Flow through beds of porous particles

Intraparticle convection is receiving increased attention in studies of beds of porous particles, especially in biotechnology applications involving cell immobilization and perfursion chromatography. This work presents two approximate models for describing the flow field within a porous particle contained in a fixed or fluidized bed. The first is a swarm model where a spherical porous particle of a specified permeability is contained in a matrix of a different permeability that is equated to the overall bed permeability. Brinkman's equations are solved in both the particle and matrix domains. The second is a cell model in which the spherical porous particle is placed in a spherical envelope of fluid whose diameter is chosen so that the overall bed porosity is conserved. The Stokes equations are solved for the envelope fluid, and Brinkman's or Darcy's equations are solved for the porous particle. For both models, a vector invariant solution is employed which yields the pressure and velocity fields directly in terms of the fundamental solutions to Laplace's equation and the modified Helmholtz equation. Results are presented for the drag force per particle, the overall bed permeability, and the velocity and pressure profiles within the particle. The results of the two different models are similar. An important observation is that the intraparticle velocity is approximately two orders of magnitude larger for particle in a typical packed bed than for an isolated particle under similar conditions, owing to the increased resistance to flow outside the particle caused by the other bed particles. As a result, intraparticle convection plays a key role in reactant transport within the porous particle phase.