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Dispersion of flagellated swimming microorganisms in planar Poiseuille flow
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The presence of an external fluid flow significantly impacts the properties of swimming microorganisms between two surfaces. By performing computer simulations of dilute populations of flagellated swimming microorganisms, we calculate the dispersivity of the microorganisms at different flow rates by tracking each individual organism in the direction of the flow. Our results show how the dispersion of swimming microorganisms is different from passive particles. For low flow rates, the dispersivity is higher than that of non-motile organisms because of their swimming motion. As the flow rate increases, the dispersivity drops, reaching a minimum before increasing at high flow rates. The minimum occurs approximately when the swimming speed of the organism equals the mean velocity of the external flow. A scaling analysis is used to qualitatively capture the dispersion at both low and high flow rates. Closed-form expressions for the dispersivity were derived at low and high flow rates using an analytical theory. This analysis showed that at low flow rates, the alignment of the organisms by the flow is responsible for the reduction of the dispersion in comparison to the dispersion without any external flow. At high flow rates, the distribution and dynamics across the channel produce a dispersivity that is lower than that of passive particles.
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