Compaction behavior, mathematical

Heckel considered the compaction of powders analogous to that of a first-order chemical reaction. The pores were the reactant and the densification of the material the product. The proportionality between the change of density with pressure and the pore fraction was the process kinetics.Heckel explained mathematical constants that described the compaction behavior of a given powder and developed a mathematical relationship, Eq. (2). ... 

Patel S, Kaushal A. Bansal A. Effect of particle size and compression force on compaction behavior and derived mathematical parameters of compressibility. Pharm. Res. 2007 24(1), 111-24. 

Mathematical models provide a convenient and compact way of expressing the behavior of a process as a function of process physical parameters and process inputs. The same mathematical model can be expressed in several ways for example, a continuous-time model based on a differential equation can be converted to a discrete-time system, or it can be transformed to a different type of independent variable altogether (e.g., Laplace transforms or z transforms). Transform models generally feature a simplified notation, which greatly facilitates analysis of comphcated systems. 

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