Transport of micro-organisms in confined flows can be characterized by a one-dimensional overall dispersion mechanism, of importance to various biotechnological applications. Based on Brenner’s generalized Taylor dispersion theory, an overall dispersion model is analytically studied in the present work for a dilute suspension of active particles in confined unidirectional flows. With the confined section of the channel and the swimming orientation space taken together as the local space and the longitudinal coordinate standing for the one-dimensional global space, this model is analytically accurate and possessed of wide adaptability in terms of the swimming Péclet number. The Robin boundary condition is introduced to account for wall accumulation of active particles, and compared with a typical reflection boundary condition. Complications associated with the boundary conditions for analytical derivation are removed respectively by a decomposition of the distribution function and an extension of the flow field. Interesting solutions are concretely found and intensively illustrated. Detailed case studies on the transport of spherical and rod-like particles to illustrate the dispersion mechanism are presented with respect to a Couette flow and a plane Poiseuille flow. Associated with the local distribution of particles, extensive descriptions are given for the dynamical system behaviours such as accumulation near both stable points/lines and boundaries, symmetric polarization structure, closed orbits, trapping effect, nematic alignments and bimodalization of swimming direction. For spherical particles, the accumulation is shown leading to a reduction of the overall dispersivity in both of the flows, while for rod-like active particles in the Couette flow, the accumulation can result in an enhancement of dispersion, due to the nematic alignments of particles towards streamlines.

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Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For the active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1–34; vol. 899, 2020, A18), this work makes a semi-analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section–orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, initial condition, wall accumulation and particle shape on the transient dispersion process. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Although the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but impacts slightly on the drift and the skewness.

Predicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications in water resources. While a semianalytical study has been made for the steady dispersion with a continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907), an in‐depth analytical investigation has yet to be performed for the more complicated case of transient dispersion due to an instantaneous release. In regard to the pioneering benchmark observation (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229) of transient solute dispersion in a submerged vegetated flow for an instantaneous source release at the top of the canopy, an extensive analytical effort is paid in this work to derive the time‐dependent basic properties and to investigate the temporal evolution of concentration distribution. Obtained large‐time asymptotic dispersivities agree well with available experimental results (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229), with higher significance ( R2=0.87, n=24) for correlation between analytical results and experimental data. Analytical solutions covering effects of dispersivity, skewness, and kurtosis of detailed concentration distribution are compared satisfactorily with numerical results obtained by the random displacement method. The findings illuminate the applicability of this analytical approach in environmental risk assessment and water quality management.