Simulation of Drainage and Imbibition in a Random Packing of Equal Spheres

Abstract

The sizes and connections of the pores in a network of tetrahedral pores have been derived using the center coordinates of 3367 randomly close-packed equal spheres. The center coordinates of each sphere were measured by J. L. Finney, who took apart an actual packing of spheres. A. C. Wright mathematically divided the packing into 14,870 irregular tetrahedra by joining the center coordinates of spheres which were geometric neighbors. Their aim was to model the structure of liquids and glass. The present work uses their data in a different way and analyzes the capillary properties of the individual tetrahedral pores together with the network effects of the combination of pores during simulated drainage and imbibition. The meniscus drainage curvatures of the faces (bonds on the network) of the pores were calculated using the Mayer and Stowe–Princen method using a value of zero for the contact angle. Imbibition curvatures of the cavities (sites on the network) were initially estimated from the Haines insphere approximation. However, the constraint that a tetrahedral pore can, in isolation, at best show no hysteresis enables a new approximation to be proposed for the imbibition curvature of cavities formed by spheres. Drainage was simulated by using the meniscus curvature associated with each bond in conjunction with the bond network to determine whether a pore actually drained. Imbibition used the site curvatures. The results indicated that the tetrahedral (diamond) lattice is a good approximation to the pore network structure in a random packing of spheres. However, neither the bonds nor the sites are randomly distributed on the network. In drainage the bonds cooperate so as to make drainage harder. Conversely, in imbibition the sites cooperate so as to make imbibition easier. Thus the degree of nonrandomness in the location of the pore sizes in the packing produces an effect in drainage opposite to that produced in imbibition.