Fig. 1. Overview of the unit cells of the considered pillar arrangements for the three different considered pillar shapes: (a) cylinders; (b) equilateral hexagons; (c) diamond-like pillars. For each pillar shape, three of the six cases considered in Table 2 are represented.

Fig. 2. Comparison of the calculated velocity fields for the three different considered pillar shapes under the condition of an identical domain size and cross-sectional particle area (case 3). The streamlines are coloured in relation to the local velocities.

Fig. 3. Plot of ΔP vs. u₀ for the three different considered pillar shapes (case 3). Using the straight line slopes to calculate K_v from Eq. (4), the following values are obtained: K_v=2.08×10⁻¹⁵ m² (▪, cylinders); K_v=2.25×10⁻¹⁵ m² (, hexagons); K_v=3.05×10⁻¹⁵ m² (, diamonds).

Fig. 4. Evolution of σ_x² (full lines) and t_r (dashed lines) with x for one of the considered cylindrical pillar domains (case 1, u₀=0.93 mm/s).

Fig. 5. Comparison of the obtained Van Deemter plots for the three different considered pillar shapes: (a) case 1: identical d_lat; (b) case 2: identical d_f,min; (c) case 3: identical d_dom, d_eq and A_p; (d) case 4: identical d_FR,eq; (e) case 5: identical S_p/V_p; (f) case 6: identical d_f,mean. (▪) Cylinders; () hexagons; () diamonds.

Fig. 6. Reduced Van Deemter plots and fittings with Knox equation (solid lines): (▪) cylinders; () hexagons; () diamonds.

Fig. 7. Separation impedance as a function of the reduced velocity for the three considered pillar shapes: (▪) cylinders; () hexagons; () diamonds.

Fig. 8. E_min vs. the d_lat/d_ax ratio of the cylinders (d_lat/d_ax=1), the hexagons (d_lat/d_ax=1.15) and the diamonds (d_lat/d_ax=1.73).

Table 1. Geometrical parameter values for the different considered pillar shapes in relation to their main characteristic dimension (diameter d_p for cylinders and side length s for the hexagons and diamonds) and the bed porosity

Table 2. Relations between a number of important characteristic dimensions for the six different considered cases

The underlined values refer to the dimension kept constant in the given case.

Table 3. Summary of the most relevant chromatographic performance parameters