Variation of superficial energy with pressure

Glass bead granular media have been chosen as a model in order to study the dependence of the superficial energy γ upon the pressure applied to a packing, γ represents the difference between the superficial energy corresponding to the gas-solid interface and half the energy corresponding to the solid-solid interface created under pressure. A theoretical 3D study has been developed on monosized spheres. Thermodynamic considerations show that the variations of γ with P are connected to the volume, the compressibility coefficient of the solid, and the partial derivative of P with respect to the area of the gas-solid interface. The derivative is evaluated in each case, considering the microscopic point of view stated by Hertz or a macroscopic treatment from empiric relationships between strain and stress-or pressure. Consequently γ obeys the following law: γ - γo = - A R χ (P - P 0 ) β where A, R, χ represent respectively a positive constant, the radius of the objects, and the compressibility coefficient. The value of the exponent ß is 4/3 for spheres in the microscopic approach, but varies from 1.33 to 1.74 for spheres in the macroscopic description. These theoretical relationships are helpful to predict the macroscopic variations of superficial energies of different hydrated or anhydrous lactoses. The higher the tablet cohesion, the larger the variations of γ are. The twining of two grains seems to be better for systems of lactoses having a poor elasticity, and a larger grain size.