Associate Professor Hu Shiyuan from the School of Physics at Beihang University, in collaboration with experimental partners, has published new findings on the accumulation behavior of swimming bacteria in confined environments. The study, titled "Confinement Reduces Surface Accumulation of Swimming Bacteria," was recently published in the prestigious journal Physical Review Letters.

Bacteria constitute a significant portion of the Earth's biomass. However, their microscopic scale often leads to their being overlooked. While we observe fish and crustaceans in the ocean, we rarely see the vast numbers of marine bacteria that far exceed them. Similarly, on land, we notice animals and plants but often forget the immense bacterial populations living within our own bodies. Bacteria typically inhabit confined environments on the micrometer scale, and their dynamic behavior in such settings plays a critical role in microbial processes such as colony growth, biofilm formation, and pathogenic infection. It also holds significant implications for the study of collective behavior in active matter.

In fluid environments, bacteria exhibit notable surface accumulation. Over the past decades, near-surface swimming behaviors have been extensively studied. Numerous experimental and theoretical studies have shown that hydrodynamic interactions (HIs) and anisotropic steric interactions jointly influence this accumulation phenomenon. However, previous research has primarily focused on semi-infinite spaces bounded by a single surface, with limited attention given to confined geometries.

This collaborative work combines experiments, continuum modeling, and particle-based simulations to investigatethe accumulation behavior of Escherichia coli bacteria confined between two parallel plates with varying separations. Associate Professor Hu Shiyuan from Beihang University derived theoretical expressions for the force dipole and force quadrupole contributions to the flow field generated by swimming bacteria. He developed a continuum model based on the Smoluchowski equation to describe the evolution of bacterial distribution, incorporating both HIs and anisotropic steric interactions. Furthermore, he advanced a numerical algorithm using multipolar expansion to solve the Stokes equation within the parallel-plate confinement, introducingfor the first time the combined effects of both the force dipole and the force quadrupole in the hydrodynamic interactions.

Through quantitative comparison with experimental results, the study reveals that the force quadrupole, previously neglected in research, is a key factor leading to bulk accumulation of bacteria in confined spaces. As the plate separation decreases, bacterial accumulation near the surfaces reduces and can even shift into the bulk. Single bacterium tracking reveals that confinement enhances bacterial escape from surface entrapment. Simulations incorporating both HIs and steric interactions demonstrate that a higher-order singularity—the image force quadrupole—is essential to quantitatively reproduce the density profile near surfaces. This quadrupolar term induces a rotational flow, reorienting bacteria away from surface, consistent with experimental observation. While the quadrupole flow decays rapidly with distance from the surface, its rotational effect, coupled with bacterial swimming, affects the population deep in the bulk even at large plate separation. In strongly confined environments, bacteria follow straighter trajectories rather than circular paths near a single surface, consistent with boundary element simulations.

These findings advance the understanding of microswimmer surface accumulation under confinement and highlight the fundamental role of force-quadrupole hydrodynamics, with implications for microbial ecology, infection control, and industrial applications.

Associate Professor Hu Shiyuan is a co-first author of the paper, responsible for the theoretical and numerical components. The experimental work was conducted by the research groups of Associate Researcher Wei Da and Researcher Peng Yi from the Institute of Physics, Chinese Academy of Sciences. Collaborators also included the research group of Researcher Meng Fanlong at the Institute of Theoretical Physics, Chinese Academy of Sciences.

This work was supported by the National Natural Science Foundation of China, the Fundamental Research Funds for the Central Universities at Beihang University, and other grants.

Link to the article: https://journals.aps.org/prl/abstract/10.1103/dvc8-tlh1

Editor: Lyu Xingyun