Percolation/Diffusion through the Void Space of a Bed of Randomly Packed Particles of Different Sizes
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Percolation/Diffusion through the Void Space of a Bed of Randomly Packed Particles of Different Sizes Daniel P Riley, Irina V Belova and Graeme E Murch Diffusion in Solids Group, Dept. Mechanical Engineering The University of Newcastle, Callaghan, NSW 2308 AUSTRALIA ABSTRACT In this paper a Monte Carlo method is introduced for determining the diffusivity in the void space of porous media constructed from spheres. We studied ordered and random arrangements of spheres, the latter with different sizes. It is found that the effect of structure on the diffusivity is fairly slight. The empirical curve of Neale and Nader is shown to provide a convenient upper bound. The result of Bruggemann provides a convenient lower bound. INTRODUCTION In porous media, the diffusivity, which is a convenient measure of the percolation characteristics, is reduced compared with the diffusivity in the absence of the media. This is a result of the reduced cross-sectional area and the larger path length which must be negotiated. In the case of gases, two limiting conditions are usually identified, Knudsen diffusion sometimes called free molecular flow, and bulk or normal diffusion. In Knudsen diffusion the mean free path of the molecules is long compared with the pore diameter. The collisions with the walls of the media are then the limiting factor. In bulk or normal diffusion, however, the gas-gas collisions themselves are the limiting factor. In this paper we are concerned only with bulk diffusion. From a phenomenological diffusion theory point of view such bulk diffusion in porous media is also entirely analogous to ionic diffusion in an electrolyte in contact with porous media. Other analogies such as electrical conductivity and thermal conductivity in the presence of an insulating phase, are also known. Although a large literature exists on the subject of the bulk diffusivity in porous media, see for example, the review by German [1], the theory is fairly empirical with little attempt made to address actual packing arrangements and their effect on the bulk diffusivity. In the present study we generated various ordered and random packing arrangements of impermeable spheres (particles). We then introduce a Monte Carlo method for investigating bulk diffusion in the pore space of these arrangements. METHOD Random distributions of spherical particles were generated in the following way. We introduced the spheres randomly into a volume (non-periodic) without overlap. Packing densities were typically 30-40 % depending on particle size. Higher densities are possible of course with particles of two different sizes such that the smaller particles are introduced into the pore spaces of the larger particles. For dense random packing we first imposed a simple 6-12 Lennard – Jones potential between particles (of the same or AA7.11.1
different sizes) in which the repulsive part of the potential dominated (this approximates a hard sphere interaction). The potential energy function was then minimized by fixed small steps chosen in random directions. The
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