A Comparison of Equations for Powder Compression

Abstract

Abstract Several equations representing the relation between the pressure and the apparent volume of a powdered mass under compression, as proposed by various authors, sometimes have essentially the same form as one other, and sometimes have contradictory characters. Various equations can be modified so as to be a function of the porosity and thus compared with each other. As a result, they can be classified into two types by means of the gradient of the porosity with the pressure (−dn⁄dP, n=porosity). One is −dn⁄dP=knx (Athy: x=1, Kawakita: x=2), and the other is −dn⁄dP=k(1−n)y⁄Pz (Smith: y=0, z=2⁄3, Nutting: y=1, z\doteqdot1, Balshin: y=2, z∼1, Terzaghi: y=2, z∼1, Jones: y=3, z=1), where k is a constant and x,y and z are parameters. In Kawakita’s equation the rate of the decrease of the porosity is considerably larger in an early period of compaction than in Athy’s equation. The second type of equation indicates that a major part of the porosity disappears at lower pressures.