Environmental Transport of Gyrotactic Microorganisms in an Open-Channel Flow

The rich and complex phenomena of the transport of active particles like microorganisms in shear flows are of great significance to various biological and environmental applications. Recent studies have shown that the motility and gyrotaxis of algae could greatly influence their transport in waters. However, little attention has been paid to the initial and transient transport regime when the classical Taylor dispersion model is not applicable. To tackle this problem, we resort to Gill's generalized dispersion model for passive particles like solute, which has the potential for accurately describing the entire transport process. For the first time, we extend Gill's model to the active particles, and the effects of swimming, gyrotaxis, and flow shear on the microorganism dispersion in an open-channel flow have been thoroughly investigated. We first theoretically solve the transient drift and dispersion coefficients, based on which we obtain analytical solutions for concentration distributions of microorganisms, and further validate these results by numerically solving the governing equation. We find that when there is no flow, the longitudinal dispersion of microorganisms can be weakened by the gravitactic accumulation in the vicinity of water surface, while enhanced by a stronger swimming ability of the microorganisms. The effect of the flow shear does not affect the form of the asymptotic concentration distribution, but can greatly enhance the transient drift velocity and the dispersivity. We further analyze the effect of turbulence on microorganisms' dispersion by combing the direct numerical simulation and the random walk simulation. The increase of turbulence is shown to decrease the vertical non-uniformity of the concentration distribution, as well as the relative contribution of active behavior to both the drift and Taylor dispersivity during transport.