Manipulating alignment and dispersion of confined micro-swimmers through gradient-induced orienting fields

Oriented locomotion in micro-swimmer populations is commonly observed in response to various stimuli through self-propulsion (taxis). In simple linear orienting fields, swimmers align by rotating with the field. However, their mean locomotion does not always follow the gradient, and the theory for the overall orientational and spatial dynamics of micro-swimmers still needs to be developed. Following Shaik et al. [Soft Matter 19, 1384 (2023)] and Théry et al. [Phys. Rev. Lett. 132, 108301 (2024)], we investigate how to manipulate the dispersion of confined micro-swimmers through gradient-induced orienting fields. Using Smoluchowski analysis and multi-timescale expansions, we solve analytically the number density, polar order vector, nematic order tensor, drift, dispersivity, and orientation distributions. Micro-swimmers exhibit distinct preferential alignment and density distributions. In the bulk, elongated micro-swimmers accumulate in regions of low angular speed within external orienting fields, while highly active swimmers can reorient and escape centerline focusing. Near the walls, swimmers preferentially orient upstream, resulting in negative longitudinal polar order and weak vertical fluxes. We also examine the inhomogeneous external fields, e.g., those induced by gyrotaxis and rheotaxis, to highlight potential mechanisms for preferential alignment and shear trapping. When both gradient-induced orienting fields co-exist, the population of micro-swimmers propels itself in a plane offset from the meridional plane by an angle. Although taxis-induced orientation could hinder the longitudinal migration, we demonstrate that it significantly enhances swimmer diffusion in relation to activity in the orientation space, akin to Taylor dispersion, under both homogeneous and spatially varying orienting fields. This study provides insights into the control and design strategies for micro-robots and gyrotactic microorganisms in natural and biotechnological contexts.