Experimental and theoretical study of oxygen diffusion within packed beds of carbon black

Abstract

Abstract Modelling the performance of regenerative soot traps for Diesel exhausts requires a knowledge of oxygen diffusivity within beds of Diesel soot. For convenience carbon black, a commercial product with similar properties to Diesel soot, is often used for combustion experiments. Both of these carbonaceous materials are composed of spherules of approximately 20 nm in diameter assembled within aggregates. The oxygen diffusivity within beds of carbon black with different densities was measured at 22°C. An increase in the porosity of the bed from 0.746 to 0.820 increased the diffusion coefficient of oxygen from 0.7×10 −6 to 2.0×10 −6 m 2 s −1 . Two simulations of molecular movement in aggregates of spheres or ‘cannonball’ solids were performed. The kinetic theory (KT) model assumes that the carbon spherules are regularly placed at the summits of cubes and a mean travel distance replaces the mean free path. The Monte Carlo (MC) model is based on a random walk among spherules placed randomly but homogeneously. The diffusivity values returned by the two models are strongly dependent on the tortuosity of the bed. The KT model returned oxygen diffusivities that were similar to those measured while the MC model gave values which were higher. When the MC values were modified to allow for non-homogeneous packing, i.e., uneven distribution of density, the results were improved. The concept of tortuosity, which is based on interconnected cylindrical pores, seems unrealistic in the case of beds of highly porous cannonball materials. Beds of Diesel soot are so open that Fickian diffusion of oxygen should occur, whereas combined Fickian and Knudsen diffusion seems to operate within the beds of carbon black. The mechanisms are uncertain since Knudsen diffusion within aggregates of carbon black or Diesel soot probably controls the overall diffusion process.