Numerical simulations

The mathematical model is based on first computing the 3D velocity field inside the microchannel (with COMSOL Multiphysics) and then using it to simulate the transport of individual bacteria, for the same geometry and flow conditions as in the experiments. We modeled bacteria as prolate ellipsoids with an effective aspect ratio q, which accounts for the combined hydrodynamic resistance of cell body and flagellar bundle, and swimming speed V directed along the cells’ long axis. A cell’s equations of motion in the 2D flow that occurs in the experimental observation plane (i.e., channel mid-depth; Fig. 1b) are

where ψ is the stream function and ξ_R is the rotational noise represented as a Gaussian-distributed angular velocity with mean zero and variance 2D_R/Δt, where Δt is the elapsed time and D_R is the cell’s effective rotational diffusivity. The equations of motion were integrated numerically for up to 5 × 10⁵ bacteria using a fourth-order Runge–Kutta scheme implemented in Matlab (The MathWorks). The number of simulated bacteria is comparable to the number of bacteria (10⁵–10⁶) crossing a 500 µm-wide section of the channel, during a 5 h experiment, with a cell concentration of 10⁶ cells mL⁻¹ and for an average flow velocity in the range of 150 μm s⁻¹ < U < 2 mm s⁻¹. The swimming speed and rotational diffusivity were measured experimentally (Supplementary Fig. ¹), while the effective aspect ratio, q, was computed from resistive force theory (Supplementary Methods). For P. aeruginosa we used q = 9.4, V = 45 μm s⁻¹, and D_R = 1.4 rad² s⁻¹ (Supplementary Fig. ¹). For E. coli we used q = 8.5, V = 21.6 μm s⁻¹, and D_R = 0.32 rad² s⁻¹ (Supplementary Methods). For spherical nonmotile bacteria (Fig. 7e, f) we used q = 1, V = D_R = 0. In the simulations, the swimmers start 400 µm upstream of the pillar (i.e., the beginning of the flow field) with random positions across the channel width (y) and random orientations (θ). Each time a swimmer contacts the pillar surface or exits the flow field it is reinjected with prescribed initial conditions. For contact between bacteria and surfaces, we used a “perfectly sticking” condition, i.e., any collision between the simulated trajectory and the boundary of the pillar or of the corrugation is considered as the bacterium irreversibly attaching to the surface. This condition, which neglects any hydrodynamic or specific interaction between the cell and the surface of the pillar, represents a good approximation for the surface attachment of biofilm-forming bacteria, such P. aeruginosa and E. coli.