Diffusion, convection, and reaction in catalyst particles: analogy between slab and sphere geometries

Electroosmotic Flow Phenomena in Packed Capillaries: From the Interstitial Velocities to Intraparticle and Boundary Layer Mass Transfer

“…These mechanisms are characterized by different driving forces and the concentric circles seen in Figure 3 (representing purely diffusive transport in the radial direction with a constant D intra ) loose their spherical symmetry, because convection in the sphere occurs along the axial direction. [78][79][80] For an approximate calculation of a now apparent mass transfer rate constant B intra ap based on the continued use of eq 8, our analysis neglects this geometrical aspect. It further does not realize convection as an independent transport mechanism, but relies on the simplifying concept of a convection-augmented diffusivity.…”

Sol‐Gel and Porous Glass‐Based Silica Monoliths with Hierarchical Pore Structure for Solid‐Liquid Catalysis

“…Due to their continuous solid phase, it is difficult to define an appropriate structural unit for monoliths that characterizes the diffusion limitation (stagnant mobile phase mass transfer resistance) and the flow resistance (hydraulic permeability) in these materials and to determine relevant shape and size distribution factors as for particulate packings. While for particulate systems equivalence between different geometries regarding diffusion, convection, and reaction is recognized [53], a direct comparison with monoliths is less obvious due, not least, to the complex shape of their skeleton.…”

Fluid Dynamics in Monolithic Adsorbents: Phenomenological Approach to Equivalent Particle Dimensions

“…These involve molecular diffusion in the interconnected pore network, a mechanical contribution due to velocity fluctuations in the flow field induced by the randomly distributed solid phase, nonmechanical dispersion associated with the no-slip condition at the solid-liquid interface (in general), and the particular access to intraparticle or intraskeleton stagnant zones in which diffusion remains the dominating transport mechanism [13]. While equivalence between different geometries concerning the convection, diffusion and reaction is well recognized for particulate systems [14], a direct comparison with monolithic structures is less obvious due, not least, to the complex shape of the skeleton domain. Although monoliths are considered as a new generation of adsorbents, appropriate characteristic lengths that competitively relate their hydrodynamic properties (i.e.…”