Confinement reduces surface accumulation of swimming bacteria

Abstract

Many swimming bacteria naturally inhabit confined environments, yet how confinement influences their swimming behaviors remains unclear. Here, we combine experiments, continuum modeling and particle-based simulations to investigate near-surface bacterial swimming in dilute suspensions under varying confinement. Confinement reduces near-surface accumulation and facilitates bacterial escape. These effects are quantitatively captured by models incorporating the force quadrupole, a higher-order hydrodynamic singularity, that generates a rotational flow reorienting bacteria away from surfaces. Under strong confinement, bacterial trajectories straighten due to the balancing torques exerted by opposing surfaces. These findings highlight the role of hydrodynamic quadrupole interactions in near-surface bacterial motility, with implications for microbial ecology, infection control, and industrial applications.

Figures (4)

• Figure 1: Experimental measurements of bacterial density profiles. (a) Probability distribution function (PDF) $\Psi (z)$ for various confinement height $H$. The PDFs are vertically shifted for clarity. (b) $\Psi (z)$ plotted against scaled height $z/H$. Inset: contrast-enhanced confocal image near the bottom plate; bright regions indicate cell bodies. (c) Peak location of $\Psi(z)$, $z_{\rm peak}$ and (d) ratio $\Psi_{\rm mid}/\Psi_{\rm peak}$ as functions of $H$. Symbols and error bars denote mean $\pm$ SD over 3--4 experiments. Lines in (d) show predictions of the Smoluchowski model with fixed dipole strength $D=0.6$ pN$\cdot \mu$m, varying exclusion length $L_{\rm e}$, and quadrupole strength $Q$ (in pN$\cdot \mu$m$^2$).
• Figure 2: The effect of quadrupole on bacterial population distribution. (a), (b) Image flow fields induced by a (a) force dipole and (b) force quadrupole. White crosses mark the positions of point singularities; white arrows indicate bacterial motion under image flows. (c) Model schematic of the bacterial body plan (top) and the accessible configuration space constrained by steric exclusion (bottom, white region). The exclusion length ($L_{\rm e}$) is tested to span merely the bacterial body ($2a$) and the entire bacterium ($2a+L_{\rm f}$). (d) Time evolution of $\Psi(z,t)$ from the Smoluchowski model (lines) and the particle simulations (circles), initialized with $\Psi_0$. (e) Steady-state $\Psi(z)$ for $D=0.6$ pN$\cdot \mu$m and $Q=0$. (f) Steady-state $\Psi(z)$ for $D=0.6$ pN$\cdot \mu$m and $Q=-0.5$ pN$\cdot \mu$m$^2$.
• Figure 3: Side-wall collision dynamics and the role of force quadrupole. (a) Left: schematic of the side-wall experiment. Right: definition of incident and outgoing angles, $\alpha_{\rm in}$ and $\alpha_{\rm out}$. (b) Experimentally measured incident and outgoing trajectories. Each trajectory is translated such that the closest approach to the wall aligns with the origin. (c) Distributions of $\alpha_{\rm in}$ measured experimentally (circles) and imposed in particle-based simulations (line). (d) Distribution of $\alpha_{\rm out}$ from experiment (circles) and simulations (line) with dipole strength $D=1.2$ pN$\cdot \mu$m, varying bacterial exclusion length $L_{\rm e}$, and quadrupole strength $Q$ (in pN$\cdot \mu$m$^2$). The value $Q=-2.2$ pN$\cdot \mu$m$^2$ is calculated for an elongated bacterium from the rod-spheroid model, rather than a fitting parameter. Inset: $Q=-0.3$ pN$\cdot \mu$m$^2$ gives the best fit for $L_\mathrm{e}=2a$. Simulations use a rotational diffusion coefficient $D_r=0.06$ rad$^2$/s, consistent with Ref. Drescher2011.
• Figure 4: Curvature of bacterial swimming trajectories under confinement. (a) Probability distributions of trajectory curvature $\kappa$ measured experimentally for various $H$. Inverted triangles mark the most probable curvatures $\kappa_{\mathrm{peak}}$. (b) $\kappa_{\mathrm{peak}}$ as a functions of $H$. Solid line shows prediction from BEM simulations.