Analysis of diffusion in hollow geometries

The diffusion in hollow particles of solid adsorbent materials was analyzed based on analytical solutions to the basic diffusion equation. Three geometric shapes (plane sheet, cylinder, and sphere) of sorbent material were considered for two kinds of boundary conditions. The equations for determining the equivalent sizes compared to their corresponding solid particles were obtained directly from the theoretical expressions of sorption uptake curves. Among the three hollow particles of impermeable inner surface, the sphere gives the highest gain in effective diffusion rate compared to the corresponding solid particle. For permeable inner surface, at lower hollow volume fractions, the plane sheet shows the highest gain, while at higher hollow volume fractions, the sphere shows the highest gain in effective diffusion rate.