Numerical simulations combine geometry and viscoeleastic properties to model microbes in tubes

From blood cells migrating through veins to bacteria navigating intercellular channels, microbes undergo complex hydrodynamic behaviors inside cylindrical tubes. Better understanding this process may be crucial in developing future drug delivery systems using microcarriers. Despite the relatively straightforward geometry, modeling the effect of fluid viscoelasticity and tube confinement togetherhasn’t been fully described.

Lin et al. have systematically characterized the swimming dynamics of microorganisms and the hydrodynamic mechanisms within a viscoelastic fluid-filled circular tube. The researchers used a partial differential equations technique called the fictitious domain method and the classical squirmer model of microbial propulsion to describe the influence of fluid elasticity and tube blocking ratio on the squirmer swimming speed, power, and efficiency.

“The study addresses key unresolved aspects regarding the combined effects of fluid viscoelasticity and geometric confinement on microbial locomotion, as well as the distinct motion modes exhibited by different squirmer types,” said author Zhaosheng Yu. “By studying these, it provides a holistic understanding of microbial locomotion in physiologically relevant environments, rather than oversimplified single-factor setups.”

The group found that how microbes propelled themselves — pushing, pulling and neutral — had distinct effects on the modes of trajectories for each microbe. Key drivers in these changes were the Weissenberg number, a value corresponding to fluid elasticity, and the squirmer parameter, which corresponds to the hydrodynamic force dipole of squirmers.

Pullers migrate radially at first and then settle in the low-viscosity, low-Reynold’s number centerline, or the high-Reynold’s number closer to the tube’s walls. The irregular trajectories of pushers send them into the wall. Fluid elasticity increases with increasing neutral swimmers’ periodic motions as they zigzag through fluid.

The group next looks to the effect of multi-particle interactions on traveling microbes.

Source: “Numerical study of microorganisms swimming through the viscoelastic fluids in a circular tube,” by Zhaowu Lin, Rujiang Li, Yan Xia, Zhenyu Ouyang, Zhaosheng Yu, and Wei Lu, Physics of Fluids (2025). The article can be accessed at https://doi.org/10.1063/5.0289345 .