volume.
Tableting materials must undergo dominant plastic deformation in order to compress and consolidate sufficiently to form a stable compact mass after ejection.
Bold text== References ==
- ^ Cundall, P.A. and O.D.L. Strack, Discrete Numerical-Model for Granular Assemblies. Geotechnique, 1979. 29(1): p. 47-65.
- ^ H. J. Herrmann, J.-P.H., and S. Luding., Physics of dry granular media - NATO ASI Series E 350. 1998, Dordrecht: Kluwer Acad. Publ.
- ^ P. A. Vermeer, S.D., W. Ehlers, H. J. Herrmann, S. Luding, and E. Ramm., Continuous and Discontinuous Modelling of Cohesive Frictional Materials. 2001, Berlin: Springer.
- ^ Oda, M. and H. Kazama, Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Geotechnique, 1998. 48(4): p. 465-481.
- ^ Thornton, C., Numerical simulations of deviatoric shear deformation of granular media. Geotechnique, 2000. 50(1): p. 43-53.