Active tumbling plays a key role in microswimmer transport. Using a continuum model based on the Smoluchowski equation, moment method, and generalized Taylor dispersion theory, the dispersion process of tumbling microswimmers is analyzed and characterized by a case study for a plane Poiseuille flow. The Galerkin spectral solutions are validated through comparison with individual-based simulations, showing good consistency between the two approaches. The study is primarily concerned with the cross-sectional concentration, orientation distribution, and effective dispersion coefficients in narrow channels, and reveals how key parameters influence long-time transport behavior. The results indicate that, in most cases, tumbling promotes the uniformity of the cross-sectional concentration distribution, suppresses shear-induced orientation polarization, and reduces both the drift velocity and the dispersivity. Strong shear weakens the influence of tumbling, the swimming ability of microswimmers enhances cross-stream migration, and translational diffusion promotes the uniformity of the cross-sectional concentration distribution. These findings help understand the tumbling effect in microswimmer transport in confined environments.
Zeng et al. (2025) studied this question.