Vertical distribution and longitudinal dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow

Dispersion of active Brownian particles is a fundamental issue in biological, environmental, and related applications. However, due to the restriction in former models, a detailed analysis of Taylor dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow is still lacking. In the present paper, with a recently proposed method [Jiang and Chen, J. Fluid Mech. 877, 1 (2019)], we illustrate the influences of the swimming ability, gyrotaxis intensity, shape anisotropy of microorganisms, and velocity of the ambient fluid on the dispersion process. Compared with nongyrotactic ones, there is a double accumulation mechanism for gyrotactic microorganisms: gravitactic focusing and wall accumulation. By using different boundary conditions, we show the effects of gravitactic focusing alone and double accumulation together. The variations of vertical distribution, overall drift, and effective dispersivity are characterized by changing the characteristic parameters of the microorganisms and the flow. Consisting of a swimming-induced part and an advection-induced part, the overall drift and effective dispersivity are coupled with the shape factor, flow Peclet number, and swimming Peclet number, which leads to nonmonotonic variations as functions of these parameters.