Intra-particle Convection for Enhanced Mass Transfer

Key Insight

Intra-particle convection, or perfusion, refers to the flow of the mobile phase within the pores of adsorbent particles, which can significantly enhance the overall rate of mass transfer for slowly diffusing molecules. This mechanism becomes relevant when intra-particle pores are very large, the protein's diffusivity in the mobile phase is very small, the particles are small, and the mobile phase velocity is high. While the intra-particle flow (F_p) is generally a small fraction of the total liquid flow, it can substantially contribute to intra-particle transport, especially for large biopolymers where intra-particle diffusion is exceedingly slow.

Estimates of F_p can be obtained using models such as the ratio of intra-particle and extra-particle hydraulic permeabilities (Karman-Cozeny equation) or extensions of the free surface model which describe flow in a packed bed of spherical particles. The impact of intra-particle convection on mass transfer is quantified by a convection-enhanced effective intra-particle diffusivity, D_tilde_e, and the intra-particle Peclet number (Pe_p). An enhancement factor (D_tilde_e/D_e) of 2 over pore diffusion alone requires a Pe_p of approximately 30; at high Pe_p values, transport becomes linearly proportional to the mobile phase flow rate, indicating a convection-dominated regime.

For example, calculations for 20 micrometer particles with 400 nanometer pore size operated at 1000 cm/h can show D_tilde_e/D_e values as high as 5.33, demonstrating significant enhancement of mass transfer. Practical large-pore matrices are often designed to augment mass transfer by employing bimodal pore networks, featuring large pores for convective flow and smaller pores to provide surface area for binding. This approach limits the diffusional resistance to the size of constituent microparticles and can lead to lower column pressure drops compared to columns packed with unaggregated microparticles.