Fig. 4: Vortical trapping in disordered geometries of higher dimension.

a Magnetotactic bacteria trajectories strongly localize in specific pores (red hexagons) of a microfluidic packed bed of hydrogel beads. White arrows indicate magnetic field (1.75 mT) and mean flow directions. Scale bar, 10 μm. b Sample pore containing a single, trapped cell (indicated by cell sketch). The tetrahedral pore is comprised of a triad of in-plane beads and one out of plane (center). Scale bar, 10 μm. c Distribution of positions for a single localized cell, tracked for 6.5 min (cyan square from b; Supplementary Movie 5). The blue curve is a 20 s long sample segment of the trajectory, and the colormap indicates the cell’s distribution over time. Scale bar, 5 μm. d, e, 2D flow fields through regular and disordered arrays of cylindrical pillars. f, g Cell trajectories in ordered and disordered media. Flow conditions correspond to colored boxes in (f and g) and red and blue markers in the sample scale trapping regime of (h), respectively. Red and blue hexagons mark local pores in the trapping and upstream regimes, respectively. h Sample scale conductivity 〈V_x〉/V_s for ordered (red curve) and disordered (blue curve) geometries, as a function of the flow strength for steady-state transport conditions. For each curve, regimes with 〈V_x〉/V_s ≈ [0.5, 0, −0.5] are marked by circles. i, j, Cumulative distribution functions (CDFs) of number of cells per trapping site (pore) in the ordered and disordered geometries, for Φ = 0 and 〈V_x〉/V_s ≈ [0.5, 0, −0.5]. Colors refer to specific regimes marked in (h). CDFs are artificially offset for clarity. k, l Location of cells for 〈V_x〉/V_s = 0 in the disordered geometry for initial and steady-state conditions. Colored dots mark cells in the upstream (green), trapping (red), and downstream (blue) regimes. m Populations of cells in the upstream (green), trapping (red), and downstream (blue) regimes as a function of time for the disordered geometry for 〈V_x〉/V_s = 0.