a) Heckel equation In 1961, Heckel proposed the most widely used equation describing pharmaceutical powder behavior in compaction. It was initially used to study the densification of ceramics and its correlation with pressure. It a first order process where powder pores elimination rate is correlated to the number of pores present. The rate of volume reduction increases as the number of pores decrease. Heckel equation relates the density, pressure and the pore fraction of the powder [16],. This was expressed mathematically as: If the compaction is achieved by plastic deformation and there is no particle rearrangement, heckel plot will give a straight line, but pharmaceutical powder don’t produce straight lines, and this deviation gives
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The constant a represents the minimum porosity of the powder before compression, while b (the coefficient of compression) is linked to the plasticity of the material. (1 – a) represents the initial relative density of the material. (1/b) corresponds to pressure Pk that is the pressure needed to reduce powder bed by 50%, it is inversely proportional to the ability of powder to deform plastically [7,21,22]. Later studies indicated that this equation could be used to powder form only, and it can be adapted by substituting the initial compaction volume with an initial bulk volume in order to study granules. Another limitation for this equation is that it is applicable to a certain pressure limit, and above this pressure the equation is no longer linear. In general, Kawakita equation is more adapted for high porosity and low pressure [15].
c) Adam’s equation Adam’s equation calculates granules strength from in-die compression data. It considers granules are arranged in parallel columns. Mathematically it is expressed
The constant a represents the minimum porosity of the powder before compression, while b (the coefficient of compression) is linked to the plasticity of the material. (1 – a) represents the initial relative density of the material. (1/b) corresponds to pressure Pk that is the pressure needed to reduce powder bed by 50%, it is inversely proportional to the ability of powder to deform plastically [7,21,22]. Later studies indicated that this equation could be used to powder form only, and it can be adapted by substituting the initial compaction volume with an initial bulk volume in order to study granules. Another limitation for this equation is that it is applicable to a certain pressure limit, and above this pressure the equation is no longer linear. In general, Kawakita equation is more adapted for high porosity and low pressure [15].
c) Adam’s equation Adam’s equation calculates granules strength from in-die compression data. It considers granules are arranged in parallel columns. Mathematically it is expressed