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Bulk random packings of solid core–porous shell (permeable) particles with varied shell thickness and shell diffusion coefficient

Panel A. Schematic of the flow velocity field in the eddy dispersion theory of Giddings, as seen from the frame of reference of the center of the analyte zone. The black cells are from the transchannel layer of the velocity field (index 1) and the red cells are from the short-range interchannel layer (index 2). Although we have only drawn four transchannel and two short-range interchannel cells, they fill up space regularly and infinitely. The distance l represents the jump of the random walker relative to the center of the analyte zone.

Panel B. Slice of a simulated velocity field with the corresponding length scales, α₁d_p (transchannel) and α₂d_p (short-range interchannel). The color map indicates the velocity component along the superficial flow direction (red regions correspond to high velocity, blue regions to low velocity).

Panel C. Simulated reduced plate height h (symbols) as a function of the reduced velocity for different normalized shell diffusivities Ω = D_shell/D_m and core-to-particle diameter ratios ρ = d_core/d_p. The external porosity of the packings is 0.4, the particles’ shell porosity is 0.44. Solid lines correspond to fits of the data by the expression developed to extend Giddings' theory of coupled eddy dispersion to packings of core–shell particles.