Abstract
We consider the phenomenon of self-focusing pattern formation of motile micro-organisms (“streamer”). The focusing mechanism is based on gyrotaxis, a physical phenomenon, and it results from the balance between viscous and gravitational moments on the organisms. Under particular circumstances such streamers are stabilized and sink, resulting in vertical transport of micro-organisms as well as horizontal heterogeneity in cell concentration. We develop a plume model for the streamer, which consists of the equations of continuity, momentum, and cell concentration. These equations are further simplified to three basic equations representing volume, momentum and concentration fluxes of the steady-state plume. Asymptotic analytical solutions for the plume are obtained. From numerical solutions we find the shape of the plume which takes the form of a vertical string with lengths ranging from 1 to 10 cm. The streamer formation can be related to algal blooms occurring in the sea and to algal cultures grown in the laboratory.
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Timm, U., Okubo, A. Gyrotaxis: A plume model for self-focusing micro-organisms. Bltn Mathcal Biology 56, 187–206 (1994). https://doi.org/10.1007/BF02460639
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DOI: https://doi.org/10.1007/BF02460639